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BUSINESS ECONOMICS Origin of Business Economics • Business Economics emerged in 1951 with the publication of Managerial Economics by Joel, Dean, to bridge the gap between the theory and practice of economics. What is Economics? • Science of wealth. Some earlier economists defined Economics as follows: “An inquiry into the nature and causes of the wealth of the nations’’ (Adam Smith) - Science which deals with wealth" (J.B. Say) • Science of material well-being. • "Economics is a study of mankind in the ordinary business of life. It examines that part of individual and social action which is most closely connected with the attainment and with the use of the material requisites of well-being. (Alfred Marshall). What is Economics Cont’d? • Science of material well-being. • "Economics is a study of mankind in the ordinary business of life. It examines that part of individual and social action which is most closely connected with the attainment and with the use of the material requisites of well-being. (Alfred Marshall). • Science of choice making. Robbins gave a more scientific definition of Economics. • "Economics is the science which studies human behaviour as a relationship between end and scarce means which have alternative uses". What is Economics cont’d? • Science of dynamic growth and development. • - "Economics is the study of how men and society choose, with or without the use of money, to employ scarce productive resources which could have alternative uses, to produce various commodities over time and distribute them for consumption now and in the future amongst various people and groups of society. It analyses the costs and benefits of improving the patterns of resource allocation". (Paul A. Samuelson) What is Economics cont’d? • From the above definitions, it is clear that: • an important problem faced by each and every nation of the world is the creation and distribution of wealth • Since the problems of poverty, unemployment etc. can be solved to a greater extent when wealth is produced and is distributed equitably • How to maximise individual welfare • Economics is a science; it studies economic human behaviour scientifically. It studies how humans try to optimise (maximize or minimize) certain objective under given constraints. • Human ends (wants) are Unlimited • Means (resources) are scarce What is Economics cont’d? • Since resources (natural productive resources, man-made capital goods, consumer goods, money and time etc.) are limited economic problem arises. • Resources have alternative uses • Resources are simply anything used to produce a good or services or, more generally, to achieve a goal. • Making a choice involves a cost, an alternative foregone ( an opportunity cost) • Economic resources - physical, human, financial are not fixed and can be increased by human ingenuity, exploration, exploitation and development. • Economics is the science of making decisions in the presence of scarce resources. • Economics is a science of management of limited resources given unlimited wants of economic agents. It is concerned with the allocation of scarce resources among alternative uses. These are the main issues confronted regularly by business firms What is Business? • The term business refers to a system created to satisfy society’s needs and desires. • It is an organized effort of enterprises to produce or distribute goods and services. • The goods and services are limited and have alternative uses. • These are used to satisfy human wants which are unlimited. • In short, business includes all activities connected with production, trade, banking, insurance, finance, agency, advertising, packaging and other several related activities. What is Business Economics? • Business economics is "the integration of economic theory with business practice for the purpose of facilitating decision-making and forward planning by management". (Spencer and Siegelman) • "Business economics deals with the use of economic modes of thought to analyse business situation" (Mc Nair and Meriam) • The purpose of business economics is show how economic analysis can be used in formulating business policies (Joel Dean) • Business economics is primary concerned with the applicability of economics concepts and analyses to decisions made by businesses (Collberg) • From the above definitions, business economics can be said to be a discipline which deals with the application of economic principles, theory and methodology in the management of business. What is Business Economics? It helps a business manager in: • decision making (i.e. selecting from alternative options/ making informed choices) to achieve the desired results. • planning in advance for the future. For example, demand forecasting, pricing, type of competition envisaged, etc. • analyzing and solving business problems Typically all firms have different departments or units: • (1) production and operations • (2) marketing • (3) finance and accounting and • (4) human resources. What is Business Economics? • An important characteristic of business economics is that it is normative or prescriptive in nature rather than positive or descriptive • It is, therefore, concerned with “what ought to be” rather than “what is” and cannot be neutral about ends. It deals with how decision should be made by the business executives to achieve the goals of the business. • As a normative science, business economics gives suggestions regarding the best possible way to achieve the goals of the firm. It passes value judgments on the actions of the business manager. This involves two aspects: • (1) it tells the aims and objectives a firm or manager should pursue and • (2) it shows how best to achieve these aims in a particular situation. What is Business Economics? • Thus, business economics is concerned with “what should happen” rather than “what does happen”. Instead of explaining what a firm is doing, it