PS4 Solutions - 479 Competitive Market Equilibrium 14.5 Business Application “Economic Rent" and Profiting from Entrepreneural Skill Suppose

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Unformatted text preview: 479 Competitive Market Equilibrium 14.5 Business Application: “Economic Rent" and Profiting from Entrepreneural Skill: Suppose, as in ex- ercise 14.4, that you are operating a hamburger restaurant that is part of a competitive industry Now you are also the owner; and suppose throughout that the owner of a restaurant is also one of the workers in the restaurant and collects the same wage as other workers for the time he/she puts into the business each week. (In addition, of course, the owner keeps any weekly profi ts.) A: Again, assume that all the restaurants are using the same homothetic decreasing returns to scale technology, but now the inputs include the level of entrepreneural capital c in addition to weekly labor I and capital k. As in exercise 14.4, assume also that all restaurants are required to pay a recurring weekly fixed cost F. (a) First assume that all restaurant owners possess the same level of entrepreneural skill c. Draw the long run AC curve (fi2r weekly hamburger production) fi2r a restaurant and indicate how many weekly hamburgers the restaurant will sell and at what price assuming that the indus- try is in long run equilibrium. Answer: This is illustrated in panel (a) of Graph 14.3 where the long run average cost curve of each firm is U-shaped because of the recurring fixed cost. Each restaurant will produce 16* and sell it at p*. Graph 14.3: Rent on Entrepreneural Skill (b) Suppose next that you are special and possess more entrepreneural and management skill than all those other restaurant owners. As a result of your higher level of c, the marginal product of labor and capital is 20% greater for any bundle of! and k than it is fi2r any of your competitors. Will the long run equilibrium price be any different as a result? Answer: No, a single firm in a competitive industry is not large enough to affect market prices. (c) Ifyour entrepreneural skill causes the marginal product of capital and labor to be 20% greater for any combination of! and k than fi2r your competitors, how does your isoquantmap differ from theirs? For a given wage and rental rate, will you employ the same labor to capital ratio as your competitors? Answer: We know that the slopes of isoquants are TRS = —MP€/MPk. If both marginal products increase by the same percentage, then the ratio is unchanged — which implies that your isoquant map looks exactly the same as your competitors’ except that it is differently labeled because you can produce more with less capital and labor. Since the shapes of the isoquants are the same as those for your competitors’, isocosts will be tangent along the same ray from the origin — which implies that you will employ the same labor to capital Competitive Market Equilibrium 480 ratio as you minimize your costs. You will simply require less capital and labor for any given level of output. ((1) Will you produce more or less than your competitors? Illustrate this on your graph by deter- mining where the long run MC and AC curves fi2r your restaurant will lie relative to the AC curve of your competitors. Answer: Since you need less labor and capital for any given level of output, your average costs are lower. Similarly, the lowest point of your AC curve will occur at a higher level of output than for your competitors. This is illustrated in panel (b) of Graph 14.3 where AC is your competitors’ average cost curve and AC' is yours. Finally, we can put your long run MC' curve into the graph (making sure it crosses your average cost curve AC' at its lowest point. Since the market price is unchanged at p*, we know you will profit maximize where p* intersects MC’ — at output level x’. You will therefore produce more than your competitors. (e) Illustrate in your graph how much weekly profit you will earn from your unusually high en- trepreneural skill. Answer: In panel (b) of Graph 14.3, two rectangular boxes emerge from the dotted lines combined with the axes. The larger of these is equal to total revenues for your firm (price times output); the smaller one is your total cost (average cost times output); and the dif- ference — area a + b+ c — is the difference between the two. Since those without your en- trepreneural skill make zero profit, the profit you derive from your skill is therefore a+ b+ c. (f) Suppose the owner ofMacroSoft, a new computer firm, is