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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 Ushaped 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 CobbDouglas 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 CobbDouglas 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 NonPrice 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 reestablished 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 reestablished — 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 NonPrice 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: Rewriting 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 NonPrice 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 NonPrice 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 standalone 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.
 Fall '08
 Woroch
 Microeconomics

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