explains what a firm should do to make it s decision effective. The Economic Problems and the Firms • The problem of allocation (what to produce and in what quantity?)This is the first concern of every potential business firm. What to produce to satisfy the wants of people? This problem directly arises from the problem of scarcity of resources. • The problem of choice of production method (how to produce?). I.e. what production methods are employed for the production of the various goods and services? • The problem of distribution (to whom to produce?). Who should have how much of what has been produced and by what means should they acquire the good? • The problem of Efficiency (Are the use of productive resources economically efficient? Given that resources are scarce, it is prudent to ensure that resources are put to the most efficient utilization. A firm that is operating efficiently is operating on its production possibility frontier ( this concept is explained in subsequent session) The Economic Problems and the Firms • The problem of full employment of resources. Are resources being fully utilized? This question is important in that it helps to determine whether there exist underutilsation of resources in the firm. • The problem of growth/expansion (is the productive capacity of the firm increasing, declining or remaining static over time?). Growth is important for every economy and also for business firms. If a firm grows, it is able to expand its capacity or scale of production. Production Possibility Frontier Definition • A graph that shows the alternatives production capabilities of an economy or a production unit. • It shows the maximum combination of two goods that a production unit can produce when it utilizes all the available resources, given technology. • As the productive capacities of the firm/economy are limited, a choice must be made among quantities of different goods. This demands a decision on how much resource should be allocated among the different possible goods. for example, how Production Possibility Frontier cont’d Assumptions • There are given amount of productive resources and remain fixed • Resources can be shifted from the production of one commodity to the other • Resources are being used fully and with utmost technical efficiency. i.e. resources are neither unemployed, underemployed nor inefficiently utilized • Technology is constant. i.e. does not undergo changes Production Possibility Frontier cont’d Production Combinations Cocoa (tonnes) Gold (Ounces) A 350 0 B 330 10 C 300 20 D 250 30 E 150 40 F 0 50 Production Possibility Frontier cont’d 400 350 Cocoa (Metric Tonnes) A B C 300 .Z D 250 200 .X 150 E 100 50 F 0 0 10 20 30 40 50 Gold (Ounces) Illustrating the Basic Economic Questions The problem of scarcity, choice and resource allocation • the limit provided by the possibility curve illustrates scarcity • all the wants of the firm cannot be satisfied because of scarcity • The firm cannot increase the production of both goods • However, different combinations can be produced ( choice) • If the firm can produce more of one product only by reducing the quantity of the other. This means that it has to withdraw resources from the production of one to the other( resource allocation and cost) The problem of Unemployment and under employment • Discuss attainable and unattainable points • Discuss points below the possibility frontier • There will be full employment aggregate demand is large enough to buy the total ouput produced by full employment • Increase in AD leads to increase employment and thereby a reduction in unemployment • The problem of growth • The combination of consumer goods ( x-axis) and capital goods( y-axis) • Allocating more resources to capital goods and less for consumer goods. capital accumulation increases the productive capacity of the firm • The principle of increasing opportunity cost • Why opportunity cost increases? Resources are not perfectly substitutable. i.e. not equally efficient in the production of all goods. THE COMPETITIVE MARKET MODEL • For many firms, prices are determined not by them but by the market. • The market dominates a firm’s activities. • The more competitive the market, the greater this domination becomes. • In the extreme case, the firm may have no power at all to change its price • In competitive markets, consumers are price takers • So how does a competitive market work? • For simplicity we will examine the case of a perfectly competitive market • In a competitive market, we have too main forces: the forces of Demand and Supply The structure of the demand and supply model. Households • Who attempt to maximize utility, they face diminishing marginal utility, and are subject to a budget constraint. Firms • Attempt to maximize profits. Firms face cost constraints, and are subject to the law of diminishing returns in production. What is Demand? • it refers to the quantities that people are or would be willing to buy at different prices during a given time period, assuming that other factors affecting these quantities remain the same. This definition incorporates 3 important concepts: • It involves three parameters – price, quantity and time. • It refers to quantities in the plural, therefore a whole relationship, not a single quantity. • It involves the ceteris paribus (other things being equal) assumption, which is a very common one in making statements in economics. Tables, graphs and equations Tables • These are the simplest method of representation. The table shows the general ‘law of demand’, that less is demanded at higher prices. Price of Coke (pesewa Quantity sold (cans per can) per day) 30 120 40 100 50 80 60 60 70 40 • Tables are not very useful for analytical purposes. Tables, graphs and equations Cont’d Graphs/Demand Curve • These are much more useful for analysis. The demand relationship in this case is both inverse and linear. 