Econ 33 Microeconomic Analysis Chapter : Firm Supply Instructor: Hiroki Watanabe Fall Watanabe Econ 33 Firm Supply / 8 Warning. (An Awkward Representation) In supply/demand analysis, an explanatory variable is on the y-axis and a response variable is on the x-axis. a Proceed with extreme caution. a This won t be a problem for public goods. See Ch.36. Watanabe Econ 33 Firm Supply / 8 Introduction Short-Run Supply Decision : Marginal Cost = Market Price 3 Short-Run Supply Decision : Shut Down 4 Long-Run Supply Decision 5 Smallness 6 Summary Watanabe Econ 33 Firm Supply 3 / 8
Introduction Types of Market Environment Demand for a Competitive Firm Road Map Short-Run Supply Decision : Marginal Cost = Market Price 3 Short-Run Supply Decision : Shut Down 4 Long-Run Supply Decision 5 Smallness 6 Summary Watanabe Econ 33 Firm Supply 4 / 8 Types of Market Environment This chapter is producer s answer to Ch.6: Demand. Unlike consumers, though, some firms can change the equilibrium price. Watanabe Econ 33 Firm Supply 5 / 8 Types of Market Environment Project. (Overview of Producer Theory) 8 Technology 9 Profit Maximization Problem Cost Minimization Problem Cost Curves Firm Supply 3 Aggregate Supply 4 Monopoly 5 Monopoly Behavior 6 Oligopoly Watanabe Econ 33 Firm Supply 6 / 8
Types of Market Environment How does Jack decide the number of cheesecakes y? Determining factors include: Technology (Ch.8-) Market environment (Here) 3 Competitors behavior (Ch.4-6) Watanabe Econ 33 Firm Supply 7 / 8 Types of Market Environment Monopoly: Just Jack who determines the quantity supplied and the market-clearing price. Oligopoly: A few firms, the decisions of each influencing the payoffs of the others. Watanabe Econ 33 Firm Supply 8 / 8 Types of Market Environment Monopolistic Competition: Many firms each making a slightly different product. Each firm s output level is small relative to the total. Perfect Competition: Many firms, all making the same product. Each firm s output level is small relative to the total. Watanabe Econ 33 Firm Supply 9 / 8
Types of Market Environment Competitive market satisfies the following: identical products infinitesimally small agents 3 free mobility 4 perfect knowledge 5 exclusion 6 rivalry 7 free entry Watanabe Econ 33 Firm Supply / 8 Demand for a Competitive Firm Jack in a perfectly competitive market knows it has no influence over the equilibrium price for its product. Jack is a price taker. Jack is free to vary its own price if he wants to. Deviation from the market price won t pan out though (to be explained later). Watanabe Econ 33 Firm Supply / 8 Road Map Jack s decision is twofold: Find the best y using marginal condition (an umbrella term for tangency condition). See if he is not loosing money. Watanabe Econ 33 Firm Supply / 8
Road Map Marginal Cond Find y* Time Frame? Short Long Is Spi(y*)>? Yes Take y* Is Lpi(y*)>? Yes No Take y* Revise y*= Watanabe Econ 33 Firm Supply 3 / 8 Introduction Short-Run Supply Decision : Marginal Cost = Market Price Recast from to y Finding the Optimal Scale Supply Curve Example 3 Short-Run Supply Decision : Shut Down 4 Long-Run Supply Decision 5 Smallness Watanabe 6 Summary Econ 33 Firm Supply 4 / 8 Recast from to y We know how to express Jack s short-run profit maximization problem in terms of y (Ch.): Problem. (Short-Run Profit Maximization Problem in Terms of y) Jack maximizes his short-run profit given p, ( C, K ): () Watanabe Econ 33 Firm Supply 5 / 8
