Introduction. Producer s Surplus. Total Costs: Fixed and Variable

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1 Introduction Producer s Surplus Philip A. Viton Novemer 12, 2014 We hve seen how to evlute consumer s wtp for mrket-induced price chnge: we mesure it (with pproprite cutions, primrily tht we tret it s n pproimtion) y the chnge in consumer s surplus, the re under the demnd function etween the two price horizontls. We now ddress to the remining question in mrket-induced (price) chnges: how to evlute the enefits to producers or firms. Fortuntely this is esy, nd hs none of the complictions of consumer s surplus. The oviously correct mesure of enefits to firms is profits, nd we mesure project s impct on firm y the chnge in its profits. Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Profits Totl Costs: Fied nd Vrile Wht re profits? Consider firm selling 1 units of output t price. Its Totl Revenues (TR) re 1. Its Totl Costs re TC. Then profits re Totl Revenues minus Totl Costs or: Π = TR TC. Typiclly firm will hve oth fied (TFC ) nd vrile (TVC ) costs. In this cse we cn re-write totl costs s: TC = TFC + TVC Then we hve: Π = TR (TFC + TVC ) Note tht this is n empiriclly oservle quntity. Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27

2 Chnge in Profits (I) Chnge in Profits (II) So the chnge in profits is: Suppose project chnges revenues from TR to TR nd costs from TC to TC. Using our decomposition of costs, we hve: Π = Π Π = (TR TC ) (TR TVC ) = (TR (TFC + TVC )) (TR (TFC + TVC )) = (TR TVC ) (TR TVC ) note tht TVC y definition is the sme in the pre- nd post-project settings. Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Π = (TR TVC ) (TR TVC ) The difference etween totl revenue nd totl vrile cost, PS = TR TVC is clled the firm s Producer Surplus. So the chnge in the firm s profits ( Π) is the sme s the chnge in producer s surplus: Π = PS PS = PS Note tht since the chnge in profits is oservle, so is producer s surplus: unlike consumer s surplus we don t need to ppel to ny notions of pproimtion to some theoreticlly correct mesure. Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Producer s Surplus (I) Producer s Surplus (II) It is importnt to understnd tht while the chnge in profits equls the chnge in producer s surplus, profits nd producer s surplus re not the sme. The two differ y the mount of fied costs: Π = TR (TVC + TFC ) = TR TVC TFC = PS TFC But since for project evlution we will lwys e looking t the chnge in profits induced y the project, this won t mtter. We now hve two equivlent wys of mesuring project s impct on firms: the chnge in profits ( Π) nd the chnge in producer s surplus ( PS). Producer s surplus hs two dvntges: 1. It does not require us to understnd fied costs; nd empiriclly, fied costs (which will e the vlue of the constnt or intercept in cost-function regression eqution) is often imprecisely estimted. 2. Totl vrile costs re the re under the mrginl cost curve from 1 = 0 (zero output) to 1 (oserved output). See the net slide. So if we cn estimte mrginl costs, we re in position to compute TVC. Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27

3 Totl Vrile Costs 0 1 MC 1 The figure shows competitive firm s upwrd-sloping mrginl cost curve. If it is profit-mimizing price-tker, then, if it fces mrket price p1 its output will e 1. Totl revenue is 1 1 (htched). Totl vrile costs re the re under MC from 1 = 0 to 1 = 1 ( drk shde). So producer s surplus is the re ove MC ut elow the price horizontl (light shde). Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Project 0 1 MC 1 Suppose our project hs the effect of rising the mrket price to p1. The firm responds y rising its output to 1. The new totl revenue is the htched re, totl vrile costs re drkly shded nd producer s surplus is lightly shded. Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Chnge in Producer s Surplus Multiproduct Producer s Surplus MC 1 Compring the previous pictures, we cn see tht the chnge in producer s surplus is the re to the left of the mrginl cost curve nd etween the two price horizontls. Note tht this is vlid only for competitive firm tht sees its mrket price chnge with no shift in its cost curves. When firm produces severl products nd the project chnges their prices, we nturlly mesure the full impct s the chnge in producer s surplus in ech of the product mrkets. So: PS = PS 1 + PS (just s we did for consumer s surplus). It cn e shown tht PS is not pth-dependent: tht is, for multiproduct firm you will get the sme nswer in whtever order you do the clcultion (unlike consumer s surplus). Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27