80 70 60 50 40 30 20 10 0 40 47 54 61 68 75 82 89 96 103 110 117 Demand Curve Quantity (Cans per day) Tables, graphs and equations Cont’d • the concepts of demand and quantity demanded is illustrated: • the former relates to the whole demand curve whereas the latter relates to a single point on the curve. • it is mainly limited to examining two-variable relationships. • Demand relationships often involve many variables and although the effects of these can be shown on a graph, as seen in subsequent sections, they are difficult to measure. Tables, graphs and equations Cont’d • Equations • These are the most useful method of representation for analytical purposes since they explicitly show the effects of all the variables affecting quantity demanded, in a concise form that at the same time reveals important information regarding the nature of the relationship. • The general form of the demand function in terms of price and quantity demanded is: Q f ( P) (2.1) • This is the most general way of describing the relationship since it does not involve any specific mathematical form Tables, graphs and equations Cont’d • This can be expanded by including any number of variables that might affect quantity demanded on the right hand side of the equation, for example: Q f ( P, A, Y , Ps ,...) (2.2) • A represents advertising expenditure, Y represents average income of the market and Ps represents the price of a substitute product. • In the two-variable case the demand function can be expressed in a linear form: Q a bP (2.3) • The coefficients a and b can then be calculated for the demand schedule in Table above Tables, graphs and equations Cont’d • One way of doing this is to use simultaneous equations and substitute any two pairs of values in the table to solve for a and b. • it is more insightful to calculate the value of b first, using the mathematical concept that b represents Q / P • Again any two pairs of values can be used to establish that • if the first two pairs of values are taken b 2 b 20/10 2. Q 180 2 P (2.4) Interpretation of equations • The value of ‘a’ represents the maximum sales that will occur if the price is zero • ‘b’ represents marginal effect of price on quantity demanded Q a bP cY (2.6) • the value of c represents the marginal effect of Y (income) on Q • Sometimes the demand function may be non-linear such as equation (2.7) this demand function is in the power form b Q aP (2.7) As with the linear form, the function can be extended to include other variables; in this case the function is multiplicative Q aP Y (2.8) b c The Demand Function • A general equation representing the demand curve Qxd = f(Px , PY , M, H,) • Qxd = quantity demand of good X. • Px = price of good X. • PY = price of a related good Y. • Substitute good. • Complement good. • M = income. • Normal good. • Inferior good. • H = any other variable affecting demand. Inverse Demand Function • Price as a function of quantity demanded. • Example: • Demand Function • Qxd = 10 – 2Px • Inverse Demand Function: • 2Px = 10 – Qxd • Px = 5 – 0.5Qxd Determinants of Demand Change in Quantity Demanded Price A to B: Increase in quantity demanded 10 A B 6 D0 4 7 Quantity Change in Demand Price D0 to D1: Increase in Demand 6 D1 D0 7 13 Quantity Consumer Surplus • The demand curve reveals the amount of a product consumers will buy at a given price. • Consumer surplus is the value consumers get from a good but do not have to pay for. • This concept is important to managers because it tells how much extra money consumers would be willing to pay for a given amount of a purchased product. • Geometrically, consumer surplus is the area above the price paid for a good but below the demand curve Consumer Surplus cont’d Price Price 5 Consumer Surplus 4 3 2 P0 1 0 1 2 3 (a) 4 D 5 Qty D 0 Q0 (b) Qty I got a great deal! • That company offers a lot of bang for the buck! • Dell provides good value. • Total value greatly exceeds total amount paid. • Consumer surplus is large. I got a lousy deal! • That car dealer drives a hard bargain! • I almost decided not to buy it! • They tried to squeeze the very last cent from me! • Total amount paid is close to total value. • Consumer surplus is low. THE THEORY OF INDIVIDUAL BEHAVIOUR Overview Consumer Behaviour • Indifference Curve Analysis. • Consumer Preference Ordering. II. Constraints • The Budget Constraint. • Changes in Income. • Changes in Prices. III. Consumer Equilibrium IV. Indifference Curve Analysis & Demand • Individual Demand. • Market Demand. Curves Consumer Behaviour • Consumer Opportunities • The possible goods and services consumer can afford to consume. • Consumer Preferences • The goods and services consumers actually consume. • Given the choice between 2 bundles of goods a consumer either: • Prefers bundle A to bundle B: A B. • Prefers bundle B to bundle A: A B. • Is indifferent between the two: A B. Indifference Curve Analysis Indifference Curve • A curve that defines the combinations of 2 or more goods that give a consumer the same level of satisfaction. Marginal Rate of Substitution • The rate at which a consumer is willing to substitute one good for another and maintain the same satisfaction level. Good Y III. II. I. Good X Consumer Preference Ordering Properties •Completeness •More is Better •Diminishing Marginal Rate of Substitution •Transitivity Complete Preferences • Completeness Property • Consumer is capable of expressing preferences (or indifference) between all possible bundles. (“I don’t know” is NOT an option!) • If the only bundles available to a consumer are A, B, and C, then the consumer • is indifferent between A and C (they are on the same indifference curve). • will prefer B to A. • will prefer B to C. Good Y III. II. I. A B C Good X More Is Better! • More Is Better Property • Bundles that have at least as much of every good and more of some good are preferred to other bundles. • Bundle B is preferred to A since B contains at least as much of good Y and strictly more of good X. • Bundle B is also preferred to C since B