Intermediate Microeconomics (22014)

Transcription

1 Theor Intermediate Microeconomics (22014) II. Producer Theor Instructor: Marc Teignier-Baqué First Semester, 2011

2 Theor Outline Part II. Produer Theor Monopol Oligopol 1. Producer Theor Review Maximization 1.3 Cost Minimization 1.4 Cost s 1.5 Firm's Suppl 1.6 Industr Suppl 2. Topic 4. Monopol and Monopol Behavior 3. Topic 5. Game Theor and Oligopol

3 Theor Firm's suppl Industr suppl Monopol Oligopol TOPIC 0b. PRODUCER THEORY REVIEW How do rms decide how much product to suppl? This depends upon the market environment, the rms' technolog, their goals. Market environments: Monopol : Just one seller that determines the quantit supplied and the market-clearing price. Oligopol : A few rms, the decisions of each inuencing the paos of the others. Dominant Firm: Man rms, but one much larger than the rest, which aects the paos of small rms. Monopolistic Competition: Man rms each making a slightl dierent product, each of them small relative to the total. Pure Competition : Man rms, all making the same product, each of them small relative to the total. Firms have no inuence over the market price for their product, the are price-takers.

4 Theor Firm's suppl Industr suppl Monopol Oligopol Denitions A technolog is a process b which inputs are converted to an output. The technolog's production function states the maximum amount of output possible,, from an input bundle (x 1, x 2,..., x n ), = f (x 1, x 2,..., x n ). The marginal product of input i is the rate-of-change of the output level as the level of input i changes, holding all other input levels xed, MP i = x i. Output Level One input, one output example = f(x) is the production function = f(x ) is the maximal output level lobtainable bl from x input units is an output level that is feasible from x input units x Input Level

5 Theor Firm's suppl Industr suppl Monopol Oligopol Returns to Scale Denitions Returns-to-scale describes how the output level changes as all input levels change in direct proportion (e.g. all input levels doubled, or halved). For an input bundle (x 1, x 2,..., x n ), if f (kx 1, kx 2,..., kx n ) = k, then we sa the technolog described b the production function f exhibits constant returns-to-scale, if f (kx 1, kx 2,..., kx n ) < k, decreasing returns-to-scale, if f (kx 1, kx 2,..., kx n ) > k, increasing returns-to-scale. One input, one output example Output Level Constant returns to scale Decreasing returns to scale Increasing returns to scale Input Level

6 Theor Firm's suppl Industr suppl Monopol Oligopol Iso-prot lines Denitions The economic prot generated b the production plan (x 1,...,x m, 1,..., n ) is Π = p p n n w 1 x 1 w m x m, where (p 1,...,p n ) are product prices and (w 1,...,w m ) are input prices. A Π-iso-prot line contains all the production plans that provide a prot level Π: {(,x) : 0, x 0, p wx = Π} One input, one output example '' w x p p ' ' w x p p w x p p x

7 Theor Firm's suppl Industr suppl Monopol Oligopol Denitions The competitive rm takes all output prices p 1,...,p n and all input prices w 1,...,w m as given constants. The prot problem of the competitive rm is to locate the production plan that attains the highest possible iso-prot line, given the rm's constraint on choices of production plans. At the prot-maximizing plan, the slopes of the production function and the maximal iso-prot line are equal: MP }{{} = w p p } {{ MP } = w mg product mg revenue One input, one output example =f(x) * * x x

8 Theor Firm's suppl Industr suppl Monopol Oligopol Returns to scale and prot If a competitive rm's technolog exhibits decreasing returns-to-scale then the rm has a single long-run prot-maximizing production plan. If a competitive rm's technolog exhibits exhibits increasing returns-to-scale then the rm has no prot-maximizing plan. So an increasing returns-to-scale technolog is inconsistent with rms being perfectl competitive. If a competitive rm's technolog exhibits constant returns-to-scale, earning a positive economic prot is inconsistent with rms being perfectl competitive because if an production plan earns a positive prot, the rm can double up all inputs to produce twice the original output and earn twice the original prot. Hence constant returns-to-scale requires that competitive rms earn zero economic prots. Decreasing returns to scale to scale Increasing returns to scaleto scale Constant returns to scaleto scale fx ( ) fx ( ) f( ( x ) * x* x x x x x x x

9 Theor Firm's suppl Industr suppl Monopol Oligopol Isoquants Denitions The -output unit isoquant is the set of all input bundles that ield the same output level. The complete collection of isoquants is the isoquant map, which is equivalent to the production function. The slope of an isoquant is its technical rate-of-substitution, the rate at which input 2 must be given up as input 1's level is increased so as not to change the output level. d = f (x 1, x 2 ) dx 1 + f (x 1, x 2 ) dx 2 TRS dx 1 = MP 1 x }{{ 1 x }}{{ 2 dx } 2 MP 2 MP 1 MP 2 x 2 < < x 1

