UNIT II:Firms & Markets Theory of the Firm Profit Maximization Perfect Competition Review 7/23 MIDTERM 7/14

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 also construct a general equilibrium model of Smith’s vision.

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

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.

Perfect Competition Implications 1)Firms produce at minimum average cost, i.e., “efficient scale.” (AC = AC min ) 2)Price is equal to marginal cost. (P = MC) 3)Firms earn zero (economic) profits. (  = 0) 4)Market equilibrium is Pareto-efficient.

Perfect Competition In the Long-run… 1)Firms produce at minimum average cost, i.e., “efficient scale.” (AC = AC min ) 2)Price is equal to marginal cost. (P = MC) 3)Firms earn zero (economic) profits. (  = 0) 4)Market equilibrium is Pareto-efficient.

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. 

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). Firm A Firm B Firm C q q q $P$P MC AC q: firm Q: market 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). Firm A Firm B Firm C q q q $P$P MC AC AVC AC 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). Firm A Firm B Firm C q q q $P$P In the long run, Firm C will exit the market. MC AC MC AC 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. Firm A Firm B Firm D q q q $P$P MC AC MC AC Perfect Competition

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

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

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

Consider a perfectly competitive industry characterized by the following total cost and demand functions: TC = q 2 Q D = 1000 – 20P Find the market equilibrium in the long-run. How many firms are in the market?

Perfect Competition TC = q 2 Q D = 1000 – 20P q* q 600 Q $ LRS MC = 2q AVC = q AC = 100/q + q  1)  Firms produce at AC min i) AC = MC 100/q + q = 2q q 2 = 2q 2 q 2 = 100; q* = 10 ii) AC’ = /q = 0 q 2 = 100; q* = 10 $ P* = 20 q* is the efficient scale We know AC = MC at AC min

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

Perfect Competition TC = q 2 Q D = 1000 – 20P $ q* = 10 q 600 Q $ LRS MC = 2q AVC = q AC = 100/q + q  3)  = TR – TC = 0 = Pq – (100 + q 2 ) = 0  = (2q)q – (100 + q 2 ) = 0 2q 2 – q 2 = 0 q 2 = 100; q* = 10 2) P = MC = 2q

Perfect Competition TC = q 2 Q D = 1000 – 20P q* = 10 q 600 Q $ LRS MC = 2q AVC = q AC = 100/q + q  3)  = TR – TC = 0 = Pq – (100 + q 2 ) = 0  = (2q)q – (100 + q 2 ) = 0 2q 2 – q 2 = 0 q 2 = 100; q* = 10 $ P* = 20 P = MC = 2q

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

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

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

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

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. What determines the number of firms in long run equilibrium?

Perfect Competition In the Long-run … 1)Firms produce at minimum average cost, i.e., “efficient scale.” 2)Price is equal to marginal cost. 3)Firms earn zero (economic) profits. 4)Market equilibrium is Pareto-efficient.

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.

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.

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. D Q Q* Q P At Q < Q*, a buyer and seller can exchange and both be better off Willing to pay P b P b = P s Willing to sell for P s S

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. D: MRS = Px/Py S: MR = MC Q* Q P P o P* Consumer Surplus The total difference between what consumers are willing to pay and the market price CS = ½(P o - P*)Q* CS

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. D: MRS = Px/Py S: MR = MC Q* Q P P o P* Producer Surplus The total difference between the firms’ marginal cost of production and the market price PS =  (- FC) CS PS

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. D: MRS = Px/Py S: MR = MC Q* Q P P o P* CS PS Social Surplus The sum of consumer and producer surplus SS = CS + PS

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. D: MRS = Px/Py S: MR = MC Q* Q P P o P* CS PS Social Surplus The sum of consumer and producer surplus SS = CS + PS Greatest at Q*

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.