contains at least as much of good X and strictly more of good Y. • More generally, all bundles on ICIII are preferred to bundles on ICII or ICI. And all bundles on ICII are preferred to ICI. Good Y III II I. 100 A B C 33.33 1 3 Good X Diminishing MRS MRS • The amount of good Y the consumer is willing to give up to maintain the same satisfaction level decreases as more of good X is acquired. • The rate at which a consumer is willing to substitute one good for another and maintain the same satisfaction level. • To go from consumption bundle A to B the consumer must give up 50 units of Y to get one additional unit of X. • To go from consumption bundle B to C the consumer must give up 16.67 units of Y to get one additional unit of X. • To go from consumption bundle C to D the consumer must give up only 8.33 units of Y to get one additional unit of X. Good Y III. II. I. 100 50 33.33 25 A B C D 1 2 3 4 Good X Consistent Bundle Orderings • Transitivity Property • For the three bundles A, B, and C, the transitivity property implies that if C B and B A, then C A. • Transitive preferences along with the more-is-better property imply that • indifference curves will not intersect. • the consumer will not get caught in a perpetual cycle of indecision. Good Y III. II. I. 100 75 50 A C B 1 2 5 7 Good X The Budget Constraint • Opportunity Set • The set of consumption bundles that are affordable. • PxX + PyY M. • Budget Line • The bundles of goods that exhaust a consumers income. • PxX + PyY = M. • Market Rate of Substitution • The slope of the budget line • -Px / Py. Y The Opportunity Set Budget Line M/PY Y = M/PY – (PX/PY)X M/PX X Changes in the Budget Line • Changes in Income • Increases lead to a parallel, outward shift in the budget line (M1 > M0). • Decreases lead to a parallel, downward shift (M2 < M0). • Changes in Price • A decreases in the price of good X rotates the budget line counter-clockwise (PX0 > PX1). • An increases rotates the budget line clockwise (not shown). Y M1/PY M0/PY M2/PY Y M0/PY X M2/PX M0/PX M1/PX New Budget Line for a price decrease. M0/PX0 M0/PX1 X Consumer Equilibrium • The equilibrium consumption bundle is the affordable bundle that yields the highest level of satisfaction. • Consumer equilibrium occurs at a point where MRSxy = PX / PY. • Equivalently, the slope of the indifference curve equals the budget line. Y M/PY Consumer Equilibrium III. II. I. M/PX X Price Changes and Consumer Equilibrium • Substitute Goods • An increase (decrease) in the price of good X leads to an increase (decrease) in the consumption of good Y. • Examples: • Coke and Pepsi. • Verizon Wireless or AT&T. • Complementary Goods • An increase (decrease) in the price of good X leads to a decrease (increase) in the consumption of good Y. • Examples: • DVD and DVD players. • Computer CPUs and monitors. Complementary Goods Pretzels (Y) When the price of good X falls and the consumption of Y rises, then X and Y are complementary goods. (PX1 > PX2) M/PY1 B Y2 II A Y1 I X1 X2 M/PX2 Beer (X) Income Changes and Consumer Equilibrium • Normal Goods • Good X is a normal good if an increase (decrease) in income leads to an increase (decrease) in its consumption. • Inferior Goods • Good X is an inferior good if an increase (decrease) in income leads to a decrease (increase) in its consumption. Normal Goods Y An increase in income increases the consumption of normal goods. (M0 < M1). M1/Y B Y1 M0/Y II A Y0 I 0 X0 M0/X X1 M1/X X Decomposing the Income and Substitution Effects Initially, bundle A is consumed. A decrease in the price of good X expands the consumer’s opportunity set. Y The substitution effect (SE) causes the consumer to move from bundle A to B. C A higher “real income” allows the consumer to achieve a higher indifference curve. A II B The movement from bundle B to C represents the income effect (IE). The new equilibrium is achieved at point C. IE 0 SE X Individual Demand Curve Y • An individual’s demand curve is derived from each new equilibrium point found on the indifference curve as the price of good X is varied. II I X $ P0 P1 D X0 X1 X Market Demand • The market demand curve is the horizontal summation of individual demand curves. • It indicates the total quantity all consumers would purchase at each price point. $ Individual Demand Curves $ Market Demand Curve 50 40 D1 1 2 D2 DM Q 1 2 3 Q Limitations of the Theory of Individual Behaviour Concentration on price Search costs:-Consumers have to obtain information regarding price, quality and availability of products and there is a cost attached to this. Rationality:-It is sometimes argued, particularly by behaviourists, that humans rarely make the relevant computations that are necessitated by the neoclassical model, particularly with practical time constraints ESTIMATING THE DEMAND FUNCTION • The Regression Equation is given as: Y a bX (1) • The Estimated Regression Equation is given as: ˆ Y aˆ bX (2) Demonstration of Demand Estimation Cont’d • bcan be derived by the formula: xy b x 2 Where x X X and y Y Y X is the mean of X and Y is the mean of Y a can be derived by the formula: a Y b X Demonstration of Demand Estimation Cont’d Given the data on quantity demanded and Price in Table 1 Observation 1 2 3 4 5 6 7 8 9 10 Quantity 180 590 430 250 275 720 660 490 700 210 Price (GHC) 475 400 450 550 575 375 375 450 400 500 Demonstration of Demand Estimation Cont’d • The data above can be described by the regression equation Q a bP (3) • The estimated regression line can be represented as: Q a b P (4) pq b p 2 a Q bP ..