10 Theor Firm's suppl Industr suppl Monopol Oligopol Iso-cost lines Denition An iso-cost is a curve that contains all of the input bundles that cost the same amount: w 1 x 1 + w 2 x 2 = c x 2 = c w 2 w 2 w 1 x 1. x 2 c w 1 x 1 +w 2 x 2 c w 1 x 1 +w 2 x 2 c < c x 1

11 Theor Firm's suppl Industr suppl Monopol Oligopol Cost Minimization Denitions A rm is a cost-minimizer if it produces an given output level at the smallest possible total cost. The total cost function of the rm, c (w 1, w 2 ; ), denotes the rm's smallest possible total cost for producing units of output. The conditional input demands, x 1 (w 1, w 2 ; ) and x 2 (w 1, w 2 ; ), are the least-costl input bundle. x 2 w1 MP1 * TRS at( x1, x w MP 2 2 * 2 ) x 2 * x 1 * * * f( x1, x2) x 1

12 Theor Firm's suppl Industr suppl Monopol Oligopol Cost s Denitions The rm's xed cost function, F, is the cost which does not var with the rm's output level. The variable cost function, c v (), is the total cost to a rm of its variable inputs when producing output units. The total cost of producing is the sum of the xed and variable costs: c () = F + c v (). For positive output levels, a rm's average total cost of producing units is equal to the average xed cost plus the average variable cost: AC () = c() = F + c v (). AC() AVC() AFC()

13 Theor Firm's suppl Industr suppl Monopol Oligopol Marginal cost function Denition The marginal cost is the rate-of-change of the variable production cost as the output level changes: MC () = c v () = c(). The marginal cost curve intersects both the average variable cost and the average cost curves from below each curve's minimum: AVC () = cv () = MC () c v () 2 = 1 (MC () AVC ()). MC() AC() AC()

14 Theor Firm's suppl Industr suppl Monopol Oligopol Firm's suppl Demand curve faced b a competitive rm: If the rm sets its own price above the market price then the quantit demanded from the rm is zero. If the rm sets its own price below the market price then the quantit demanded from the rm is the entire market quantit-demanded. Market Demand p e e The individual rm's technolog causes it alwas to suppl onl a small part of the total quantit demanded at the market price p e.

15 Theor Firm's suppl Industr suppl Monopol Oligopol Firm's suppl The suppl function of a rm is the the upward part of the Marginal Cost curve. Formall, FOC : p c () maxπ = p c () = 0 MC ( s ) = p SOC : 2 c () 2 0 MC ( s ) 0 MC() At = s*, p = MC and MC slopes upwards, so s * is profit maximizing. p e At =, p = MC and MC slopes downwards, so is profit minimizing. s *

16 Theor Firm's suppl Industr suppl Monopol Firm's suppl The short run suppl curve lies above the AVC, since the producer surplus must not be negatve: Π = p F c v () F. The long run suppl curve lies above the AC, since the rm can exit the market so its economic prot level must not be negative: Π = p F c v () 0. Oligopol MC() MC() Shutdown point AC() Exit point AC() AVC() AVC() Firm s short run suppl curve Firm s long run suppl curve

17 Theor Firm's suppl Industr suppl Monopol Oligopol Industr suppl In a competitive industr, ever rm is a price-taker so total quantit supplied at a given price is the sum of quantities supplied at that price b the individual rms: S (p) = n i=1 S i (p). In the short-run, the number of rms in the industr is temporaril xed since neither entr nor exit can occur. Consequentl, rms ma earn positive economics prots, suer economic losses, or ma earn zero economic prot. p e s Firm 1 Firm 2 Firm 3 AC AC AC MC MC MC > 0 < 0 = 0 1 * 2 * 3 *

18 Theor Firm's suppl Industr suppl Monopol Industr suppl In the long-run ever rm now in the industr is free to exit and rms now outside the industr are free to enter. The long-run number of rms in the industr is the largest number for which the market price is at least as large as min AC(). Oligopol p The Market Long Run Suppl Curve p A Tpical Firm MC() AC() p The Market Long Run Suppl Curve p A Tpical Firm MC() AC() Y 3 * Notice that the bottom of each segment of the suppl curve is min AC(). Y * As firms get smaller the segments get shorter. In the limit, as firms become infinitesimall small, the industr s long run suppl curve is horizontal at min C().

19 Theor Monopol and Monopol Behavior Monopol Oligopol [TO BE ADDED SOON]

20 Theor Game Theor and Oligopol Monopol Oligopol [TO BE ADDED SOON]