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Production Production- creation of any good services that has economic value to either consumers or other producers Production Function- mathematical description of the various technical production possibilities faced by a firm Q f ( x , y) where Q is output and x and y are inputs Short-run- corresponds to the period of time in which one or more inputs are fixed Fixed input- quantity employed in production is constant Long-run- corresponds to the period of time in which all inputs are variable Variable input- quantity employed in the production process varies at the discretion of the decision maker Marginal product- incremental change in total output for a change in an input – note by assumption all other inputs are held constant MPx Q x Average product- ratio of total output to the amount of variable input used in producing the output APx Q x 3 –Stage Production Function (Total Product, TP or Q) Increasing returns- MP, slope of the TP curve is increasing – total product is increasing at an increasing rate Decreasing returns- TP is increasing at a decreasing rate, MP is positive but decreasing Negative returns- TP is decreasing, MP is negative Stage I – range over X average product is increasing Stage II – point from max AP to where MP=0 Stage III – range total product is decreasing Economic Stage of Production Stage III – no-MPx is negative, can reduce amount of input and increase output, not rationed to produce beyond X3 Stage I – no, add input productivity is rising so keep adding Stage II – yes, in general, as long as no budget constraint, can purchase as much of X as you want Elasticity of production - measures the responsiveness of output changes to m arg inal product %Q Q x changes in the given input x E x x Q average product %x Law of diminishing marginal returns – given all other inputs remain constant, the increasing use of one input in the production process will beyond some point result in diminishing marginal increases in total output TVP- total value product, the value of the output and is given by the price of the product times the amount of physical product produced- TVP = p Q where p is price MVP- marginal value product, the exact rate of exchange of total value product resulting from an infinitesimal change in X holding other factors constant MVPx TP x AVP-average value product, ratio of total value to the amount of variable input used holding other inputs constant AVPx TP x Total cost- total input cost is the sum of input prices times the quantity of the factor employed plus fixed costs C rx x ry y b where ri is the input price and b is fixed costs. Productive isoquant- locus of input combinations giving the same output Perfect subsidies- isoquants are a series of parallel lines, change X and Y in fixed proportions to get same output Perfect complements – series of right angle isoquants, zero substitutability Marginal rate of technical substitution- rate at which one input may be substituted for another input in the production process while total output MPx remains constant MRTS MPy Isocost lines- locus of input combinations that entail the same total cost Returns to scale- the proportionate increase in output that results from the given proportionate increase in all the inputs Increase all inputs by a factor of K what is the increase in output? Increasing returns to scale- output increases by more than k that is Q(2) > KQ(1) Note. Q(1) refers to the output before the change in inputs and Q(2) refers to the output after the change in inputs. Decreasing returns to scale- output increases by less than k that is Q(2) < KQ(1) Constant returns to scale- output increases by exactly K that is Q(2) = KQ(1) Homogeneous function- a function that if each input in the function is multiplied by an arbitrary constant K and this constant can be factored out of the function Cost- sacrifice incurred whenever an exchange or transformation of resources takes place Opportunity costs- value of a resource next best alternative Sunk cost- cost incurred regardless of the alternative action chosen in a decision making problem Cost function-relationship showing the minimum achievable cost of producing various quantities of output Total cost function- total cost of producing a given quantity of output TC VC FC Fixed costs- cost of inputs to the production process that are constant over the short term, FC Variable costs- costs of the variable inputs to the production process, VC Marginal cost- incremental increase in total cost that results in an infinitesimal change in output, Q, MC TC Q Average Cost Functions AFC FC Q AVC VC Q ATC TC AFC AVC Q Cost curves shapes – see graph FC doesn’t change as you change Q TC & TVC – increase as you increase output o Initially at a decreasing rate Corresponding MC is decreasing Min. point on MC corresponds to maximum point on MP Beyond this point TVC & TC increasing at increasing rate, MC must be increasing AVC- decreases to start of stage II, then increases Long run curves see graph Economies of scale- initially as increase output average costs decrease Diseconomies of scale- as increase output average costs increase