\Documents\Managerial Econs\data on demand and regression analysis.xlsx SUPPLY • What is Supply? The supply of a commodity refers to the various quantities of that commodity that producers are willing and able to sell at various prices during a given period of time. Important elements in the definition a. Schedule of intentions: An estimate b. Price/Quantity relationship: Price is the most important determinant of quantity. c. Ready, willing and able: Defines the market of relevant suppliers. Ready: Has access to market. Willing: Is a reasonable use of resources, Able: Has productive means d. Per unit of time: Time must be specified e. other things constant. f. Up-sloping due to the law of diminishing returns SUPPLY CONT’D The Law of Supply • The law of supply asserts that quantity supplied of a good or service is directly (positively) related to the selling price, ceteris paribus. • Symbolically, the law of supply may be summarized as follows: Qs g ( P) (2.16a) dQs 0 (2.16b) dP • Equation (2.16a) states that the quantity supplied QS of a good or service is functionally related to the selling price P. Inequality (2.16b) asserts that quantity supplied of a product and its price are directly related. The Supply Curve • This relationship is illustrated in the diagram below Price B S P2 P1 0 A Q1 Q2 Quantity Supplied The Supply Function The supply function of a good describes how much of the good will be produced at alternative prices of the good, alternative prices of inputs, and alternative values of other variables that affect supply. Q f ( Px , Pr ,W , H ) (2.17) s x Where Px is the price of the good, Pr is the price of technologically related goods, W is the price of an input and H is the value of some other variable that affects supply (such as existing technology, the number of firms in the market, taxes, or producer expectations). The Supply Function Cont’d • The coefficients i ' s represent given numbers that that have been estimated by the firm’s research department or an economic consultant. Numerical Example The research department of Ama and Co. Ltd estimated that the supply function for their television sets is given by Q 2000 3Px 4 Pr Pw s x Where Px is the price of TV sets, Pr represents the price of a computer monitor, and Pw is the price of an input used to make televisions. Suppose TVs are sold for GH¢400 per unit, computer monitors are sold for GH¢100 per unit, and the price of an input is GH¢2000. How many television sets are produced? The Supply Function Cont’d Solution To find out how many television sets are produced, we insert the given values of the prices into the supply equation to get Qxs 2000 3(400) 4(100) 1(2000) 800 The information summarized in a supply function can be used to graph a supply curve. Since a supply curve is the relationship between price and quantity, a representative supply curve holds everything but price constant. This means one may obtain the formula for a supply curve by inserting given values of the supply shifters into the supply function, but leaving Px • If we do this for the supply function in example above, (where Pr = GH¢100 and Pw = GH¢2000), we get The Supply Function Cont’d Q 2000 3Px 4(100) 1(2000) s x Which simplifies to Q 3Px 400 s x Since we usually graph this relation with the price of the good on the vertical axis, it is useful to represent the new equation with price on the left-hand side and everything else on the right-hand side. This is known as the inverse supply function. In this particular case, the inverse supply function is 400 1 s Px Qx 3 3 This equation is graphed below Producer Surplus • The supply curve reveals the amount producers will be willing to produce at a given price. Price Producer Surplus A GH¢400 ∙ B S ∙ C GH¢400/3∙ Quantity 800 0 • Geometrically, producer surplus is the area above the supply curve but below the market price of the good. Producer Surplus Cont’d • Producer surplus is the amount of money producers receive in excess of the amount necessary to induce them to produce the good. • For example, the supply curve in the figure above indicates that a total of 800 units will be produced when the price is GH¢400 • The area ABC, is the producer surplus when the price is GH¢400. Mathematically, this area is one-half of 800 times GH¢266.67, or GH¢106,668. Supply Shifters • Input prices • Technology or government regulations • Number of firms • Entry • Exit • Substitutes in production • Taxes • Excise tax • Ad valorem tax • Producer expectations The Market Mechanism: The Interaction Of Demand And Supply P Excess Supply D P* S E S Excess Demand Q* D Q The Interaction Of Demand And Supply cont’d Example • Suppose you are the special assistant to a member of parliament on the Foreign affairs committee of parliament. The Togolese government plans to privatize an industry, and you have been asked to help the committee determine the market price and quantity that would prevail in the Togolese market if competitive forces were allowed to equilibrate the market. The best estimates of the market demand and supply for the Togolese good (in Ghana cedi equivalent prices) are given by Qd = 10 – 2P and Qs = 2+2P, respectively. Determine the competitive equilibrium price and quantity. • Soln In equilibrium Qd = Qs. 10 – 2P = 2+2P; 8 = 4P; Pe = 2 Qe = 10 – 2(2) = 6. Price Restrictions • Price Ceilings • The maximum legal price that can be charged. • Examples: • Gasoline prices in the 1970s. • Housing in New York City. • Proposed restrictions on ATM fees. • Price Floors • The minimum legal price that can be charged. • Examples: • Minimum wage. • Agricultural price supports. Impact of a Price Ceiling Price S PF P* P Ceiling D Shortage Qs Q* Qd Quantity Full Economic Price • The dollar amount paid to a firm under a price ceiling, plus the non-pecuniary price. PF = Pc + (PF - PC) • PF = full economic price • PC = price ceiling • PF - PC = nonpecuniary price An Example from the 1970s in the US • Ceiling price of gasoline: $1. • 3 hours in line to buy 15 gallons of gasoline: • Opportunity cost: $5/hr. • Total value of time spent in line: 3 $5 = $15. • Non-pecuniary price per gallon: $15/15=$1. • Full economic price of a gallon of gasoline: $1+$1=2. Impact of a Price Floor Price Surplus S PF P* D Qd Q* QS Quantity Comparative Static Analysis • How do the equilibrium price and quantity change when a determinant of supply and/or demand