2. 1 Chapter 7 Behind the Supply Curve:

3. 2 Recall: Optimal Consumer Behavior Consumer Behavior –(behind the demand curve): Consumption of G&S (Q) produces satisfaction Satisfaction measured as utility Budget as constraint

4. 3 Optimal Consumer Behavior: One product with no constraint TU maximized when MU=0 Two products, optimal consumption bundle MUx / Px = MUy / Py Two products with budget constraint budget line and indifference curves MUx / MUy = Px / Py = dY / dX

5. 4 Producer Behavior Behind the supply curve: –Inputs produces outputs –Outputs measured as Q –Cost of inputs as constraint

6. 5 Optimal Producer Behavior: One input with no constraint TP maximized when MP=0 Two inputs, optimal input combination MPL / w = MPk / r Two inputs with cost constraint Iso-Cost lines and Iso-Quant Curves MPL / MPk = w / r = dK / dL

7. 6 K: was fixed and is variable --Long-Run: The period of time in which all inputs are variable.

8. 7 Optimal Input Combination: Marginal Analysis Given cost budget, buy L and K at MP L /w = MP K /r

9. 8 optimal choice with two variable inputs Two inputs, both variable Given input prices Given cost Iso-cost Line: a line that shows the various combinations of inputs that cost the same amount to purchase, given input prices.

10. 9 Characteristics of Iso-cost lines: C=wL+rK The slope of the Iso-cost curve is the negative of the relative input price ratio, -w/r. A change in total cost will lead to a parallel shift of the Iso-cost curve. A change in an input price will rotate the Iso-cost curve.

11. 10 Substitutability among Inputs Variable Proportions Production: more than one combinations of inputs are possible (substitutions allowed) Fixed proportions Production: only one combination of inputs is feasible (fixed ratio, no substitutions)

12. 11 Iso-quant: a curve showing all possible combinations of inputs that would produce the same level of output.

13. 12 Characteristics of Iso-quant: Downward sloping: to keep the same total product. An infinite number of Iso-quants makes up an Iso-quant map. The farther away from the origin, the higher the output level it represents.

14. 13 Characteristics of Iso-quant: (cont.) No two curves can intersect: Completeness and Transitivity Convex to origin: Diminishing marginal rate of technical substitution (MRTS)

15. 14 Marginal rate of Technical Substitution: MRTS the rate at which one input is substituted for another along an Iso-quant the slope of the Iso-quant MRTS= - (dK/dL) dQ=(MP L *dL)+(MP K *dK) since dQ=0, (MP L *dL)= - (MP K *dK) MP L / MP K = - (dK / dL) MRTS= - (dK/dL) = MP L /MP K

16. 15 Optimization: Constrained Minimization min C = wL + rK s.t Q = f(L, K) by choosing L, K Rule: cost of producing a certain level of output will be minimized when MRTS = - w/r

17. 16 Optimization (minimization): Marginal Product Approach MRTS = MP L /MP K cost is minimized when MRTS = - w/r cost of producing a certain level of output will be minimized when MRTS=MP L /MP K =w/r, or (MP L /w)=(MP K /r)

18. 17 Optimization: Constrained Maximization MaxQ = f(L, K) s.t.C = wL + rK by choosing L, K Rule: MRTS = MP L /MP K = w/r orMP L /w = MP K /r

19. 18 Expansion Path: A curve or locus of points that shows the cost-minimizing input combination for each level of output, holding input prices constant. Each point on the path is both technically and economically efficient. MRTS = w/r everywhere on the path.

20. 19 Return to Scale: Assume:Q = f(L, K) andzQ = f(cL, cK) there is constant return to scale if z=c. there is increasing return to scale if z>c. there is decreasing return to scale if z<c.

21. 20 Long-run Costs LTC = wL + rK LAC = LTC/Q LMC = ΔLTC/ΔQ

22. 21 LTC, LAC, & LMC Least Cost Combination (w=5) (r=10) QLKLTCLACLMC 1001071201.20 2001281400.700.20 30020102000.670.60 40030153000.751.00 50040224200.841.20 60052305600.931.40 70060427201.031.60

23. 22 LMC<LAC,LAC  ; LMC>LAC,LAC  ; LMC=LAC,LAC min. C Q LAC LMC LTC, LAC, & LMC

24. 23 (Internal) Economies of Scale LAC decreases as output increases. --specialization and division of labor --technological factors

25. 24 (Internal) Diseconomies of Scale LAC increases as output increases. --limitations to efficient management

26. 25 External Economy vs. External Diseconomy -industry development provides better transportation, information, and human resources. *competition causes higher costs

27. 26 Economies of Scope: there is economies of scope if C(X, Y) < C(x) + C(Y), otherwise, there is diseconomies of scope. 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.