Recast from to y Problem. is an analogue of Problem.3 in Ch.9: Problem. (Short-Run Profit Maximization Problem in Terms of ) Jack maximizes his short-run profit given p, ( C, K ): max C π( C, K ) = pƒ ( C, K ) } {{ } C C K } {{ K} total revenue total cost = pƒ ( C, K ) C C FC. Watanabe Econ 33 Firm Supply 6 / 8 Recast from to y Solution to Problem. was found by tangency condition: C p = MP C( C, K ). C p : chef is as pricey as C slices of cheesecake. p MP C ( C, K ): chef can produce additional MP C ( C, K ) slices of cheesecake. Watanabe Econ 33 Firm Supply 7 / 8 Recast from to y 5. Isoprofit.5 Prod Fn Cheesecakes y (slices). 7.5 5..5. 7.5 5..5 8 3 7 6 5 4 3 4 5 6. 3 4 5 6 Chef x C Watanabe Econ 33 Firm Supply 8 / 8
Recast from to y To solve Problem., we recycle the same idea, except that Jack is making his decision on the ground of y rather than C. One cheesecake is worth $p. One additional cheesecake will cost $. Watanabe Econ 33 Firm Supply 9 / 8 Finding the Optimal Scale Instead of plugging in random y s in π(y), we ask: If Jack sells one more slice, does it increase his profit? If it does, go ahead. If it decreases the profit, downsize. 3 If it doesn t change, then that s the y he was looking for. Watanabe Econ 33 Firm Supply / 8 Finding the Optimal Scale Change in profit from an additional slice sold has two sources: MR(y): additional revenue that the additional slice brings in (just p in a perfectly competitive market) : additional cost that the additional slice inflicts (varies with y) Watanabe Econ 33 Firm Supply / 8
Finding the Optimal Scale Condition.3 (Marginal Condition) The output level y that maximizes Jack s profit satisfies: MR(y ) = MC(y ). () Remark In particular, if Jack is a price taker, MR(y) = p so that () is p=mc(y ). If Jack is a monopolist, then () still holds but (See Ch.4). p>mc(y ). Watanabe Econ 33 Firm Supply / 8 Finding the Optimal Scale Example.4 (Finding the Optimal Production Scale) Suppose that Jack has the following production environment: y TR(y) TC(y) π(y) MR(y) Δπ 3-3 - - - 6 5 6 8 4 6 3 8 6 6 4 4 7 7 6 5 3 3 7 6 6 36 3 6 6 7 4 38 5 6 8 48 47 6 Watanabe Econ 33 Firm Supply 3 / 8 Finding the Optimal Scale Total Revenue [$] 45 4 35 3 5 5 5 TR(y) TC(y) π(y) 3 4 5 6 7 8 Watanabe Econ 33 Firm Supply 4 / 8
Finding the Optimal Scale MR(y) 8 π(y) Total Revenue [$] 6 4 4 3 4 5 6 7 8 Watanabe Econ 33 Firm Supply 5 / 8 Finding the Optimal Scale In general, y can be found where TC(y) runs in parallel with TR(y). p =.6 in the following. Watanabe Econ 33 Firm Supply 6 / 8 Finding the Optimal Scale 8 TC(y) TR(y) 6 π(y) Costs [$] 4 4 6 8 4 Watanabe Econ 33 Firm Supply 7 / 8
Finding the Optimal Scale.5 Costs [$].5 MR(y) π(y)/ y 4 6 8 4 Watanabe Econ 33 Firm Supply 8 / 8 Supply Curve Graph might make you think as if y determines p Recall Warning.. p determines y. Not the other way around. Watanabe Econ 33 Firm Supply 9 / 8 Supply Curve Watanabe Econ 33 Firm Supply 3 / 8