interested in hiringyou as the man- ager of one of its branches. How high a weekly salary would it have to offer you in order fi2r you to quit the restaurant business assuming you would work fi2r 36 hours per week in either case and assuming the wage rate in the restaurant business is $15 per hour: Answer: It would have to offer you a salary equal to the level of compensation you currently get for spending your time in the restaurant business. Since you are one of the workers drawing an hourly wage w = 15, you are making $540 per week as one of the workers in your restaurant plus you earn a profit of a+ b+ c as indicated in Graph 14.3. MacroSoft would therefore have to offer you a minimum weekly salary of a + b + c + 540. (g) The benefit that an entrepreneur receives from his skill is sometimes referred to as the eco- nomic rent of thatskill — because the entrepreneur could be renting his skill out ( to someone like MacroSoft) instead of using it in his own business. Suppose MacroSoft is willing to hire you at the rate you determined in part (f). If the economic rent of entrepreneural skill is in- cluded as a cost to the restaurant business you run, how much profit are you making in the restaurant business? Answer: You would then be making zero profit because a+ b+ c in Graph 14.3 would become an additional periodic fixed cost in your restaurant business. (h) Would counting this economic rent on your skill as a cost in the restaurant business affect how many hamburgers you produce? How would it change the AC curve in your graph? Answer: Since the economic rent is a recurring long run fixed cost, it does not impact the long run MC curve in panel (b) of Graph 14.3. Thus, price p* continues to intersect MC’ at x’ — implying you will produce exactly the same amount as if we did not count economic rent on your skill as a cost. The only thing that would change in panel (b) of the graph is that the average cost curve would be higher because a+ b+ c is now included as a recurring aver- age cost — and this average cost curve (denoted A—C in the graph) — would reach its lowest point as it intersects the unchanged MC'. Thus, price equals MC' at the lowest point of A—C — giving us zero profit for the firm if economic rents on entrepreneural skill are counted as a cost for the firm (and a payment to the owner). B: Suppose that all restaurants are employing the production function f (l , k, c) = 30!“4 k‘"4 c where l stands fi2r weekly labor hours, k stands fi2r weekly hours of rented capital and c stands fi2r the en- trepreneural skill of the owner: Note that, with the exception of the c term, this is the same produc- tion technology used in exercise 14.4. The weekly demand fi2r hamburgers in yourcity is, again as in exercise 14.4, x(p) = 100,040— 1,000p. 481 Competitive Market Equilibrium (a) First, suppose thatc = 1 for all restaurant owners, that w = 15 and r = 20, that there is a fixed weekly cost $4,320 of operatinga restaurant, and the industry is in long run equilibrium De- termine the weekly number of hamburgers sold in each restaurant, the price at which ham- burgers sell, and the number of restaurants that are operating. (If you have done exercise 1 4. 4, you should be able to use your results from there.) Answer: Since c = 1 for all restaurants, the production function becomes identical to that used in exercise 14.4. In parts (a) through (c) of exercise 14.4, you calculated that each restaurant will produce 4,320 hamburgers per week, that the long run equilibrium price will be $5 per hamburger and that there will be 22 restaurants in your city. (b) Next, suppose that you are the only restaurant owner that is dijferentfi'om all the others in that you are a better manager and entrepreneur and that this is reflected in c = 1.24573 for you. Determine your long run AC and M C functions. (Be careful not to use the cost function given in exercise 14.4 since c is no longer equal to 1. You can instead rely on the cost func- tion derived fi2r Cobb-Douglas technologies given in equation (13.45) in exercise 13.5 (and remember to add the fixed cost). ) Answer: Your production function can then be written as f (l, k) = [30(1.24573)] [0'4 k0'4 = 37.3719!“ k“. The cost function for a Cobb-Douglas production process f (l, k) = A!