change? Applications: Demand and Supply Analysis • Event: The WSJ reports that the prices of PC components are expected to fall by 5-8 percent over the next six months. • Scenario 1: You manage a small firm that manufactures PCs. • Scenario 2: You manage a small software company. Use Comparative Static Analysis to see the Big Picture! • Comparative static analysis shows how the equilibrium price and quantity will change when a determinant of supply or demand changes. Scenario 1: Implications for a Small PC Maker • Step 1: Look for the “Big Picture.” • Step 2: Organize an action plan (worry about details). Big Picture: Impact of decline in component prices on PC market Price of PCs S S* P0 P* D Q0 Q* Quantity of PC’s Big Picture Analysis: PC Market • Equilibrium price of PCs will fall, and equilibrium quantity of computers sold will increase. • Use this to organize an action plan: • • • • • contracts/suppliers? inventories? human resources? marketing? do I need quantitative estimates? Scenario 2: Software Maker • More complicated chain of reasoning to arrive at the “Big Picture.” • Step 1: Use analysis like that in Scenario 1 to deduce that lower component prices will lead to • a lower equilibrium price for computers. • a greater number of computers sold. • Step 2: How will these changes affect the “Big Picture” in the software market? Big Picture: Impact of lower PC prices on the software market Price of Software S P1 P0 D* D Q0 Q1 Quantity of Software Big Picture Analysis: Software Market • Software prices are likely to rise, and more software will be sold. • Use this to organize an action plan. Conclusion • Use supply and demand analysis to • clarify the “big picture” (the general impact of a current event on equilibrium prices and quantities). • organize an action plan (needed changes in production, inventories, raw materials, human resources, marketing plans, etc.). Elasticity Overview The Elasticity Concept • • • • Own Price Elasticity Elasticity and Total Revenue Cross-Price Elasticity Income Elasticity II. Demand Functions • Linear • Log-Linear III. Regression Analysis The Elasticity Concept • How responsive is variable “G” to a change in variable “S” The Elasticity Concept • How responsive is variable “G” to a change in variable “S” EG , S % G % S If EG,S > 0, then S and G are directly related. If EG,S < 0, then S and G are inversely related. If EG,S = 0, then S and G are unrelated. The Elasticity Concept Using Calculus • An alternative way to measure the elasticity of a function G = f(S) is EG , S dG S dS G If EG,S > 0, then S and G are directly related. If EG,S < 0, then S and G are inversely related. If EG,S = 0, then S and G are unrelated. Own Price Elasticity of Demand EQX , PX %QX %PX d • Negative according to the “law of demand.” Elastic: EQ X , PX 1 Inelastic: EQ X , PX 1 Unitary: EQ X , PX 1 Perfectly Elastic & Inelastic Demand Price Price D D Quantity Perfectly Elastic ( EQX , PX ) Quantity Perfectly Inelastic ( EQX , PX 0) Own-Price Elasticity and Total Revenue • Elastic • Increase (a decrease) in price leads to a decrease (an increase) in total revenue. • Inelastic • Increase (a decrease) in price leads to an increase (a decrease) in total revenue. • Unitary • Total revenue is maximized at the point where demand is unitary elastic. Elasticity, Total Revenue and Linear Demand P 100 TR 0 10 20 30 40 50 Q 0 Q Elasticity, Total Revenue and Linear Demand P 100 TR 80 800 0 10 20 30 40 50 Q 0 10 20 30 40 50 Q Elasticity, Total Revenue and Linear Demand P 100 TR 80 1200 60 800 0 10 20 30 40 50 Q 0 10 20 30 40 50 Q Elasticity, Total Revenue and Linear Demand P 100 TR 80 1200 60 40 800 0 10 20 30 40 50 Q 0 10 20 30 40 50 Q Elasticity, Total Revenue and Linear Demand P 100 TR 80 1200 60 40 800 20 0 10 20 30 40 50 Q 0 10 20 30 40 50 Q Elasticity, Total Revenue and Linear Demand P 100 TR Elastic 80 1200 60 40 800 20 0 10 20 30 40 50 Q 0 10 20 Elastic 30 40 50 Q Elasticity, Total Revenue and Linear Demand P 100 TR Elastic 80 1200 60 Inelastic 40 800 20 0 10 20 30 40 50 Q 0 10 Elastic 20 30 40 Inelastic 50 Q Elasticity, Total Revenue and Linear Demand P 100 TR Unit elastic Elastic Unit elastic 80 1200 60 Inelastic 40 800 20 0 10 20 30 40 50 Q 0 10 Elastic 20 30 40 Inelastic 50 Q Demand, Marginal Revenue (MR) and Elasticity • For a linear inverse demand function, MR(Q) = a + 2bQ, where b < 0. • When P 100 Elastic Unit elastic 80 60 Inelastic 40 20 0 10 20 40 MR 50 Q • MR > 0, demand is elastic; • MR = 0, demand is unit elastic; • MR < 0, demand is inelastic. Factors Affecting the Own-Price Elasticity • Available Substitutes • The more substitutes available for the good, the more elastic the demand. • Time • Demand tends to be more inelastic in the short term than in the long term. • Time allows consumers to seek out available substitutes. • Expenditure Share • Goods that comprise a small share of consumer’s budgets tend to be more inelastic than goods for which consumers spend a large portion of their incomes. Cross-Price Elasticity of Demand EQX , PY %QX %PY d If EQX,PY > 0, then X and Y are substitutes. If EQX,PY < 0, then X and Y are complements. Predicting Revenue Changes from Two Products Suppose that a firm sells to related goods. If the price of X changes, then total revenue will change by: R RX 1 EQX , PX RY EQY , PX %PX Income Elasticity EQX , M %QX %M d If EQX,M > 0, then X is a normal good. If EQX,M < 0, then X is a inferior good. Uses of Elasticities • Pricing. • Managing cash flows. • Impact of changes in competitors’ prices. • Impact of economic booms and recessions. • Impact of advertising campaigns. • And lots more! Example 1: Pricing and Cash Flows • According to an FTC Report by Michael Ward, AT&T’s own price elasticity of demand for long distance services is -8.64. • AT&T needs to boost revenues in order to meet it’s marketing goals. • To accomplish this goal, should AT&T raise or lower it’s price? Answer: Lower price! • Since demand is elastic, a reduction in price