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NAME: JIMOH IBRAHIM DEPARTMENT: ACCOUNTING COLLEGE: S.M.S MATRIC NO: 13/SMS02/021 COURSE: ECO201 AN INTRODUCTION TO MODERN MICROECONOMICS (Page 80, Q 3&5) #3. The substitution effect of an increase in the price of rice on households’ demand, if the price of rice has risen beyond bearable proportions, the quality demand will fall via the substitution effect Hence, the consumer will reduce her demand for rice and buy more of other commodities. The substitution effect of the increase in the price of rice Is the fall in the quantity demand of rice that was motivated by the decrease in the relative price of other goods. WHILE The income effect of an increase in the price of rice on households’ demand, if the price of rice increase, the implication is that a given amount of the consumer’s income previously expended on rice can now buy less of the commodity, technically we say that the rise in price leads to decrease in the consumer’s purchasing power. #5. Engel curve can be defined as the curve used to depict the relationship between the income of the consumer and the quantity of a commodity that is purchased. It was named after Earnest Engel, a nineteenth century economist. (I) For a normal goods, the Engel curve is upward-sloping. (II) For an inferior goods, it is downward-sloping. (Page 172, Q 4, 7&8) #4. The law of diminishing returns is at best a short run phenomenon. First, for a firm to be able to employ the knowledge of the law of diminishing returns in its profit maximization or loss minimization decisions, it must be able to measure the productivity of each of the factor inputs employed. However, since capital is fixed in the short run, and hence its productivity cannot be measured directly, the average product of labour, is usually taken as a measures of the efficiency of labour while the total product of labour is used as a proxy to measure the efficiency of the fixed factor (capital or land). Given the behaviour of the short run productivity curves, we can distinguish three stages in the production process of the firm in the short run. In stage I, both the AP and TP curves are rising. That is the efficiency of the fixed and variable factors is increasing. In stage II, there is decreasing average and marginal productivity of the variable factor, but marginal product is still positive because total productivity continues to rise, though at a decreasing rate. However stage III, constitutes an inefficient combination of both factors. Consequently, no rational producer will produce in this stage. #7. An Isocost is the locus of various combinations of factor inputs that give the same level of expenditure (cost). It can be derive from a give firm’s budget constraint, where by it is a downward sloping straight line intercepting the labour and capital axis at their maximum possible level of purchase. #Firm’s output maximizing decision subject to a cost constraint using the tools of ISOQUANT, an isoquant is a curve that defines the locus of various combinations of factor inputs that gives the same level of output. Using the tools of isoquant, we assume that a firm has two factors (capital & labour), both variables in the long run and hence substitutable because of the principle of diminishing marginal rate of technical substitution of one factor for the other. But using the tools of ISOCOST, the slope of the isocost curve is given by the ratio of the factor prices. So, if the firm decides to use only labour in the process, the total units of labour that can be employed is C/Pl. hence the isocost has a constant slope. #8. GO-GETTERS LTD. Labour=#1 Capital=#2 Budget=#100 (PAGE 189, Q 2&3) #2. Q 10 20 30 40 50 60 STC 1OOO 1200 (1350) 1450 (1600) 1850 TFC 500 500 (500) 500 (500) 500 TVC 500 SAC (100) AFC (50) SMC (100) (700) 850 (950) 1100 (1350) (60) (45) (36.3) (32) (30.8) (25) (16.7) (12.5) (10) (8.3) (20) (15) (10) (15) (25) #3. RELATIONSHIP BETWEEN AFC, SAC AND AVC CURVES Since SAC=AVC+AFC, the SAC curve will always lie above the AVC curve. The difference between the two curves at any output level will be equal to the value of the AFC for that level of output. Since the AFC is high for lower levels of output, it follows that there will be a wider gap between the SAC and AVC curves at lower levels of output. The