“ kp is C(w, r,x) = (a + fl) (14.19) Substituting in a = fl = 0.4, A = 37.3719, w = 15 and r = 20, and adding the fixed cost of $4,320, this gives us the cost function C(x) = 0.374895x1'25 + 4320. (14.20) The marginal and average cost functions are then dC(x) dx C (x) 4320 MC(x) = = 0.468619xo'25 and AC(x) = T = 0.374895x0'25 + 7. (14.21) (c) How many hamburgers will you produce in long run equilibrium? Answer: The long run equilibrium price must still be equal to $5 per hamburger because the rest of the firms must be operating at zero long run profit. Your restaurant will, however, produce where price equals your MC curve which is different from those of the other firms. Thus, we set price equal to MC — i.e. 5 = 0.4686x0'25 and solve for x to get x z 12, 960. (d) How many restaurants will there be in long run equilibrium given your higher level of c? Answer: Your production of 12,960 hamburgers per week is 3 times the production of the 4,320 hamburgers per week in the other restaurants. Before, there were 22 restaurants — which implies that now there will only be 20 including your restaurant. Thus, your entry into the restaurant market drives two of the other restaurants out of business. (e) How many workers (including yourself) and units of capital are you hiring in your business compared to those hired by your competitors? (Recall that the average worker is assumed to work 36 hours per week.) Answer: You can either solve the profit maximization problem to derive the labor and capital demand curves and use these to determine how many hours of labor and capital will be used. Alternatively, we could (as we did in part (h) of exercise 14.4) differentiate the cost function with respect to the input prices to get the conditional labor and capital demand functions — then plug in the input prices and output levels to get to the answer. Either way, we get that the other firms are hiring 576 labor hours and 432 capital hours per week, and your firm is hiring 1,728 labor hours and 1,296 hours of capital per week. At a work week of 36 hours, this implies that other firms hire 16 workers and your firm hires 36 workers. (D How does your restaurant’s weekly long run profitdifler from that ofthe other restaurants? Answer: Other restaurants are selling 4,320 hamburgers at a price of $5 to make total weekly revenues of $21,600; and they pay a weekly fixed cost of $4,320 and hire 576 worker hours at Competitive Market Equilibrium 482 wage $15 and 432 capital hours at rental rate $20 for total cost of 4320 + 576(15) + 432 (20) = $21,600. Thus, profits of other restaurants are zero (as we knowhas to be in long run equi- librium). Your firm, on the other hand, is selling 12,960 hamburgers at a price of $5 for a total revenue of $64,800. Your costs include the $4,320 weekly fixed cost plus the cost of 1,728 hours of labor hired at a wage of $15 and 1,296 hours of capital hired at a rental rate of $20 for a total cost of 4320+ 1728(15) + 1296(20) = $56, 160. This implies a profit for you of 64, 800 — 56, 160 = $8, 640 per week. (g) Suppose Macrosofi‘ is interested in hiring you as described in part A(f). How high a weekly salary would MacroSoft have to offer you in order fi2r you to quit the restaurant business and accept the MacroSoft offer? Answer: Since you are also one of the workers who works 36 hours per week in your restau- rant, your overall compensation is your labor income of 36(15) = $540 plus the profit of $8,640 per week — for a total of $9,180 per week. This is the least that MacroSoft would have to offer you in weekly compensation in order to attract you away from your restaurant business. (h) If you decide to accept the MacroSoft offer and you exit the restaurant business, will total employment in the restaurant business go up or down? Answer: With you in the restaurant business, we have 36 workers working in your business and 16 in each of the 19 others — for a total of 340 restaurant workers. With you out of the business, there are 22 restaurants employing 16 workers each — for a total of 352 work- ers. Thus, if you accept the MacroSoft offer, the number of workers (including owners) in restaurants increases by 12. 