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Unformatted text preview: Economics 111 Exam 1 Fall 2004 Prof Montgomery
Answer all questions. Explanations may be brief. 105 points possible. 1. (30 points) Consider a small country with 3 factories. Each factory can produce guns
or butter or both. The table below reports, for each factory, the potential output per hour
for each good, and the number of hours of production per week. number of guns pounds of butter hours of production
that could be that could be per week
produced per hour produced per hour factory I 4 4 80
factory 2 3 5 40
factory 3 10 6 40 a. Derive and plot the (weekly) production possibilities curve for each factory. [HINT2
Graphs don’t need to be perfect, but should be clearly labeled, and you should give the
horizontal and vertical intercept on each graph.] Comparing factories 2 and 3, which
factory has the comparative advantage at producing butter? b. Factory production in this country is determined by a government ofﬁcial. He has
currently ordered factory I to split its production time evenly between the two goods
(spending 40 hours/week producing each good), while ordering factories 2 and 3 to
produce only butter for 40 hours/week. Is this plan efﬁcient? Brieﬂy explain. Holding
constant the country’s current production of guns, what is the maximum amount of butter
that could have been produced? How should you set production at each factory in order
to achieve this outcome? 0. The government ofﬁcial now decides that the country should produce 3 guns for every
1 pound of butter. Given this required ratio of guns to butter, what is the maximum
number of guns and pounds of butter that can be produced? How would you set
production at each factory to achieve this outcome? 2. (15 points) Suppose that com is an inferior good, that wheat is a substitute for corn,
and that fertilizer is a factor used in corn production. For each of the following cases,
what will be the effect on the supply and demand for corn, and the equilibrium price and
quantity of corn? Illustrate each case with an appropriate supplyanddemand diagram.
[HINTz Obviously, you’ve been given no numerical information. I’m merely looking for
qualitative effects] a. An increase in consumer income.
b. An increase in the price of wheat.
c. A decrease in the price of fertilizer. 3. (30 points) A consumer spends her income on goods 1 and 2. Both goods are normal
goods for this consumer. Suppose that, as part of a new marketing campaign, the makers
of good 1 offer 5 free units of good 1 to any consumer who purchases at least 20 units of
good 1. (Consumers can receive the free units only once. Thus, even if she buys 40 or
60 units, the consumer still receives only 5 free units.) a. Draw the consumer’s budget constraint before and after this offer. [HINT: You don’t
have enough information to derive the equations for these curves, but your graph should
use the information that you were given. Note that the marketing campaign does not alter
the price of good 1.] b. If the consumer initially purchased more than 20 units, how will this offer affect the
number of units of good 1 that she now purchases (net of the 5 free units)? Brieﬂy
explain. Be sure to note any relevant income and substitution effects, and illustrate your
answer with a budget constraint / indifference curve diagram. 0. If the consumer initially purchased slightly less than 20 units, how will this offer affect
the number of units of good 1 that she now purchases (net of the 5 free units)? Brieﬂy
explain. Again, illustrate your answer with the relevant diagram. 4. (30 points) You are the manager of a factory that produces output according to the
production function Q=«/—KZ where K is the number of units of capital, and L is the number of units of labor. Further
assume that the price per unit labor is w = 1, that the price per unit capital is r = 4, and
that the firm has no ﬁxed costs. a. Depending on demand for the ﬁrm’s output, you may be instructed by corporate
headquarters to produce either Q = 20 or Q = 30 or Q = 40 units of output. For each of
these three cases, ﬁnd the costminimizing method of production. [HINT: You can use
the equation for each isoquant to solve for the amount of capital that must be hired given
some amount of labor. If you solve this problem by constructing a table, you might
consider increasing labor in increments of 10 units.] For each case, give the optimal
number of units of K and L that you would hire, and the total cost that you would incur.
Using this information, plot the total cost curve and marginal cost curve for your factory.
