UNIT II: Firms & Markets

1. UNIT II: Firms & Markets • Theory of the Firm • Profit Maximization • Perfect Competition • Review • 7/14 MIDTERM 7/7

2. Perfect Competition Is it true that the rational pursuit of private interests produces coherence rather than chaos, and if so, how is it done? -- Frank Hahn Adam Smith described a world in which market competition weed-outs inefficient behavior, so that the ‘pursuit of private interests’ is led, as if by an invisible hand, to promote the general welfare of society. Today, we will solve for a competitive equilibrium and consider its welfare implications.We will alsoconstruct a general equilibrium model of Smith’s vision.

3. Perfect Competition • Assumptions and Implications (from last time) • Solving for the Competitive Equilibrium • Equilibrium and Efficiency • General Equilibrium • Welfare Analysis

4. Perfect Competition Assumptions • Firms are price-takers: can sell all the output they want at P*; can sell nothing at any price > P*. • Homogenous product: e.g., wheat, t-shirts, long-distance phone minutes. • Perfect factor mobility: in the long run, factors can move costlessly to where they are most productive (highest w, r). • Perfect information: firms know everything about costs, consumer demand, other profitable opportunities, etc.

5. Perfect Competition Implications • Firms produce at minimum average cost, i.e., “efficient scale.” (AC = ACmin) • Price is equal to marginal cost. (P = MC) • Firms earn zero (economic) profits. (p = 0) • Market equilibrium is Pareto-efficient.

6. Perfect Competition In the Long-run… • Firms produce at minimum average cost, i.e., “efficient scale.” (AC = ACmin) • Price is equal to marginal cost. (P = MC) • Firms earn zero (economic) profits. (p = 0) • Market equilibrium is Pareto-efficient.

7. Perfect Competition The Short-run & the Long-run In the short-run, firms adjust to price signals by varying their utilization of labor (variable factors). In the long-run, firms adjust to profit signals by • varying plant size (fixed factors); and • entering or exiting the market. We can use this account to understand (and solve for) the long-run competitive equilibrium. P = 0 P = 0

8. Perfect Competition Short-run equilibrium with three firms. Firm A is making positive profits, Firm B is making zero profits, and Firm C is making negative profits (losses). q: firm Q: market MC MC $ P MC AC AC AC q q q Firm A Firm B Firm C

9. Perfect Competition Short-run equilibrium with three firms. Firm A is making positive profits, Firm B is making zero profits, and Firm C is making negative profits (losses). In the long run, Firm C will exit the market. MC $ P MC AC AC q q q Firm A Firm B Firm C

10. Perfect Competition In the long-run, inefficient firms will exit, and new firms will enter, as long as some firms are making positive economic profits. MC $ P MC MC AC AC AC q q q Firm A Firm B Firm D

11. Perfect Competition In the long-run, if there are no barriers to entry, then new firms have access to the most efficient productiontechnology. We call this the efficient scale. $ P* MC MC MC AC AC AC q* q q* q q* q Firm A Firm D Firm E

12. Perfect Competition Long-run equilibrium. Firms are producing at the efficient scale. P* = ACmin; P = 0. $ $ P* MC AC LRS D q* q Q* Q

13. Perfect Competition Consider a perfectly competitive industry characterized by the following total cost and demand functions: TC = 100 + q2 QD = 1000 – 20P Find the market equilibrium in the long-run. How many firms are in the market?

14. Perfect Competition TC = 100 + q2QD = 1000 – 20P Firms produce at ACmin i) AC = MC 100/q + q = 2q 100 + q2 = 2q2 q2 = 100; q* = 10 ii)AC’ = 0 -100/q2 + 1 = 0 q2 = 100; q* = 10 $ MC = 2q $ P* = 20 AC = 100/q + q AVC = q LRS q* is the efficient scale q* = 10 q 600 Q

15. Perfect Competition TC = 100 + q2 QD’ = 1500 – 20P q.n = (MC/2)n = (P/2)n => QS = 30P SRS $ MC = 2q $ P* = 20 AC = 100/q + q SRS P’ = 30 AVC = q LRS D’ D n = 60 q’ = 15 q Q’ = 900 Q

16. Perfect Competition TC = 100 + q2 QD’ = 1500 – 20P $ MC = 2q $ P* = 20 AC = 100/q + q AVC = q LRS D’ D n = 110 q* = 10 q Q** = 1100 Q

17. Perfect Competition In the Long-run … • Firms produce at minimum average cost, i.e., “efficient scale.” • Price is equal to marginal cost. • Firms earn zero (economic) profits. • Market equilibrium is Pareto-efficient.

