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Firm Supply 厂商供给 How does a firm decide how much product to supply? This depends upon the firm’s technology market environment goals competitors’ behaviors Are there many other firms, or just a few? Do other firms’ decisions affect our firm’s payoffs? Is trading anonymous, in a market? Or are trades arranged with separate buyers by middlemen? Monopoly (垄断): Just one seller that determines the quantity supplied and the marketclearing price. Oligopoly (寡头垄断): A few firms, the decisions of each influencing the payoffs of the others. Dominant Firm: Many firms, but one much larger than the rest. The large firm’s decisions affect the payoffs of each small firm. Decisions by any one small firm do not noticeably affect the payoffs of any other firm. Monopolistic Competition (垄断竞争): Many firms each making a slightly different product. Each firm’s output level is small relative to the total. Pure Competition (完全竞争): Many firms, all making the same product. Each firm’s output level is small relative to the total. Later chapters examine monopoly, oligopoly, and the dominant firm. This chapter explores only pure competition. A firm in a perfectly competitive market knows it has no influence over the market price for its product. The firm is a market price-taker. The firm is free to vary its own price. If own price above the market price then the quantity demanded is zero. If own price below the market price then the quantity demanded is the entire market quantity-demanded. So what is the demand curve faced by the individual firm? $/output unit Market Supply pe Market Demand Y $/output unit Market Supply p’ pe At a price of p’, zero is demanded from the firm. Market Demand y $/output unit Market Supply p’ pe p” At a price of p’, zero is demanded from the firm. Market Demand y At a price of p” the firm faces the entire market demand. So the demand curve faced by the individual firm is ... $/output unit Market Supply p’ pe p” At a price of p’, zero is demanded from the firm. Market Demand y At a price of p” the firm faces the entire market demand. $/output unit p’ pe p” Market Demand Y What does it mean to say that an individual firm is “small relative to the industry”? $/output unit Firm’s MC pe Firm’s demand curve y The individual firm’s technology causes it always to supply only a small part of the total quantity demanded at the market price. Each firm is a profit-maximizer in a short-run. Q: How does each firm choose its output level? A: By solving max s ( y ) py cs ( y ). y 0 max s ( y ) py cs ( y ). y 0 What can the solution ys* look like? d s ( y ) (a) ys* > 0: (i) (y) dy 2 p MCs ( y ) 0 d s ( y) * ( ii ) 0 at y y s . dy 2 ys* y max s ( y ) py cs ( y ). y 0 What can the solution y* look like? (b) ys* = 0: d s ( y ) p MCs ( y ) 0 (y) dy * at y y s 0. y ys* = 0 For the interior case of ys* > 0, the firstorder maximum profit condition is d s ( y ) p MC s ( y ) 0. dy * That is, p MCs ( y s ). So at a profit maximum with ys* > 0, the market price p equals the marginal cost of production at y = ys*. p = MC is a necessary condition(必要条件) for profit maximization, but It is not a sufficient condition(充分条件). For the interior case of ys* > 0, the secondorder maximum profit condition is 2 d s ( y) d dMCs ( y ) p MCs ( y ) 0. dy dy dy 2 dMCs ( y*s ) That is, 0. dy So at a profit maximum with ys* > 0, the firm’s MC curve must be upward-sloping. $/output unit At y = ys*, p = MC and MC slopes upwards. y = ys* is profit-maximizing. pe MCs(y) y’ ys* y At y = y’, p = MC and MC slopes downwards. y = y’ is profit-minimizing. $/output unit pe y’ At y = ys*, p = MC and MC slopes upwards. y = ys* is profit-maximizing. So a profit-max. supply level can lie only on MCs(y) the upwards sloping part ys* y of the firm’s MC curve. but…… not every point on the upward-sloping part of the firm’s MC curve represents a profit-maximum. The Firm’s Short-Run Shut-Down Condition The firm’s profit function is s ( y ) py cs ( y ) py F c v ( y ). If the firm chooses y = 0 then its profit is s ( y ) 0 F c v ( 0 ) F. So the firm will choose an output level y > 0 only if s ( y ) py F c v ( y ) F. So the firm will choose an output level y > 0 only if sif( y ) py F c v ( y ) F. I.e., only pyif c v ( y ) 0 Equivalently, only cv ( y) p AVCs ( y ). y $/output unit MCs(y) ACs(y) AVCs(y) y $/output unit MCs(y) ACs(y) AVCs(y) y $/output unit p AVCs(y) MCs(y) ACs(y) AVCs(y) y $/output unit p AVCs(y) ys* > 0. MCs(y) ACs(y) AVCs(y) y $/output unit p AVCs(y) ys* > 0. MCs(y) ACs(y) AVCs(y) p AVCs(y) y ys* = 0. $/output unit p AVCs(y) ys* > 0. MCs(y) ACs(y) AVCs(y) p AVCs(y) The firm’s short-run supply curve y ys* = 0. $/output unit Shutdown MC (y) s point ACs(y) AVCs(y) The firm’s short-run supply curve y Shut-down (关门) is not the same as exit (退出). Shutting-down means producing no output (but the firm is still in the industry and suffers its fixed cost). Exiting means leaving the industry, which the firm can do only in the long-run. The long-run is the circumstance in which the firm can choose amongst all of its short-run circumstances. How does the firm’s long-run supply decision compare to its short-run supply decisions? A competitive firm’s long-run profit function is ( y ) py c( y ). The long-run cost c(y) of producing y units of output consists only of variable costs since all inputs are variable in the long-run. The firm’s long-run supply level decision is to max ( y ) py c( y ). y 0 The 1st and 2nd-order maximization conditions are, for y* > 0, p MC( y ) and dMC( y ) 0. dy Additionally, the firm’s economic profit level must not be negative since then the firm would exit the industry. So, ( y ) py c( y ) 0 c( y ) p AC( y ). y $/output unit MC(y) AC(y) y $/output unit MC(y) p > AC(y) AC(y) y $/output unit MC(y) p > AC(y) AC(y) y $/output unit The firm’s long-run supply curve MC(y) AC(y) y Firm‘s long-run supply curve is the portion of the long-run marginal cost curve that lies above the average cost curve. In this case, the firm’s long-run supply curve is a horizontal line. Why? Average Total Production Costs (平均总生产成本) c( w 1 , w 2 , y ) AC( w1 , w 2 , y ) . y If a firm’s technology exhibits constant returns-toscale then doubling its output level from y’ to 2y’ requires doubling all input levels. Total production cost doubles. Average production cost does not change. $/output unit AC(y) decreasing r.t.s. constant r.t.s. increasing r.t.s. y $/output unit LMC=long-run supply Cmin When p=Cmin When p<Cmin When p>Cmin Y Willing to supply any amount Y Y=0 Arbitrarily large amount How is the firm’s long-run supply curve related to all of its short-run supply curves? $/output unit ACs(y) MCs(y) MC(y) AC(y) y $/output unit ACs(y) MC(y) MCs(y) AC(y) p’ ys* y* y ys* is profit-maximizing in this short-run. $/output unit ACs(y) MC(y) MCs(y) p’ AC(y) s ys* y* y ys* is profit-maximizing in this short-run. $/output unit ACs(y) MC(y) MCs(y) p’ s AC(y) ys* y* y The firm can increase profit by increasing x2 and producing y* output units. $/output unit ACs(y) MCs(y) MC(y) AC(y) p” ys* y ys* is loss-minimizing (减损) in this short-run. $/output unit ACs(y) MCs(y) MC(y) AC(y) p” Loss ys* y ys* is loss-minimizing (减损) in this short-run. Loss <-F $/output unit ACs(y) MCs(y) MC(y) AC(y) p” Loss ys* y This loss can be eliminated in the longrun by the firm exiting the industry. $/output unit MC(y) AC(y) y $/output unit MC(y) p’ AC(y) ys* y ys* is profit-maximizing in this short-run. $/output unit MC(y) p’ AC(y) s ys* y ys* is profit-maximizing in this short-run. $/output unit MC(y) p’ AC(y) y* ys* y ys* is profit-maximizing in this short-run. y* is profit-maximizing in the long-run. $/output unit MC(y) p’ AC(y) y* ys* y ys* is profit-maximizing in this short-run. y* is profit-maximizing in the long-run. $/output unit MC(y) p’ AC(y) s y* ys* y The firm can increase profit by producing y* units of output. $/output unit MC(y) AC(y) y $/output unit MC(y) AC(y) y $/output unit MC(y) AC(y) y $/output unit Long-run supply curve MC(y) AC(y) y Short-run supply curves The long-run supply curve is more elastic (and is more sensitive to price) than the short-run supply curve. Because the firm has more leeway in adjusting supply in the long-run than in the short run. The firm’s producer’s surplus (生产者剩余) is the accumulation of extra revenue - extra production cost. by producing extra unit of output How is producer’s surplus related to profit? $/output unit MCs(y) ACs(y) AVCs(y) y $/output unit MCs(y) ACs(y) AVCs(y) y $/output unit MCs(y) p ACs(y) AVCs(y) y*(p) y $/output unit MCs(y) p ACs(y) AVCs(y) PS y*(p) y So the firm’s producer’s surplus is PS(p ) y*( p ) p MCs ( z)d( z) 0 py * (p ) y*( p ) MCs ( z)d( z) 0 py * (p ) c v y * (p ). That is, PS = Revenue - Variable Cost. $/output unit MCs(y) p c v ( y * (p )) ACs(y) AVCs(y) y*(p) MCs ( z)d( z) y*( p ) 0 y $/output unit MCs(y) p ACs(y) AVCs(y) Revenue = py*(p) y*(p) y $/output unit MCs(y) p ACs(y) AVCs(y) Revenue = py*(p) cv(y*(p)) y*(p) y $/output unit MCs(y) p ACs(y) AVCs(y) PS y*(p) y $/output unit MCs(y) p ACs(y) AVCs(y) y*(p) y $/output unit MCs(y) p ACs(y) AVCs(y) Y‘ y*(p) y PS = Revenue - Variable Cost. Profit = Revenue - Total Cost = Revenue - Fixed Cost - Variable Cost. So, PS = Profit + Fixed Cost. Only if fixed cost is zero (the long-run) are PS and profit the same. Market environments Market demand for a competitive firm Short-run supply decision Upward sloping MC curve Shut-down condition Long-run supply decision Comparing long-run and short-run decisions. Producer’s surplus and profits