Supply Curve Try p =.6 and p =.8. Watanabe Econ 33 Firm Supply 3 / 8 Supply Curve Watanabe Econ 33 Firm Supply 3 / 8 Supply Curve 8 TC(y) TR(y) w/ p=.6 6 π(y) w/ p=.6 TR(y) w/ p=.8 π(y) w/ p=.8 Costs, Price [$] 4 4 6 8 Watanabe Econ 33 Firm Supply 33 / 8
Supply Curve Costs, Price [$].5.5 MR(y) w/ p=.6 π(y)/ y w/ p=.8 MR(y) w/ p=.6 π(y)/ y w/ p=.8 4 6 8 Watanabe Econ 33 Firm Supply 34 / 8 Supply Curve Definition.5 (Supply Function) Jack s supply function s(p) returns the profit-maximizing amount of cheesecakes y for each p: s(p) = y. Part of s(p) comes from marginal condition Condition.3. And then some other part of s(p) comes from a different condition (coming up next). Watanabe Econ 33 Firm Supply 35 / 8 Supply Curve Watanabe Econ 33 Firm Supply 36 / 8
Supply Curve Once again, watch out for Warning.. returns the marginal cost for each y. s(p) returns the best quantity y for each p. Watanabe Econ 33 Firm Supply 37 / 8 Supply Curve Watanabe Econ 33 Firm Supply 38 / 8 Example Example.6 (Short-Run Profit Maximization Problem & Marginal Condition) Find the profit-maximizing scale of production y for p =, STC(y) = y +. S = y (you do not have to be able to compute this). Watanabe Econ 33 Firm Supply 39 / 8
Example 3 Total Cost, Total Revenue ($) 5 5 5 TC(y) TR=y TR=y 5 5 Cheesecakes y (slices) Watanabe Econ 33 Firm Supply 4 / 8 Example 3 Marginal Cost, Marginal Revenu, Price ($) 5 5 5 MR(y)= MR(y)= 5 5 Cheesecakes y (slices) Watanabe Econ 33 Firm Supply 4 / 8 Introduction Short-Run Supply Decision : Marginal Cost = Market Price 3 Short-Run Supply Decision : Shut Down When to Stop Graphical Representations Short-Run Supply Function 4 Long-Run Supply Decision 5 Smallness 6 Summary Watanabe Econ 33 Firm Supply 4 / 8
When to Stop So, that was the first step. Watanabe Econ 33 Firm Supply 43 / 8 When to Stop Marginal Cond Find y* Time Frame? Short Long Is Spi(y*)>? Yes Take y* Is Lpi(y*)>? Yes No Take y* Revise y*= Watanabe Econ 33 Firm Supply 44 / 8 When to Stop y that Jack found with marginal condition Condition.3 does not guarantee π(y ) >. E.g., p = 4 in Example.6. Watanabe Econ 33 Firm Supply 45 / 8
When to Stop 3 TC(y) TR=4y 5 TR=y TR=y Total Cost, Total Revenue ($) 5 5 5 5 Cheesecakes y (slices) Watanabe Econ 33 Firm Supply 46 / 8 When to Stop 3 MR(y)=4 5 MR(y)= MR(y)= Marginal Cost, Marginal Revenu, Price ($) 5 5 5 5 Cheesecakes y (slices) Watanabe Econ 33 Firm Supply 47 / 8 When to Stop A tricky part is Condition.3 blindly gives us best y that maximizes π(y). If π(y) < for a given price p, Condition.3 finds y that minimizes the loss. But then, instead of incurring loss, Jack can just shut down his operation by setting y = rather than y. Watanabe Econ 33 Firm Supply 48 / 8
When to Stop How do we find this threshold price? Jack has to pay FC = K K regardless of the production level y. Once Jack made a commitment to a short-run environment, FC becomes a sunk cost. Relevant profit to find out the optimal production scale is therefore not Sπ(y) = py SVC(y) FC but S ˆπ(y) = py-svc(y). Watanabe Econ 33 Firm Supply 49 / 8 When to Stop Jack has already paid K K and it does not affect its short-run decision making process. Jack should stop selling cheesecakes if S ˆπ(y) < py SVC(y) < p SVC(y) < y p SAVC(y) < p < SAVC(y). Watanabe Econ 33 Firm Supply 5 / 8 When to Stop Proposition 3. (When to Stop (Short Run)) If the current price p cuts below the unit production cost without fixed cost SAVC(y), Jack shuts down his operation so that his short-run profit level won t drop below $. Proof. See above. Watanabe Econ 33 Firm Supply 5 / 8