18. Equilibrium & Efficiency Is it true that the rational pursuit of private interests produces coherence rather than chaos, and if so, how is it done? -- Frank Hahn Equilibrium: most generally, an equilibrium is a state of the market in which decision plans are mutually consistent and therefore can be implemented. In the market, coordination takes place via prices: at a given price, all the output firms want to produce can be sold and all the goods consumers want to purchase can be bought.

19. Equilibrium & Efficiency Pareto Efficiency: an economic situation is Pareto efficient if no one can be made any better off without making someone else worse off. Pareto efficiency is a “good” thing, but it says nothing about equity; income distribution; economic justice. Competitive markets produce Pareto efficient equilibria (Q*), because at Q* the price someone is willing to pay for an additional unit of the good is equal to the price that someone must be paid to sell that unit.

20. Equilibrium & Efficiency The market equilibrium is Pareto efficient because at Q* the price someone is willing to pay for an additional unit of the good is equal to the price that someone must be paid to sell that unit. At Q < Q*, a buyer and seller can exchange and both be better off P Willing to pay Pb Pb = Ps Willing to sell for Ps S D Q Q* Q

21. Equilibrium & Efficiency We know that in a market equilibrium, both consumers and firms are optimizing, and we used these conditions to derive Demand and Supply curves. Consumer Surplus The total difference between what consumers are willing to pay and the market price CS = ½(Po- P*)Q* P Po P* S: MR = MC CS D: MRS = Px/Py Q* Q

22. Equilibrium & Efficiency We know that in a market equilibrium, both consumers and firms are optimizing, and we used these conditions to derive Demand and Supply curves. Producer Surplus The total difference between the firms’ marginal cost of production and the market price PS = P (- FC) P Po P* S: MR = MC CS PS D: MRS = Px/Py Q* Q

23. Equilibrium & Efficiency We know that in a market equilibrium, both consumers and firms are optimizing, and we used these conditions to derive Demand and Supply curves. Social Surplus The sum of consumer and producer surplus SS = CS + PS P Po P* S: MR = MC CS PS D: MRS = Px/Py Greatest at Q* Q* Q

24. Pure Exchange An Edgeworth Box Y 1 X Indifference curves for Person 1.

25. Pure Exchange An Edgeworth Box 2 Y 1 X Indifference curves for Person 1 and Person 2. The dimensions of the box represent the total amounts of X and Y in the economy.

26. Pure Exchange An Edgeworth Box 2 Y 1 X Contract Curve: the set of Pareto efficient allocations, where each person is at the highest possible indifference curve, given the indifference curve of the other person.

27. Pure Exchange An Edgeworth Box 2 Y Endowment 1 X The initial endowment is shown in the graph, above. Both are better off at a point in the shaded area.

28. Pure Exchange An Edgeworth Box 2 Y Endowment 1 X Exchange (trade) should occur until they reach a point on the contract curve.

29. Pure Exchange An Edgeworth Box 2 Y Endowment 1 X Exchange (trade) should occur s.t., MRS1= MRS2 = Px/Py.

30. Pure Exchange An Edgeworth Box 2 Y Endowment Efficient Allocation 1 X Exchange leads to a Pareto Efficient Allocation.

31. General Equilibrium Consider an economy with 2 consumers and 1 producer. Despite their small numbers, all behave as price-takers. Consumers consume leisure (X) and widgets (W), and widgets require only labor (L) to produce, according to the following production function: W = L Consumers’ preferences are described by: U1 = X11/3W12/3; and U2 = X22/3W21/3 Also, L + X = 24 (hrs/day) and the wage (w) is $1/hr. Find: X1,2, W1,2, P

32. General Equilibrium Start by constructing the market demand curve W = W1 + W2 => W = 24/Pw U1 = X11/3W12/3 U2 = X22/3W21/3 MUx = 1/3X-2/3W2/3 MUx = 2/3X-1/3W1/3 MUw = 2/3X1/3W-1/3 MUw = 1/3X2/3W-2/3 MRS1 = W/(2X) = Px/Pw MRS2 = 2W/X = Px/Pw Px=1 => X = 1/2PwW => X = 2PwW BC: I = PxX + PwW BC: I = PxX + PwW 24 = 3/2 PwW 24 = 3PwW => W1 = 16/Pw=> W2 = 8/Pw