661 Elasticities, Price Distorting Policies and Non-Price Rationing 18.9 Business and Policy Application: Subsidizing Corn through Price Floors: Suppose the domestic de- mand and supply fi2r corn intersects at p* — and suppose fitrther that p* also happens to be the world price for corn. (Since the domestic price is equal to the world price, there is no need for this country to either import or export corn.) Assume throughout that income eflects do not play a significant role in the analysis of the corn market A: Suppose the domestic government imposes a price floor? that is greater than [2* and it is able to keep imports ofcornfi'om coming into the country. (a) Illustrate the disequilibrium shortage or surplus that results from the imposition of this price floor Answer: This is illustrated in panel (a) of Graph 18.6 where domestic supply and demand intersect at p* and the price floor p is imposed above p*. This results in a disequilibrium surplus, with x5 supplied but only 16;) demanded. \f—w—g {- ‘ ‘ ~ . fioucrnn’ififi dis:j::li;f/IVM purchase. Graph 18.6: Price Floor in Corn Market (b) In the absence of anything else happening, how will an equilibrium be re-established and what will happen to producer and consumer surplus? Answer: Consumer surplus will fall from (a + b+ e) to a while producer surplus will fall from (c+ d + f) to d. This is because, in equilibrium, producers will have to exert additional effort — i.e. incur additional costs — to compete for the limited number of consumers — which will cause the effective price they receive to fall to p’ . (The additional marginal cost of effort on the part of producers must be (p— p’) in order to make point A in panel (a) of Graph 18.6 the new equilibrium in which the disequilibrium shortage has been eliminated.) (c) Next, suppose the government agrees to purchase any corn that domestic producers cannot sell at the price floor The government then plans to turn around and sell the corn it purchases on the world market (where its sales are sufficiently small to notajfect the world price ofcorn). Illustrate how an equilibrium will now be re-established — and determine the change in do- mestic consumer and producer surplus from this government program. Answer: This is illustrated in panel (b) of Graph 18.6 where the difference between x S and 16;) — previously labeled a “disequilibrium surplus” in panel (a) — now becomes the quan- tity of corn purchased by the government. In essence, the government purchasing program causes the equilibrium to settle at B rather than A (as in panel (a) of the graph) — because producers no longer have an incentive to expend addition effort to attract consumers since Elasticities, Price Distorting Policies and Non-Price Rationing 662 the government is guaranteeing itwill purchase what cannot be sold at the price floor. Con- sumer surplus is then again a (since consumers purchase xD at p as before; producer sur- plus, however, now increases to (b + c + d + e + f + g) as producers supply x S at the price p. (d) What is the deadweight loss from the price floor with and without the government purchasing program? Answer: The greatest possible surplus achievable in this market is (a+ b+ c+ d + e + f). With just the price floor (and no government purchasing program), we concluded above that con- sumer and producer surplus together will be (a + b + c + d) — implying a deadweight loss of (e+ When the price floor is supplemented with the government purchasing program, the sum of consumer and producer surplus becomes (a + b + c + d + e+ f + g). However, we now need to take into account that the government is also having to spend resources in order to buy the surplus at the price floor f and then sell it at a loss at [2”. It will there- fore cost (e + f + g+ h+ i + j) to buy the surplus corn and, when sold at p*, it will raise revenues of (f + i + j) — leaving a government loss of (e + g + h). The total surplus is then the sum of producer and consumer surplus minus the government loss — which comes to (a+ b+ c+ d+ e+f+g) — (e+g+ h)=(a+ b+ c+ d+f— h). Compared to the mostpossible surplus of (a + b+ c + d + e + f), this implies a deadweight loss of (e + h). (e) In implementing the purchasing program, the government notices that it is not very good at getting corn to the world market — and all of it spoils befi2re it can be sold. How does the deadweight loss from the program change depending on how successful the government is at selling the corn on the world market? Answer: The government loss now becomes (e + f + g + h + i + j) — which gives us total surplusof(a+b+c+d+e+f+g)—(e+f+g+h+i+j)=(a+b+c+d—h—i—j). Compared to the maximum possible surplus of (a + b+ c + d + e + f), this gives us a deadweight loss of (e+f+h+i+j). (f) Would either consumers or producers favor the price floor on corn without any additional government programs? Answer: As illustrated in part (b) of the question, both producers and consumers lose sur- plus under the price floor policy without additional government programs. Thus, neither would favor such a program. (g) Who would favor the price floor combined with the government purchasing program? Does their support depend on whether the government succeeds in