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: U 1 = X 1 1/3 W 1 2/3 ; and U 2 = X 2 2/3 W 2 1/3 Also, L + X = 24 (hrs/day) and the wage (w) is $1/hr. Find: X 1,2, W 1,2, P

General Equilibrium Start by constructing the market demand curve W = W 1 + W 2 => W = 24/P w U 1 = X 1 1/3 W 1 2/3 U 2 = X 2 2/3 W 2 1/3 MU x = 1/3X -2/3 W 2/3 MU x = 2/3X -1/3 W 1/3 MU w = 2/3X 1/3 W -1/3 MU w = 1/3X 2/3 W -2/3 MRS 1 = W/2X = P x /P w MRS 2 = 2W/X = P x /P w P x =1=> X = 1/2P w W=> X = 2P w W BC: I= P x X + P w WBC: I= P x X + P w W 24 = 3/2 P w W 24 = 3P w W => W 1 = 16/P w => W 2 = 8/P w

General Equilibrium Now consider the firm’s problem: Profit (  = Total Revenue(TR) – Total Cost(TC) TR(Q) = PQ TC(Q) = rK + wL PPrice LLabor QQuantity KCapital w Wage Rate rRate on Capital

General Equilibrium Now consider the firm’s problem: Profit (  = Total Revenue(TR) – Total Cost(TC) TR = PW TC(Q) = rK + wL PPrice LLabor WWidgetsKCapital w Wage Rate rRate on Capital

General Equilibrium Now consider the firm’s problem: Profit (  = Total Revenue(TR) – Total Cost(TC) TR = PW TC(Q) = rK + wL MR = PMC = w since w =1, we know: P = 1; W = 24 W 1 = 16; W 2 = 8 X 1 = 8; X 2 = 16 also L + X = 24, so: L 1 = 16; L 2 = 8; L = 24 rRate on Capital From the Demand curve: W = 24/P w

General Equilibrium Now consider the firm’s problem: Profit (  = Total Revenue(TR) – Total Cost(TC) TR = PW TC(Q) = rK + wL MR = PMC = w since w =1, we know: P = 1; W = 24 W 1 = 16; W 2 = 8 X 1 = 8; X 2 = 16 also L + X = 24, so: L 1 = 16; L 2 = 8; L = 24 rRate on Capital

General Equilibrium The Market for Widgets rRate on Capital W* = 24 W P P*= 1 Demand: W = 24/P w Supply: P = 1

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.

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

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. D: MRS = Px/Py Q P Demand Since all consumers are optimizing at the same output prices (Px/Py) MRS 1 = MRS 2 Consumption Efficiency d = consumer D = Market Demand

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. D: MRS = Px/Py P = mc: MRTS = w/r Q* Q P P o P* Supply Represents individual firm’s optimal factor proportion, given factor prices (w/r) mc = individual firm’s marginal cost

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. D: MRS = Px/Py P = mc: MRTS = w/r Q* Q P P o P* Supply Since all firms are optimizing (minimizing cost) at the same factor prices (w/r) MRTS x = MRTS y mc = individual firm’s marginal cost Production Efficiency

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. D: MRS = Px/Py Q* Q P P o P* Supply Represents total marginal cost of production mc = firm’s S = Market Supply S =  mc

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. D: MRS = Px/Py S: MR = MC Q* Q P P o P* Supply Since relative prices fully reflect relative costs P x /P y = MC x /MC y (MRT yx = MC x /MC y ) Product mix is optimal Marginal Rate of Transformation MRT yx = MC x /MC y

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. D: MRS = Px/Py S: MR = MC Q* Q P P o P* Supply Since relative prices fully reflect relative costs MRS yx = MRT yx (MRT yx = MC x /MC y ) Product mix is optimal Marginal Rate of Transformation MRT yx = MC x /MC y Allocative Efficiency

Welfare Consumption Efficiency: All consumers are optimizing at given output prices (P x /P y ) MRS 1 = MRS 2 Production Efficiency: All firms are optimizing (minimizing cost) at given factor prices (w/r) MRTS x = MRTS y Allocation Efficiency: Product mix will be optimal; relative prices fully reflect relative costs MRS yx = MRT yx (where MRT yx = MC x /MC y )

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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