When to Stop.5 VC(5/) TR(5/) AVC(y) Costs, Price [$].5 5 5 Watanabe Econ 33 Firm Supply 5 / 8 When to Stop Definition 3. (Shut-Down Point) Shut-down point (y SD, p SD ) is the point below which Kayak s stops its production. It satisfies or equivalently y SD is a shut-down production level. p SD is a shut-down price. Watanabe Econ 33 Firm Supply 53 / 8 Graphical Representations Recall Proposition. in Ch.: Proposition 3.3 (Average Variable Cost & Marginal Cost) If average variable cost has the smallest value AVC(y SD ), Watanabe Econ 33 Firm Supply 54 / 8
Graphical Representations Sπ(y), TR(y) and SVC(y) can be represented as an area size. Sπ(y) = py SVC(y). Sπ(y) = py SAVC(y)y. Three cases: When p > p SD. When p < p SD. 3 When p = p SD. Let s say p > p SD. Then, Watanabe Econ 33 Firm Supply 55 / 8 Graphical Representations.5 TR() VC() AVC(y) Costs, Price [$].5 5 5 Watanabe Econ 33 Firm Supply 56 / 8 Graphical Representations.5 VC(6) TR(6) AVC(y) Costs, Price [$].5 5 5 Watanabe Econ 33 Firm Supply 57 / 8
Graphical Representations.5 VC(5/) TR(5/) AVC(y) Costs, Price [$].5 5 5 Watanabe Econ 33 Firm Supply 58 / 8 Short-Run Supply Function Proposition 3.4 (Short-Run Supply Function) In the short run, supply s(p) is for p < AVC(y SD ). traces for p AVC(y SD ). Watanabe Econ 33 Firm Supply 59 / 8 Short-Run Supply Function AVC(y) Short Run Supply.5 Costs, Price [$].5 5 5 Watanabe Econ 33 Firm Supply 6 / 8
Introduction Short-Run Supply Decision : Marginal Cost = Market Price 3 Short-Run Supply Decision : Shut Down 4 Long-Run Supply Decision Long-Run Decision : Marginal Cost = Market Price Long-Run Decision : Break Even Shut Down vs Break Even 5 Smallness 6 Summary Watanabe Econ 33 Firm Supply 6 / 8 Long-Run Decision : Marginal Cost = Market Price Marginal condition Condition.3 applies to the long-term decision making as well: MR(y) =. Watanabe Econ 33 Firm Supply 6 / 8 Long-Run Decision : Marginal Cost = Market Price Marginal Cond Find y* Time Frame? Short Long Is Spi(y*)>? Yes Take y* Is Lpi(y*)>? Yes No Take y* Revise y*= Watanabe Econ 33 Firm Supply 63 / 8
Long-Run Decision : Break Even In the long run, fixed cost is not a sunk cost. Jack can avoid the fixed cost as he sees fit. The problem with Condition.3 still remains: Lπ(y ) might be <. Jack had better close his business if the price is so low that π(y). Watanabe Econ 33 Firm Supply 64 / 8 Long-Run Decision : Break Even Jack stays in business in the long run if π(y) := py TC(y) p AC(y). The lowest price that Jack can engage in production is AC(y MES ). Watanabe Econ 33 Firm Supply 65 / 8 Long-Run Decision : Break Even Recall Proposition.8 in Ch.: Proposition 4. (Average Cost & Marginal Cost) If average cost has the smallest value AC(y MES ), Watanabe Econ 33 Firm Supply 66 / 8