4 Mrket Impcts Full Anlysis Emple Monopoliztion We re now in position to evlute the full impct of policy tht chnges mrket price from its pre-project level to its post project level For the impct on consumers we use the chnge in consumer s surplus: CS = CS( ) CS( ) For the impct on firms we use the chnge in producer s surplus (ggregting over firms, if necessry): And then the full impct is: PS = PS( ) PS( ) W = CS + PS As n emple of how ll this fits together, let s consider policy tht llows n industry to ecome monopolized. So our pre-project stte () is competition, nd our post-project stte () is monopoliztion. Note tht we re ssuming tht this is the only chnge in the economy. As we know from generl microeconomics, monopoliztion hs two impcts: it reduces the quntity produced nd increses the price consumers py for the product. Intuitively, this is d thing ; ut not so fst. We would nturlly ssume tht the price increse leds to n increse in profits: nd might not this gin to producers outweigh the loss to consumers? By using our new tools, we will now see tht this is not so. Monopoliztion is n overll net d to the economy. Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Monopoliztion Setup Monopoliztion Impct on Consumers The figure shows the sic position: under competition, demnd = supply, where supply (S) is the sum of the firms mrginl costs ; the result is price nd output. Under monopoliztion, profit-mimizing output is governed y the condition MC =, leding to output. The monopolist prices to sell ll output, resulting in price. As usul, the impct on consumers is CS = signed re under the demnd function etween the two price horizontls. This is the shded re, nd it is importnt to note tht it is negtive quntity. Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27

5 Producer s Surplus under Competition Producer s Surplus under Monopoly Pre-project producer s surplus PS is TR ( = ) TVC (= re under MC from = 0 to = ). In the figure, PS is shded. Similrly, reltive to the post-project monopoly equilirium (, ), producer s surplus PS is the shded re. Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Chnge in Producer s Surplus Net Impct (I) p c p (+) d( ) Compring the two previous figures, PS is the shded re Note tht this hs two prts: rectngle (c), representing where PS is more thn PS nd hence hs positive sign ; nd tringle (d) representing prt of PS not included in PS, so this hs negtive sign. Oviously the totl effect is positive : s we d epect, monopoly increses firm profits. d For the overll net impct, we compre PS to CS. First, re in the consumer s surplus picture ectly mtches re c in the producer s surplus picture. The signs re opposite ( is negtive, c is positive) so they cncel. Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27

6 Net Impct (II) Net Impct (III) d Second, (negtive) re from the consumer s surplus picture is not included in the producer s surplus picture. So we need to include it here. Third, (negtive) re d from the producer s surplus picture is not included in the consumer s surplus picture. So we need to include tht, too d The result is tht the overll chnge in welfre W is the shded re. Note tht oth portions of this re negtive quntities. So our result is tht W < 0 : monopoliztion definitely decreses socil welfre. Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Conclusion We conclude tht going from sitution of competition to one of monopoly hs n unmiguously negtive overll impct. In the literture, this is referred to s the edweight Loss of monopoliztion. Computtionl Appendi Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27

7 Computtionl Considertions (I) In the contet of our monopoliztion emple, suppose you need to clculte the pre-project equilirium (, ). Conceptully, you wnt to equte supply (= MC) nd demnd. Note tht the mrginl cost function is MC () : tht is, it tkes quntity nd tells us its mrginl cost, in dollrs. But the demnd function is (p) : tht is, it tkes price nd tells us the demnd (quntity) t tht price. So you cn t just equte (p) nd MC () : tht would e meningless. Insted, you must first invert (solve) either the demnd function or the mrginl cost function, so they oth tell us the sme kind of thing (output or money). Then you cn equte the two. Computtionl Considertions (II) For emple, suppose in the liner cse you hve: Mrginl cost: MC () = α 0 + α 1 (α 1 > 0) emnd: (p) = β 0 + β 1 p (β 1 < 0) The in order to find the competitive equilirium you cn invert the demnd function, giving p = ( β 0 )/β 1 nd then equte demnd nd supply: ( β 0 )/β 1 = α 0 + α 1 which is n eqution in quntity only. Alterntively, ecuse under competition p = MC, you cn feed in the mrginl cost eqution into the demnd function: = β 0 + β 1 p = β 0 + β 1 (α 0 + α 1 ) which is lso n eqution in only; nd solve. Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Computtionl Considertions (III) The solution turns out to e (ssuming α 1 β 1 = 1) : = β 0 + α 0β 1 1 α 1 β 1 And the competitive price (= mrginl cost of producing this output) is: p = α 0 + α 1 = α 0 + α 1 ( β0 + α 0 β 1 1 α 1 β 1 ) Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27 Philip A. Viton CRP 6600 Producer s () Surplus Novemer 12, / 27