lower the output level, the wider will this gap be. Conversely, at higher level of output, AFC tends to become very small so that the gap between the SAC and AVC narrows down. At an infinitely large output level, when the AFC approaches zero, the SAC and the AVC will tend to coincide. RELATIONSHIP BETWEEN STC, TVC AND TFC CURVES STC and TVC curves are both upward sloping and have the same slope at all levels of output. This is not a coincidence since the difference between the two curves at any output level is the TFC. Again, since the TFC is constant, the difference between the STC and TVC curve will be constant at every level of output. Finally the STC curve cuts the vertical axis where the TFC intercepts the same axis. MICRO-ECONOMICS THEORY TEXTBOOK (Page 189, Q 1-3) #1. Measuring of expansion path of a firm, The point on an expansion path occur where the firm’s isocost curve, each showing fixed total input cost, and its isoquants, each showing a particular level of output, are tangent. The firm’s moves from one of these tangency points to the next; the line joining the tangency points is called the expansion path. It is the expansion path which is critical in determining the long-run costs of production of a firm. The shape of the expansion path changes depending upon the type of returns to scale prevalent. #2.Comparison of diminishing marginal productivity and returns to scale. It’s important to keep in mind that marginal product and return to scale are not the same concepts and need not go in the same direction. This is because marginal product is calculated by adding one unit of either labor or capital and keeping the other inputs the same, whereas returns to scale refer to what happens when all inputs to production are scaled up. It is generally true that most production processes start to exhibit decreasing marginal product of labor and capital pretty quickly as quantity increases, but this doesn’t mean that the firm also exhibits decreasing returns to scale. In fact, it’s quite common and perfectly reasonable to observe deceasing marginal products and increasing returns to scale simultaneously. #3. CONDITIONS FOR THE ATTAINMENT OF OPTIMUM INPUT-MIX IN A MULTI-INPUT PRODUCTION FUNCTION Economics output is not a function of input, because any given set of inputs can be used to produce a range of outputs. When market prices of inputs are available, the firm would seek to minimize the total input cost for a given level of output. In the decision frame of a firm making economic choices regarding production, the firm in perfect competition will choose to add input right up to the point where the marginal cost of additional input matches the marginal product in additional output. PROBLEMS #1. Demand and supply function Qdx=25-5p Qsx= -15+2.5p Find equilibrium price and quantity Qd=Qs 25-5p=-15+2.5p 25+15=2.5p+5p 40=7.5p Divide both sides by 7.5 P=5.3 Quantity Qdy=25-5p =25-5(5.3) =25-26.3 =-1.3 #2. Qsy=-15+2.5p ,,,=-1.7 Equilibrium price and quantity of two complimentary goods X&Y whose demand and supply function are; Qdx=205-2.5Px-Py Qsx=-30+1.5Px Qdx=147.5-0.5Px-1.5Py Qsx=-60+Py Qdx=Qsx 205-2.5Px-Py=-30+1.5Px 205+30-Py=1.5Px+2.5Px 25-Py=4Px 147.5-0.5Px-1.5Py=-60+Py 147.5+60-0.5Px=Py+1.5Py 207.5-0.5Px=2.5Py (Page 188, Ex 5,10,13,15). #5. Q=4x+2x^2-1/3x^3 MPx=APx when APx is at its maximum MPx=differentiate =4x+2x*2-1/3x^3 =4+4x-x^2 APx=4x+2x^2-1/3x^3 X =4+2x^2-1/3x^2 M MPx=APx 4+4x-x^2=4+2x-1/3x^2 #13. I will suggest that there shouldn’t be any change in the labour mix used by the production department because a firm making economic choices regarding production, the firm in perfect competition will choose to add input right up to the point where the marginal cost of additional input matches the marginal product in additional output. (Page 225 problem 3, 5) #3. Given the total cost function Tc=6500+10q (a) Equation for TFC & TVC. TFC=6500 TVC=10Q (b) equation for AFC, AVC, ATC & MC AFC= TFC Q =6500/Q AVC= TVC Q =10Q/Q =10 ATC= TC Q =6500+10Q Q =6500+10 MC= ^TC ^Q #5. Total cost function of a manufacturer. TC=25+10Q-2.5q^2-1/3Q^3 (a) equation for TVC TVC=TC-TFC TVC=25+10Q-2.5Q^2-1/3Q^3-25 TVC=10Q-2.5Q^2-1/3q3 (b) AVC AVC= TVC Q =10Q-2.5Q^2-1/3q^3 Q =10-2.5Q-1/3Q^2 (c ) ATC ATC=TC Q =25+10Q-2.5Q^2-1/3Q^3 Q =25+10-2.5Q-1/3Q^2 =ATC=35-2.5Q-1/3Q^2 (D) MC=^TC ^Q