selling the surplus corn? Why might they succeed in the political process? Answer: As illustrated in part (c) of the question, producers gain substantial amounts of sur- plus when the government program is added to the price floor — and the amount of surplus they gain does not depend on what the government does with the surplus corn thatwas pur- chased. Thus, producers would favor the price floor when combined with the government purchasing program — and they might succeed in the political process because they are a relatively small group (compared to consumers and tax payers) experiencing concentrated benefits. This gives them an incentive to expend resources to lobby for such a program — and the diffuse nature of the costs (spread over many consumers and taxpayers) makes it unlikely that those who lose from the program will politically organize against it. (h) How does the deadweight loss from the price floor change with the price elasticity ofdemand? Answer: It decreases as demand becomes more inelastic. B: Suppose the domestic demand curve for bushels of corn is given by p = 24— 0.00000000225x while the domestic supply curve is given by p = 1 + 0.00000000025x. Suppose there are no income effects to worry about. (a) Calculate the equilibrium price p* ( in the absence of any government interference). Assume henceforth that this is also the world price fi2r a bushel of corn. Answer: Re-writing the demand and supply curves as demand and supply functions (i.e. solving for x to be on one side), we get 24—p p—l = — = —, 18.39 0.00000000225 and x5 0.00000000025 ( ) xD 663 Elasticities, Price Distorting Policies and Non-Price Rationing Setting these equal to one another and solving for p, we get the equilibrium price p* = 3.3 per bushel. (b) What is the quantity of corn produced and consumed domestically? (Note: The price per bushel and the quantity produced is roughly equal to what is produced and consumed in the US. in an average year) Answer: Plugging the equilibrium price of 3.3 into either the demand or supply function in equation (18.39), we get 16* = 9,200, 000, 000 or 9.2 billion bushels. (c) How much is the total social (consumer and producer) surplus in the domestic corn market? Answer: Calculating these as the relevant triangles above the supply and below the demand curves, we get _ (24 — 3.3) (9, 200, 000, 000) CS 2 = 95,220, 000, 000 and 3.3 — 1 9,200,000,000 PS: % = 10, 580, 000, 000 (18.40) for a total social surplus of $105,800,000,000 or $105.8 billion. ((1) Nextsuppose the government imposes a price floor of? = 3.5 per bushel ofcorn. What is the disequilibrium shortage or surplus of corn? Answer: Plugging this price floor into the demand and supply functions of equation (18.39), we get xD = 9, 111, 111, 111 and x5 = 10, 000, 000, 000 (18.41) bushels of corn — giving us a disequilibrium surplus of (165 — 161)) = 888,888,889 bushels of corn. (e) In the absence of any other government program, what is the highest possible surplus after the price floor is imposed 7 and what does this imply about the smallest possible size ofthe deadweight loss? Answer: The consumer surplus under the price floor is easy to calculate as just the area under the demand curve down to the price floorp = 3.5 — i.e. _ (24—3.5)(9,111,111,111) CS 2 = 93,388, 888, 889. (18.42) To calculate the producer surplus given that producers will have to incur additional costs in order to compete for the lower quantity demanded by consumers requires the additional step of calculating p’ in panel (a) of Graph 18.6 — which we get by plugging in the quantity demanded into the supply curve equation; i.e. p, = 1 + 0.00000000025(9, 111, 111, 111) = 3.27777... = 3.278. (18.43) The producer surplus triangle (equivalent to the triangle d in panel (a) of Graph 18.6) is then _ (3.27777778 — 1) (9, 111, 111, 111) P s 2 = 10,376, 543,210. (18.44) Consumer and producer surplus together then sum to $103,765,432,099 or approximately $103.765 billion. If we want to arrive at the highest possible figure for social surplus, we need to assume that the costs paid by producers to compete for consumers were not so- cially wasteful — and these costs (equivalent to area (b+ c) in panel (a) of Graph 18.6) is (3.5— 3.278) (9, 111, 111, 111) = 2,024,691,358. Added to the sum of producer and consumer sur- plus, we therefore get the highest possible social surplus as approximately$105,790, 123,457. Compared the original surplus of $105,800,000,000, we therefore get a deadweight loss of $9,876,543. Elasticities, Price Distorting Policies and Non-Price