will increase quantity demanded by a greater percentage than the price decline, resulting in more revenues for AT&T. Example 2: Quantifying the Change • If AT&T lowered price by 3 percent, what would happen to the volume of long distance telephone calls routed through AT&T? Answer: Calls Increase! Calls would increase by 25.92 percent! EQX , PX % Q X 8.64 % PX d % Q X 8.64 3% d 3% 8.64 % QX d % Q X 25.92% d Example 3: Impact of a Change in a Competitor’s Price • According to an FTC Report by Michael Ward, AT&T’s cross price elasticity of demand for long distance services is 9.06. • If competitors reduced their prices by 4 percent, what would happen to the demand for AT&T services? Answer: AT&T’s Demand Falls! AT&T’s demand would fall by 36.24 percent! EQX , PY %QX 9.06 %PY %QX 9.06 4% d 4% 9.06 %QX d %QX 36.24% d d Interpreting Demand Functions • Mathematical representations of demand curves. • Example: QX 10 2 PX 3PY 2M d • Law of demand holds (coefficient of PX is negative). • X and Y are substitutes (coefficient of PY is positive). • X is an inferior good (coefficient of M is negative). Linear Demand Functions and Elasticities • General Linear Demand Function and Elasticities: QX 0 X PX Y PY M M H H d P EQX , PX X X QX Own Price Elasticity EQ X , PY PY Y QX Cross Price Elasticity M EQX , M M QX Income Elasticity Example of Linear Demand • Qd = 10 - 2P. • Own-Price Elasticity: (-2)P/Q. • If P=1, Q=8 (since 10 - 2 = 8). • Own price elasticity at P=1, Q=8: (-2)(1)/8= - 0.25. Log-Linear Demand • General Log-Linear Demand Function: ln QX d 0 X ln PX Y ln PY M ln M H ln H X Cross Price Elasticity : Y Income Elasticity : M Own Price Elasticity : Example of Log-Linear Demand • ln(Qd) = 10 - 2 ln(P). • Own Price Elasticity: -2. Graphical Representation of Linear and Log-Linear Demand P P D Linear D Q Log Linear Q Regression Analysis • One use is for estimating demand functions. • Important terminology and concepts: • • • • • • Least Squares Regression model: Y = a + bX + e. Least Squares Regression line: Yˆ aˆ bˆX Confidence Intervals. t-statistic. R-square or Coefficient of Determination. F-statistic. An Example • Use a spreadsheet to estimate the following log-linear demand function. ln Qx 0 x ln Px e Summary Output Regression Statistics Multiple R 0.41 R Square 0.17 Adjusted R Square 0.15 Standard Error 0.68 Observations 41.00 ANOVA df Regression Residual Total Intercept ln(P) SS 1.00 39.00 40.00 MS F 3.65 18.13 21.78 Coefficients Standard Error 7.58 1.43 -0.84 0.30 3.65 0.46 t Stat 5.29 -2.80 Significance F 7.85 0.01 P-value 0.000005 0.007868 Lower 95% Upper 95% 4.68 10.48 -1.44 -0.23 Interpreting the Regression Output • The estimated log-linear demand function is: • ln(Qx) = 7.58 - 0.84 ln(Px). • Own price elasticity: -0.84 (inelastic). • How good is our estimate? • t-statistics of 5.29 and -2.80 indicate that the estimated coefficients are statistically different from zero. • R-square of 0.17 indicates the ln(PX) variable explains only 17 percent of the variation in ln(Qx). • F-statistic significant at the 1 percent level. Conclusion • Elasticities are tools you can use to quantify the impact of changes in prices, income, and advertising on sales and revenues. • Given market or survey data, regression analysis can be used to estimate: • Demand functions. • Elasticities. • A host of other things, including cost functions. • Managers can quantify the impact of changes in prices, income, advertising, etc. The Production Process and Costs Overview I. Production Analysis • • • • Total Product, Marginal Product, Average Product. Isoquants. Isocosts. Cost Minimization II. Cost Analysis • Total Cost, Variable Cost, Fixed Costs. • Cubic Cost Function. • Cost Relations. III. Multi-Product Cost Functions Production Analysis • Production Function • Q = F(K,L) • • • • Q is quantity of output produced. K is capital input. L is labor input. F is a functional form relating the inputs to output. • The maximum amount of output that can be produced with K units of capital and L units of labor. • Short-Run vs. Long-Run Decisions • Fixed vs. Variable Inputs Production Function Algebraic Forms • Linear production function: inputs are perfect substitutes. Q F K , L aK bL • Leontief production function: inputs are used in fixed proportions. Q F K , L min bK , cL • Cobb-Douglas production function: inputs have a degree of substitutability. Q F K , L K a Lb Productivity Measures: Total Product • Total Product (TP): maximum output produced with given amounts of inputs. • Example: Cobb-Douglas Production Function: Q = F(K,L) = K.5 L.5 • K is fixed at 16 units. • Short run Cobb-Douglass production function: Q = (16).5 L.5 = 4 L.5 • Total Product when 100 units of labor are used? Q = 4 (100).5 = 4(10) = 40 units Productivity Measures: Average Product of an Input • Average Product of an Input: measure of output produced per unit of input. • Average Product of Labor: APL = Q/L. • Measures the output of an “average” worker. • Example: Q = F(K,L) = K.5 L.5 • If the inputs are K = 16 and L = 16, then the average product of labor is APL = [(16) 0.5(16)0.5]/16 = 1. • Average Product of Capital: APK = Q/K. • Measures the output of an “average” unit of capital. • Example: Q = F(K,L) = K.5 L.5 • If the inputs are K = 16 and L = 16, then the average product of capital is APK = [(16)0.5(16)0.5]/16 = 1. Productivity Measures: Marginal Product of an Input • Marginal Product on an Input: change in total output attributable to the last unit of an input. • Marginal Product of Labor: MPL = Q/L • Measures the output produced by the last worker. • Slope of the short-run production function (with respect to labor). • Marginal Product of Capital: MPK = Q/K • Measures the output produced by the last unit of capital. • When capital is allowed to vary in the short run, MPK is the slope of the production function (with respect to capital). Increasing, Diminishing and Negative Q Marginal Returns Increasing Marginal Returns Diminishing