Does this factory have increasing, decreasing, or constant marginal costs? b. Suppose that the price of labor (w) rises. Qualitatively (using the relevant graph
without doing any more numerical computation), how would this affect the cost
minimizing method of production at each output level? How would this affect the total cost and marginal cost curves? Econ 111 Exam 1 Fall 2004 Solutions la. [10 pts] Let g represent the number of guns, b represent the pounds of butter, and tg
and tb represent time spent in the production of each good. For factory I, g = 4tg and b = 4th and tg + tb = 80. Substituting the ﬁrst two equations into the time constraint, we
obtain g/4 + b/4 = 80, which can be rewritten as g = 320 — b, which is the equation for
factory 1’s PPC. Equations for the PPC’s for factories 2 and 3 can be derived in the same
way. Thus, we obtain the PPCs: g = 320 — b for factory I
g = 120 — (3/5)b for factory 2
g = 400 — (5/3)b for factory 3 Plotting these PPCs, we obtain g
g 400 320 factory I factory 2 factory 3 120 320 b 200 b 240 b [Note that, even without solving for the equations for the PPCs, you could have found the
intercepts very easily by multiplying potential output by hour by the number of hours of production for each factory. For example, factory 2 could produce at most 3x40 = 120
guns and 5x40 = 200 pounds of butter.] Comparative advantage is determined by the relative slopes of the PPCs, so factory 2 has
the comparative advantage at producing butter. b. [10 pts] This plan is not efficient. Comparing factories l and 3, factory 3 has the
comparative advantage at producing guns. So factory I should never produce guns
unless factory 3 is already completely specialized in gun production. Given that factory 3
is currently producing all butter, it would be more efﬁcient to shift the production of guns
from factory I to factory 3. Given the current (inefﬁcient) plan, total gun production is 4x40 = 160 and total butter
production is 4x40 + 200 + 240 = 600. If production of the 160 guns was shifted from
factory I to factory 3, then factory 3 could still produce 144 pounds of butter. Factories 1
and 2, now specialized completely in butter production, could produce 320 + 200 pounds
of butter. In this way, the country could produce 160 guns and 664 pounds of butter. 1c. [10 pts] Comparing the slopes of the PPCs, efﬁciency requires that any production of
guns should ﬁrst be assigned to factory 3, and then (after factory 3 is completely
specialized) to factory 1, and then (after factory I is completely specialized) to factory 2.
If factory 3 specialized in guns while factories 1 and 2 specialized in butter, the ratio of
guns to butter would be (400)/(320+200) = .769. Given the required ratio of 3, we would
need to produce more guns. If factories 3 and 1 specialized in guns while factory 2
specialized in butter, the ratio of guns to butter would be (400 + 320)/200 = 3.6. So now
we need to produce fewer guns. Thus, faCtory 3 should specialize in guns, factory 2
should specialize in butter, and factory I should produce some of each. More precisely,
factory I should produce b pounds of butter where b is given by (400 + (320 — b))/(2OO + b)) = 3. Solving this equation, we ﬁnd that factory 2 should produce b = 30 pounds of butter (and
hence g = 320 — 30 = 290 guns). Thus, total production of guns is 400 + 290 = 690, total
production of butter is 200 + 30 = 230, and the ratio of guns to butter is 690/230 = 3. [Note that parts b and c might also have been approached graphically, using the country’s
overall PPC. The overall PPC is found by “adding” the factory PPCs in the same manner
that we added the husband’s and wife’s PPCs to ﬁnd the overall household PPC in class.
Note that the overall PPC is not linear; the slope of each segment corresponds to the slope
of an individual PPC. Given the country’s overall PPC, parts b and c essentially asked
you to ﬁnd the point on this PPC that satisﬁes some condition (the condition g = 160 in
part b; the condition g = 3b in part c). Graphically, 840 400 g=160 200 520 760 butter Q1* Q0* Q If corn is an inferior good, an increase in consumer income will shift the demand curve to
the left, decreasing equilibrium price from P0* to P1* and decreasing quantity from Q0* to Q1*. 2b. [5 pts] Q0* Q1* Q If wheat is a substitute for corn, an increase in the price of wheat will shift the demand
for corn to the right, increasing price from P0* to P1* and increasing quantity from Qo* to Q1* 2c. [5 pts] 620* Q:1* Q If fertilizer is a factor used in corn production, an decrease in the price of fertilizer will
reduce the marginal costs of farmers, shifting the supply curve downwards, decreasing
price from P0* to P1* and increasing quantity from Qo* to Q1*. 3a. [8 pts] 3b. [12 pts] III Illll. Initially, the consumer’s budget
constraint is given by the solid line. Given the market campaign, the
lower part of the budget constraint
shifts outward by 5 units, so that the
budget constraint follows the solid
line until x1 = 20, and then follows
the dotted curve. Because good 1 is a normal good, the quantity of
good 1 consumed will rise (from a to b). However,
subtracting the 5 free units, the quantity of good 1
purchased will actually fall (from a to b—5).