33. General Equilibrium Now consider the firm’s problem: Profit (P) = Total Revenue(TR) – Total Cost(TC) TR(Q) = PQ TC(Q) = rK + wL P Price L Labor Q Quantity K Capital w Wage Rate r Rate on Capital

34. General Equilibrium Now consider the firm’s problem: Profit (P) = Total Revenue(TR) – Total Cost(TC) TR = PW TC(Q) = rK +wL P Price L Labor W WidgetsK Capital w Wage Rate r Rate on Capital

35. General Equilibrium Now consider the firm’s problem: Profit (P) = Total Revenue(TR) – Total Cost(TC) TR = PW TC(Q) = rK + wL MR = P MC = w since w =1, we know: P = 1; W = 24 W1 = 16; W2 = 8 X1 = 8; X2 = 16 also L + X = 24, so: L1 = 16; L2 = 8; L = 24r Rate on Capital From the Demand curve: W = 24/Pw

36. General Equilibrium Now consider the firm’s problem: Profit (P) = Total Revenue(TR) – Total Cost(TC) TR = PW TC(Q) = rK + wL MR = P MC = w since w =1, we know: P = 1; W = 24 W1 = 16; W2 = 8 X1 = 8; X2 = 16 also L + X = 24, so: L1 = 16; L2 = 8; L = 24r Rate on Capital

37. General Equilibrium The Market for Widgets r Rate on Capital P P*= 1 Demand: W = 24/Pw Supply: P = 1 W* = 24 W

38. Welfare First Theorem of Welfare Economics: All competitive equilibria are Pareto-efficient. Second Theorem of Welfare Economics: Any allocation (of wealth or goods) can be sustained in a competitive equilibrium.

39. Welfare We know that in a market equilibrium, both consumers and firms are optimizing, and we used these conditions to derive Demand and Supply curves. Demand Represents the horizontal sum of individual consumers’ demand curves P d = consumer D = Market Demand D = Sd Q

40. Welfare We know that in a market equilibrium, both consumers and firms are optimizing, and we used these conditions to derive Demand and Supply curves. Demand Since all consumers are optimizing at the same output prices (Px/Py) MRS1 = MRS2 P d = consumer D = Market Demand D: MRS = Px/Py Q Consumption Efficiency

41. Welfare We know that in a market equilibrium, both consumers and firms are optimizing, and we used these conditions to derive Demand and Supply curves. Supply Represents individual firm’s optimal factor proportion, given factor prices (w/r) P Po P* mc = individual firm’s marginal cost P = mc: MRTS = w/r D: MRS = Px/Py Q* Q

42. Welfare We know that in a market equilibrium, both consumers and firms are optimizing, and we used these conditions to derive Demand and Supply curves. Supply Since all firms are optimizing (minimizing cost) at the same factor prices (w/r) MRTSx = MRTSy P Po P* mc = individual firm’s marginal cost P = mc: MRTS = w/r D: MRS = Px/Py Q* Q Production Efficiency

43. Welfare We know that in a market equilibrium, both consumers and firms are optimizing, and we used these conditions to derive Demand and Supply curves. Supply Represents total marginal cost of production P Po P* mc = firm’s S = Market Supply S = Smc D: MRS = Px/Py Q* Q

44. Welfare We know that in a market equilibrium, both consumers and firms are optimizing, and we used these conditions to derive Demand and Supply curves. Supply Represents marginal social cost of production P Po P* mc = firm’s S = Market Supply S = MC D: MRS = Px/Py Q* Q

45. Welfare We know that in a market equilibrium, both consumers and firms are optimizing, and we used these conditions to derive Demand and Supply curves. Supply Since relative prices fully reflect relative costs MRSyx = MRTyx(MRTyx = MCx/MCy) Product mix is optimal P Po P* Marginal Rate of Transformation MRTyx = MCx/MCy S: MR = MC D: MRS = Px/Py Q* Q Allocative Efficiency

46. Welfare Consumption Efficiency: All consumers are optimizing at given output prices (Px/Py) MRS1 = MRS2 Production Efficiency: All firms are optimizing (minimizing cost) at given factor prices (w/r) MRTSx = MRTSy Allocation Efficiency: Product mix will be optimal; relative prices fully reflect relative costs MRSyx = MRTyx (where MRTyx = MCx/MCy)

47. Welfare The raison d'être of Welfare Economics is simple. How desirable it would be if we were able to pronounce as a matter of scientific demonstration that such and such a policy was good or bad(Robbins 1984, p. xx).

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