Rationing 664 (f) Suppose next that the government purchases any amount that corn producers are willing to sell at the price floorp but cannotsell to domestic consumers. How much does the government have to buy? Answer: To determine the amount the government has to buy, we need to subtract the amount that consumers demand — i.e. 9,111,111,111 bushels — from the amount that pro- ducers will supply at the price floor. To determine the latter, we simply plug the price floor of 3.5 into the supply function to get 10,000,000,000. Thus, the difference is 888,888,889 bushels of corn — which is the disequilibrium surplus previously calculated in (d). (g) What happens to consumer surplus? What about producer surplus? Answer: Consumer surplus stays the same as before — because consumers continue to buy the same amount at the same price floor. Producer surplus, however, is now equal to the triangle (b+ c+ d + e+f+ g) in panel (b) ofGraph 18.6 —which is _ (3.5 — 1) (10, 000, 000, 000) _ 2 (h) What happens to total surplus assuming the government sells the corn it buys on the world market at the price p* .9 Answer: The total surplus is now the sum of consumer and producer surplus minus the loss the government takes by buying corn at the price floor of 3.5 and selling it at the world price of 3.3. This gives us P8 = 12, 500, 000, 000. (18.45) Social Surplus = 93,388, 888, 889 + 12, 500, 000, 000 — (3.5 — 3.3) (888, 888, 889) = (18.46) = 105,711, 111, 111. In the absence of any program, the total surplus was $150,800,000,000. This fell to $105,790,123,457 with the imposition of just the price floor, and we have now shown it falls further to $105,711,111,111 if the government purchasing program is added to the price floor. This implies that the deadweight loss jumps from $9,876,543 under just the price floor to $88,888,889 when the government purchasing program is added — an increase of $79,012,346. (i) How much does deadweight loss jump under just the price floor as well as when the govern- ment purchasing program is added if?) = 4 instead of3.5? What if it is 5.? Answer: Going through steps similar to those above, the overall surplus falls from the origi- nal $105,800,000,000 to $105,679,012,346 under the price floor of? = 4. It furthermore falls to $104,711,111,111 if the government purchasing program is added. This implies a deadweight loss under just the price floor of $120,987,654 which increases to $1,088,888,889 when the purchasing program is added. If the price floor is raised to p = 5, the overall social surplus falls from $105,800,000,000 to $105,086,419,753 under just the floor and $99,377,777,778 if the purchasing program is added. This implies a deadweight loss of $713,580,247 under just the price floor and $6,422,222,222 when the government purchasing program is added. Distortionary Taxes and Subsidies 710 19.8 Business and Policy Application: Price Floors for Corn: Is ita Tax or a Subsidyfi In exercises 18.9 and 18.1 OWposed a price floor in the corn market. A: We will now see whether some of the price regulation proposals we considered are equivalent to taxes or subsidies. For simplicity, assume that tastes are quasilinear in corn. (a) In exercise 18.9, we began by considering a price floor without any additional government program. Illustrate the equilibrium impact ofsuch a price floor on the price ofcorn paid by consumers as well as the price of corn received by producers. Answer: This is illustrated in panel (a) of Graph 19.8. Consumers pay the legally mandated price floor p while suppliers compete for the limited number of consumers by exerting ad- ditional effort. In equilibrium, the marginal effort cost must be t — lowering the price that producers receive (net of the effort cost) to p3. Graph 19.8: Price Floors as Taxes and Subsidies (b) If you were to design a tax or subsidy policy that has the same impact as the stand-alone price floor, what would it be? Answer: Imposing a per unit tax of t will result in precisely the same prices for consumers and producers — and the same reduction in output. (c) In exercise 18.1 0, we considered the combination of a price floor and a government purchas- ing program under which the government guaranteed it would purchase any surplus corn at the price ceiling and then sell it at a price sufficiently low for all ofit to be bought. Illustrate the impact of this program — including the deadweight loss. Answer: This is illustrated in panel (b) of Graph 19.8 where the government purchases the difference between what is demanded and what is supplied