UNIT II: Firms & Markets

1. UNIT II: Firms & Markets • Theory of the Firm • Profit Maximization • Perfect Competition • Review • 11/5 MIDTERM 10/22

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 use our models of consumers, firms and markets to construct a general equilibrium and consider its welfare implications.

3. Perfect Competition • Supply in the Long-Run • Equilibrium and Efficiency • General Equilibrium • Qelfare 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 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.

6. Perfect Competition From last time: 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. Qhat determines the number offirms in the long-run?

7. Supply in the Long-Run 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 AVC AC q q q Firm A Firm B Firm C

8. Supply in the Long-Run 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

9. Supply in the Long-Run 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

10. Supply in the Long-Run 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

11. Supply in the Long-Run The long-run supply curve. P* is the lowest possible price associated with non-negative profits, P* = ACmin. s1=(mc1) s2 Sn, where n is the number of firms in the market. $ P* s3 s4 Q

12. Supply in the Long-Run The long-run supply curve. Qe can eliminate portions of the individual firms’ supply curves below P* (firms will exit). s1 s2 $ P* s3 s4 Q

13. Supply in the Long-Run The long-run supply curve. Qe can also eliminate portions of the individual firms’ supply curves above P* (demand will be met by another firm’s supply curve). s1 s2 $ P* s3 s4 Q

14. Supply in the Long-Run The long-run supply curve. As the number of firms increases, the long run supply curve approximates a straight line at P* = ACmin. $ ACmin = P* LRS Q

15. Supply in the Long-Run Long-run equilibrium. Firms are producing at the efficient scale. P* = ACmin; P = 0. $ $ P* MC AC LRS D q* q Q* Q

16. 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 info to solve for the long-run competitive equilibrium. P = 0 P = 0

17. 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?

18. Perfect Competition TC = 100 + q2QD = 1000 – 20P 1)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 We know AC = MC at ACmin AVC = q LRS q* is the efficient scale q* q 600 Q

19. Perfect Competition TC = 100 + q2QD = 1000 – 20P 1)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

20. Perfect Competition TC = 100 + q2QD = 1000 – 20P 3)p = TR – TC = 0 = Pq – (100 + q2) = 0 p = (2q)q – (100 + q2) = 0 2q2 – 100 - q2 = 0 q2 = 100; q* = 10 $ MC = 2q $ P* = 20 AC = 100/q + q AVC = q LRS P = MC = 2q q* = 10 q 600 Q

21. Perfect Competition TC = 100 + q2 QD= 1000 – 20P $ MC = 2q $ P* = 20 AC = 100/q + q AVC = q LRS D n = 60 q* = 10 q Q* = 600 Q

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

23. 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

24. 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

25. 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. Qhat determines the number of firms in long run equilibrium?

26. 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.

27. 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.

28. 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 equiliibria (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.

29. 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 Qilling to pay Pb Pb = Ps Qilling to sell for Ps S D Q Q* Q

30. Equilibrium & Efficiency Qe 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

31. Equilibrium & Efficiency Qe 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

32. Equilibrium & Efficiency Qe 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

33. General Equilibrium So far, we have been looking at individual markets, and we have seen that in equilibrium we know output price and quantity (P*, Q*) and optimal factor demand (K*, L*), which it turn determine factor prices (r*, w*). In general, output in some markets (intermediate goods, e.g., steel) are inputs in others (final goods, e.g., cars), and a change in the price of one good may affect another price. Calculating the equilibrium price of just one good, in theory, requires an analysis that accounts for all of the different goods that are available.

34. 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 (Q), and widgets require only labor (L) to produce, according to the following production function: Q = L Consumers’ preferences are described by: U1 = X11/3Q12/3; and U2 = X22/3Q21/3 Also, L + X = 24 (hrs/day) and the wage (w) is $1/hr. Find: X1,2, Q1,2, P

35. General Equilibrium Start by constructing the market demand curve Q = Q1 + Q2 => Q = 24/PQ U1 = X11/3Q12/3 U2 = X22/3Q21/3 MUx = 1/3X-2/3Q2/3 MUx = 2/3X-1/3Q1/3 MUQ = 2/3X1/3Q-1/3 MUQ = 1/3X2/3Q-2/3 MRS1 = Q/2X = Px/PQ MRS2 = 2Q/X = Px/PQ Px=1 => X = 1/2PQQ => X = 2PQQ BC: I = PxX + PQQ BC: I = PxX + PQQ 24 = 3/2 PQQ 24 = 3PwQ => Q1 = 16/PQ=> Q2 = 8/PQ

36. 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

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

38. General Equilibrium Now consider the firm’s problem: Profit (P) = Total Revenue(TR) – Total Cost(TC) TR = PQ TC(Q) = rK + wL MR = P MC = w since w =1, we know: P = 1; Q = 24 Q1 = 16; Q2 = 8 X1 = 8; X2 = 16 also L + X = 24, so: L1 = 16; L2 = 8; L = 24r Rate on Capital From the Demand curve: Q = 24/PQ

39. General Equilibrium Now consider the firm’s problem: Profit (P) = Total Revenue(TR) – Total Cost(TC) TR = PQ TC(Q) = rK + wL MR = P MC = w since w =1, we know: P = 1; Q = 24 Q1 = 16; Q2 = 8 X1 = 8; X2 = 16 also L + X = 24, so: L1 = 16; L2 = 8; L = 24r Rate on Capital

40. General Equilibrium The Market for Qidgets r Rate on Capital P P*= 1 Demand: Q = 24/PQ Supply: PQ = 1 Q* = 24 Q

41. 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.

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. Demand Represents the horizontal sum of individual consumers’ demand curves P d = consumer D = Market Demand D = Sd Q

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. 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

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 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

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 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

46. 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

47. 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 Px/Py = MCx/MCy(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

48. 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

49. 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)

50. 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).