Chapter 7 Behind the Supply Curve 1

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Chapter 7 Behind the Supply Curve: 1

Recall: Optimal Consumer Behavior n Consumer Behavior – (behind the demand curve): n Consumption of G&S (Q) produces satisfaction n Satisfaction measured as utility n Budget as constraint 2

Optimal Consumer Behavior: n One product with no constraint TU maximized when MU=0 n Two products, optimal consumption bundle MUx / Px = MUy / Py n Two products with budget constraint budget line and indifference curves MUx / MUy = Px / Py = d. Y / d. X 3

Producer Behavior n Behind the supply curve: – Inputs produces outputs – Outputs measured as Q – Cost of inputs as constraint 4

Optimal Producer Behavior: n One input with no constraint TP maximized when MP=0 n Two inputs, optimal input combination MPL / w = MPk / r n Two inputs with cost constraint Iso-Cost lines and Iso-Quant Curves MPL / MPk = w / r = d. K / d. L 5

K: was fixed and is variable --Long-Run: n. The period of time in which all inputs are variable. 6

Optimal Input Combination: Marginal Analysis n Given cost budget, buy L and K at MPL/w = MPK/r 7

optimal choice with two variable inputs n Two inputs, both variable n Given input prices n Given cost n Iso-cost Line: a line that shows the various combinations of inputs that cost the same amount to purchase, given input prices. 8

Characteristics of Iso-cost lines: n C=w. L+r. K n The slope of the Iso-cost curve is the negative of the relative input price ratio, -w/r. n A change in total cost will lead to a parallel shift of the Iso-cost curve. n A change in an input price will rotate the Iso-cost curve. 9

Substitutability among Inputs n Variable Proportions Production: more than one combinations of inputs are possible (substitutions allowed) n Fixed proportions Production: only one combination of inputs is feasible (fixed ratio, no substitutions) 10

Iso-quant: na curve showing all possible combinations of inputs that would produce the same level of output. 11

Characteristics of Iso-quant: n Downward sloping: to keep the same total product. n An infinite number of Iso-quants makes up an Iso-quant map. n The farther away from the origin, the higher the output level it represents. 12

Characteristics of Iso-quant: (cont. ) n No two curves can intersect: Completeness and Transitivity n Convex to origin: Diminishing marginal rate of technical substitution (MRTS) 13

Marginal rate of Technical Substitution: MRTS the rate at which one input is substituted for another along an Iso-quant n the slope of the Iso-quant n MRTS= - (d. K/d. L) n d. Q=(MPL*d. L)+(MPK*d. K) since d. Q=0, (MPL*d. L)= - (MPK*d. K) MPL/ MPK = - (d. K / d. L) MRTS= - (d. K/d. L) = MPL/MPK n 14

Optimization: Constrained Minimization n min C = w. L + r. K n s. t Q = f(L, K) by choosing L, K n Rule: cost of producing a certain level of output will be minimized when MRTS = w/r 15

Optimization (minimization): Marginal Product Approach n MRTS = MPL/MPK n cost is minimized when MRTS = - w/r n cost of producing a certain level of output will be minimized when MRTS=MPL/MPK=w/r, or (MPL/w)=(MPK/r) 16

Optimization: Constrained Maximization n Max Q = f(L, K) n s. t. C = w. L + r. K by choosing L, K n Rule: MRTS = MPL/MPK = w/r or MPL/w = MPK/r 17

Expansion Path: n. A curve or locus of points that shows the cost-minimizing input combination for each level of output, holding input prices constant. n Each point on the path is both technically and economically efficient. n MRTS = w/r everywhere on the path. 18

Return to Scale: Assume: Q = f(L, K) and z. Q = f(c. L, c. K) n there is constant return to scale if z=c. n there is increasing return to scale if z>c. n there is decreasing return to scale if z<c. 19

Long-run Costs n LTC = w. L + r. K n LAC = LTC/Q n LMC = ΔLTC/ΔQ 20

LTC, LAC, & LMC Least Combination Q 100 200 300 400 500 600 700 L 10 12 20 30 40 52 60 K 7 8 10 15 22 30 42 (w=5) (r=10) LTC 120 140 200 300 420 560 720 LAC 1. 20 0. 70 0. 67 0. 75 0. 84 0. 93 1. 03 LMC 1. 20 0. 60 1. 00 1. 20 1. 40 1. 60 21

LTC, LAC, & LMC<LAC, LAC ; LMC>LAC, LAC ; LMC=LAC, LAC min. C LMC LAC Q 22

(Internal) Economies of Scale n LAC decreases as output increases. --specialization and division of labor --technological factors 23

(Internal) Diseconomies of Scale n LAC increases as output increases. --limitations to efficient management 24

External Economy vs. External Diseconomy -industry development provides better transportation, information, and human resources. *competition causes higher costs 25

Economies of Scope: n there is economies of scope if C(X, Y) < C(x) + C(Y), otherwise, there is diseconomies of scope. n SC = (C(X) + C(Y) - C(X, Y))/C(X, Y) if SC>0, there exits economies of scope if SC<0, there exits diseconomies of scope. 26

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