at the price floor p. Producers therefore have to expend no additional effort and will receive a price equal to the price floor; i.e. p3 = p. In order for the government to sell its purchases of corn to consumers, however, it will have to lower the price by s to pc. Those consumers who purchase at the price floor will get consumer surplus of area a and producers will get surplus of (b + c + d + e). The government takes a loss of (d + e+ f + g) because it buys at? and sells at pc — but consumers who buy from the government get surplus of (d + f). We therefore get total surplus of (a+ d + f) for consumers, (b+ c+ d + e) for producers and a negative (d +e+ f+ g) for the government. Adding all these together, we get societal surplus of (a + b + c + d — g) — with deadweight loss of g. (d) If you were to design a tax or subsidy policy with the aim of achieving the same outcome fi2r the marginal consumer and producer as the policy in (c), what would you propose? 711 Distortionary Taxes and Subsidies Answer: You would choose a subsidy in the amount of s — which would increase output by exactly the same amount and would result in the price p; for producers and pc for con- sumers. (e) Would your proposal result in the same level of consumer and producer surplus? Would it result in the same deadweight loss? Answer: Consumer surplus would now be (a + b + d + f), producer surplus would be (b + c+ d +e) and the government cost of the subsidy would be (b+ d + e+ f + g). Summing consumer and producer surplus and subtracting the cost of the subsidy gives us (a+ b+ c+ d — g) — the same overall surplus as under the price floor with government purchasing. The deadweight loss is now also the same — i.e. area (g). B: Suppose, as in exercises 18.9 and 18.10, that the domestic demand curve fi2r bushels of corn is given by p = 24 — 0.00000000225x while the domestic supply curve is given by p = 1 + 0.00000000025x. (a) Suppose the government imposes a price ceiling of? = 3.5 (as in exercise 18.9). In the absence of any other program, how much will consumers pay (per bushel) and how much will sellers keep ( per bushel) after accounting fi2r the additional marginal costs incurred by producers to compete for consumers? Answer: In exercise 18.9, we derived the equilibrium price (without price distortions) as p* = 3.3 — which implies that a price floor of3.5 is binding (in the sense that p* is illegal). Consumers will therefore pay a price pa = 3.5 per bushel — and will buy x that solves the equation 3.5 = 24 — 0.00000000225x — i.e. the quantity of corn sold will be x = 9,111,111 bushels. Producers will expend effort until the marginal producer makes zero profit — which occurs when the effective price producers keep is p3 = 1 + 0.00000000025(9, 111, 111, 111) m 3.278. (19.79) (b) If you wanted to replicate this same outcome using taxes or subsidies, what policy would you propose? Answer: You would impose a tax that drives a wedge between prices paid by consumers pc and prices paid by producers p3. Under the price floor, we calculated above that pa = 3.5 and p3 = 3.278. If we therefore imposed a per unit tax t = (3.5 —3.278) = 0.22, we would achieve the same outcome. (c) Suppose next that the govemmentsupplemented its price floorfi'om (a) with a government purchasing program that buys all surplus corn — and then sells it at the highest possible price at which all surplus corn is bought. What is that price? Answer: First, we have to calculate how much of a surplus the government would buy (on top of the 9,111,111,111 bushels bought by consumers at the price floor). To do this, we can calculate how much producers will produce at p = 3.5 by plugging this price into the supply curve and solving for x. This gives us xs = 10, 000, 000, 000. Thus, the government purchases 888,888,889 bushels. In order for a total of 10,000,000, 000 bushels to be sold, the price of the last bushel sold must be p = 24 — 0.00000000225(10, 000, 000, 000) = 1.5. (19.80) ((1) If you were to design a tax or subsidy policy that has the same impact on the marginal con- sumer and producer; what would it be? Answer: We now have a consumer price for the marginal consumer of pa = 1.5 and a sup- plier price of p; = 3.5. To achieve this result, you could equally well impose a $2 per bushel subsidy. ...
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This note was uploaded on 11/17/2010 for the course ECON 100A taught by Professor Woroch during the Fall '08 term at University of California, Berkeley.

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