Marginal Returns Negative Marginal Returns Q=F(K,L) AP L MP Guiding the Production Process • Producing on the production function • Aligning incentives to induce maximum worker effort. • Employing the right level of inputs • When labor or capital vary in the short run, to maximize profit a manager will hire: • labor until the value of marginal product of labor equals the wage: VMPL = w, where VMPL = P x MPL. • capital until the value of marginal product of capital equals the rental rate: VMPK = r, where VMPK = P x MPK . Isoquant • Illustrates the long-run combinations of inputs (K, L) that yield the producer the same level of output. • The shape of an isoquant reflects the ease with which a producer can substitute among inputs while maintaining the same level of output. Marginal Rate of Technical Substitution (MRTS) • The rate at which two inputs are substituted while maintaining the same output level. MRTS KL MPL MPK Linear Isoquants • Capital and labor are perfect substitutes • Q = aK + bL • MRTSKL = b/a • Linear isoquants imply that inputs are substituted at a constant rate, independent of the input levels employed. K Increasing Output Q1 Q2 Q3 L Leontief Isoquants • Capital and labor are perfect K complements. • Capital and labor are used in fixed-proportions. • Q = min {bK, cL} • Since capital and labor are consumed in fixed proportions there is no input substitution along isoquants (hence, no MRTSKL). Q3 Q2 Q1 Increasing Output L Cobb-Douglas Isoquants • Inputs are not perfectly substitutable. • Diminishing marginal rate of technical substitution. • As less of one input is used in the production process, increasingly more of the other input must be employed to produce the same output level. K Q3 Q2 Q1 Increasing Output • Q = KaLb • MRTSKL = MPL/MPK L Isocost • The combinations of inputs that produce a given level of output at the same cost: wL + rK = C • Rearranging, K= (1/r)C - (w/r)L • For given input prices, isocosts farther from the origin are associated with higher costs. • Changes in input prices change the slope of the isocost line. K C1/r New Isocost Line associated with higher costs (C0 < C1). C0/r C0 C0/w C1 C1/w L K C/r New Isocost Line for a decrease in the wage (price of labor: w0 > w1). C/w0 C/w1 L Cost Minimization • Marginal product per dollar spent should be equal for all inputs: • But, this is just MPL MPK MPL w w r MPK r MRTS KL w r Cost Minimization K Slope of Isocost = Slope of Isoquant Point of Cost Minimization Q L Optimal Input Substitution • A firm initially produces Q0 by employing the combination of inputs represented by point A at a cost of C0. • Suppose w0 falls to w1. • The isocost curve rotates counterclockwise; which represents the same cost level prior to the wage change. • To produce the same level of output, Q0, the firm will produce on a lower isocost line (C1) at a point B. • The slope of the new isocost line represents the lower wage relative to the rental rate of capital. K A K0 B K1 Q0 0 L0 L1 C0/w0 C1/w1 C0/w1 L Cost Analysis • Types of Costs • Short-Run • Fixed costs (FC) • Sunk costs • Short-run variable costs (VC) • Short-run total costs (TC) • Long-Run • All costs are variable • No fixed costs Total and Variable Costs C(Q): Minimum total cost of producing alternative levels of output: $ C(Q) = VC + FC VC(Q) C(Q) = VC(Q) + FC VC(Q): Costs that vary with output. FC FC: Costs that do not vary with output. 0 Q Fixed and Sunk Costs FC: Costs that do not change as $ output changes. Sunk Cost: A cost that is forever lost after it has been paid. Decision makers should ignore sunk costs to maximize profit or minimize losses C(Q) = VC + FC VC(Q) FC Q Some Definitions Average Total Cost ATC = AVC + AFC ATC = C(Q)/Q $ MC ATC AVC Average Variable Cost AVC = VC(Q)/Q MR Average Fixed Cost AFC = FC/Q Marginal Cost MC = DC/DQ AFC Q Fixed Cost Q0(ATC-AVC) $ = Q0 AFC = Q0(FC/ Q0) MC ATC AVC = FC ATC AFC Fixed Cost AVC Q0 Q Variable Cost $ Q0AVC MC ATC = Q0[VC(Q0)/ Q0] AVC = VC(Q0) AVC Variable Cost Minimum of AVC Q0 Q Total Cost Q0ATC $ = Q0[C(Q0)/ Q0] = C(Q0) MC ATC AVC ATC Minimum of ATC Total Cost Q0 Q Cubic Cost Function • C(Q) = f + a Q + b Q2 + cQ3 • Marginal Cost? • Memorize: MC(Q) = a + 2bQ + 3cQ2 • Calculus: dC/dQ = a + 2bQ + 3cQ2 An Example • Total Cost: C(Q) = 10 + Q + Q2 • Variable cost function: VC(Q) = Q + Q2 • Variable cost of producing 2 units: VC(2) = 2 + (2)2 = 6 • Fixed costs: FC = 10 • Marginal cost function: MC(Q) = 1 + 2Q • Marginal cost of producing 2 units: MC(2) = 1 + 2(2) = 5 Long-Run Average Costs $ LRAC Economies of Scale Diseconomies of Scale Q* Q Multi-Product Cost Function • C(Q1, Q2): Cost of jointly producing two outputs. • General function form: C Q1 , Q2 f aQ1Q2 bQ cQ 2 1 2 2 Economies of Scope • C(Q1, 0) + C(0, Q2) > C(Q1, Q2). • It is cheaper to produce the two outputs jointly instead of separately. • Example: • It is cheaper for Time-Warner to produce Internet connections and Instant Messaging services jointly than separately. Cost Complementarity • The marginal cost of producing good 1 declines as more of good two is produced: MC1Q1,Q2) /Q2 < 0. • Example: • Cow hides and steaks. Quadratic Multi-Product Cost Function • C(Q1, Q2) = f + aQ1Q2 + (Q1 )2 + (Q2 )2 • MC1(Q1, Q2) = aQ2 + 2Q1 • MC2(Q1, Q2) = aQ1 + 2Q2 • Cost complementarity: a < 0 • Economies of scope: f > aQ1Q2 C(Q1 ,0) + C(0, Q2 ) = f + (Q1 )2 + f + (Q2)2 C(Q1, Q2) = f + aQ1Q2 + (Q1 )2 + (Q2 )2 f > aQ1Q2: Joint production is cheaper A Numerical Example: • C(Q1, Q2) = 90 - 2Q1Q2 + (Q1 )2 + (Q2 )2 • Cost Complementarity? Yes, since a = -2 < 0 MC1(Q1, Q2) = -2Q2 + 2Q1 • Economies of Scope? Yes, since 90 > -2Q1Q2 Conclusion • To maximize profits (minimize costs) managers must use inputs such that the value of marginal of each input reflects price the firm must pay to employ the input. • The optimal mix of inputs is achieved when the MRTSKL = (w/r). • Cost functions are the foundation for helping to determine profit-maximizing behavior in future chapters.