Long-Run Decision : Break Even.5 TC(7.9895) TR(7.9895) ATC(y) Costs, Price [$].5 5 5 Watanabe Econ 33 Firm Supply 67 / 8 Long-Run Decision : Break Even.5 TR() TC() ATC(y) Costs, Price [$].5 5 5 Watanabe Econ 33 Firm Supply 68 / 8 Long-Run Decision : Break Even.5 TC(6) TR(6) ATC(y) Costs, Price [$].5 5 5 Watanabe Econ 33 Firm Supply 69 / 8
Long-Run Decision : Break Even Proposition 4. (Long-Run Supply Function) In the long run, supply is for p < AC(y MES ). coincides with for p AC(y MES ). (y MES, AC(y MES )) is called a break-even point. Watanabe Econ 33 Firm Supply 7 / 8 Shut Down vs Break Even ATC(y) AVC(y).5 Costs, Price [$].5 5 5 Watanabe Econ 33 Firm Supply 7 / 8 Shut Down vs Break Even AVC(y) Short Run Supply.5 Costs, Price [$].5 5 5 Watanabe Econ 33 Firm Supply 7 / 8
Shut Down vs Break Even ATC(y) Long Run Supply.5 Costs, Price [$].5 5 5 Watanabe Econ 33 Firm Supply 73 / 8 Shut Down vs Break Even p y on p = py TC(y) Long Run py VC(y) Short Run AVC(y SD ) y SD AC(y MES ) y MES Assuming K happens to be the long-run choice of K. Watanabe Econ 33 Firm Supply 74 / 8 Introduction Short-Run Supply Decision : Marginal Cost = Market Price 3 Short-Run Supply Decision : Shut Down 4 Long-Run Supply Decision 5 Smallness 6 Summary Watanabe Econ 33 Firm Supply 75 / 8
Jack s operation scale is supposed to be infinitesimally small (otherwise, he won t be a price-taker). Watanabe Econ 33 Firm Supply 76 / 8 If Jack sells a cheesecake above market price, nobody buys from him. If Jack sells a cheesecake below market price, he incurs a loss of p from each slice sold. Watanabe Econ 33 Firm Supply 77 / 8 Marginal Cost, Marginal Revenu, Price ($) 4 3 Aggregate Demand 4 6 8 Cheesecakes y (slices) Watanabe Econ 33 Firm Supply 78 / 8
Introduction Short-Run Supply Decision : Marginal Cost = Market Price 3 Short-Run Supply Decision : Shut Down 4 Long-Run Supply Decision 5 Smallness 6 Summary Watanabe Econ 33 Firm Supply 79 / 8 Profit maximization problem in terms of y. Marginal condition and shut-down point. Marginal condition and break-even point. Watanabe Econ 33 Firm Supply 8 / 8 This page is intentionally left blank. Watanabe Econ 33 Firm Supply 8 / 8
AC(y), see average cost AVC(y), see average variable cost average cost, 66 average variable cost, 55 break-even point, 7, 74 exclusion, FC, see fixed cost fixed cost, 49 free entry, free mobility, identical products, infinitesimally small agents, long-run supply function, 7 marginal condition,, marginal cost, 9,, 59, 6 marginal product, 7 marginal revenue,, see marginal cost monopolistic competition, 9 monopoly, 8 MP C (y), see marginal product MR(y), see marginal revenue oligopoly, 8 output level, p, see price perfect competition, 9 perfect knowledge, π, see profit price, 6 price taker, profit maximization problem short-run, 5, 6 p SD, see shut-down price rivalry, short-run supply function, 59 shut-down point, 53, 59, 74 shut-down price, 53 shut-down production level, 53 s(p), see supply function sunk cost, 49, 64 supply function, 35 tangency condition, total revenue, 3 TR(y), see total revenue variable cost, 49 VC(y), see variable cost y, see output level y MES, see minimum efficient scale y SD, see shut-down production level, see shutdown point