Intuitively, because good 2 is also a normal good,
the consumer must be purchasing more good 2,
and hence spending less on good 1. The marketing
campaign generates a pure income effect because
it causes a parallel shift of the budget constraint.
There is no substitution effect because relative
prices have not changed. 3c. [10 pts] If the consumer initially purchased slightly less
than 20 units, she will probably now be at a
corner solution — buying just enough good 1 to
receive the 5 free units. Thus, there is an
increase in both consumption (from a to 25)
and purchase (from a to 20) of good 1. a 20 25 x1 4a. [20 pts] Given the required production level Q, we may rewrite the production
function as K = Q2/ L to obtain K as a function of L. For each possible level of L, we
can then determine required capital (K = Q2 / L) and the total cost (TC = wL + rK = L + 4K). For the three cases under consideration, Q=2o Q=30 Q=40
L K TC L K. TC L K TC
10 40 170 10 90 370 10 160 650
20 20 100 20 45 200 20 80 340
30 1333 8333 30 30 150 30 5333 24333
40 1o 80* 40 225 130 40 40 200
50 8 82 50 18 122 50 32 178
60 666 8666 60 15 120* 60 2666 16666
70 12.86 121.43 70 22.86 161.43
80 1L25 125 80 20 160* 90 17.77 161.11
100 16 164 The asterisks denote the minimum total cost in each table. Thus, your costminimizing
production plans would be Q=20 —) L=40,K=10,TC=80
Q=30 —) L=60,K=15,TC=120
Q=40 —> L=80,K=20,TC=16O The total cost curve gives TC as a function of Q (given that the ﬁrm is using the cost
minimizing method of production). The marginal cost curve shows the slope of the TC
curve at each level of Q. $ Tch) $ 160 120 80 4 MC(Q)
20 30 40 Q Q Given that MC = ATC/AQ = 40/ 10 = 4, this factory has constant marginal costs. 4b. [10 pts] An increase in the wage would cause the factory to substitute toward capital.
Plotting an isoquant (with K on the horizontal axis and L on the vertical axis), this
increase in w would cause the isocost curves to become ﬂatter, and the factory would
move along the isoquant from a to b. Both total costs and marginal costs would be higher
at each output level, so those curves would both shift upwards. Q constant K [It would have been possible to use calculus to solve part a. The plant manager’s
problem is to choose K and L to minimize wL + rK given Q = VKL . where w, r, and Q are constants. Substituting the constraint (rewritten as K = QZ/L) into
the objective function (wL + rK), the problem becomes choose L to minimize wL + rQZ/L. Differentiating with respect to L, we obtain the condition w — rQZ/ L2 = 0 which can be rewritten as L = Q JH—w .
In the current problem, r/w = 4, so this becomes L = 2Q which implies K = Q2/2Q = (1/2)Q
and thus TC = wL + rK = (1)(2Q) + (4)(1/2)Q = 4Q. The marginal cost function MC(Q) = TC’(Q) = 4.] Economics 111 Exam 2 Prof Montgomery Fall 2004
Answer all questions. Explanations can be brief. 100 points possible. 1. [18 points] Suppose that a hospital is a monopsonist, being the only employer of nurses
in the local labor market. Further assume that the market supply curve for nurses is
upward sloping, while the hospital’s demand curve for nurses is downward sloping.
(Recall that the height of the labor demand curve reﬂects the value of the marginal
product of labor — that is, the ﬁrm’s monetary gain from the last worker hired.) a) Using a graph, explain how the hospital determines the optimal number of nurses to
hire and the wage paid. [HINT: Your graph should be clearly labeled, and should show
the supply curve, demand curve, and marginal cost of labor curve.] Is the marginal cost
of labor curve above, below, or the same as the supply curve? Explain. b) Using your graph, compare the outcome that would have been generated by a
competitive market to the outcome chosen by the monopsonist. Is the wage higher or
lower under monopsony? Is the number of workers hired higher or lower under
monopsony? Is total surplus (producer surplus + worker surplus) higher or lower under
monopsony? Identity any deadweight loss on your graph. 2. [32 points] Consider a market with demand curve p = 360 — 3Q. a) Suppose that this market is monopolized by a ﬁrm that can produce costlessly (and
hence has zero marginal costs). Derive the monopolist’s optimal quantity, the price it
charges, and the proﬁt that it receives. b) Now suppose that two ﬁrms (a “duopoly”) face this market demand. Both ﬁrms
choose quantities simultaneously, and then price adjusts to clear the market given the
total quantity produced (Q = Q1 + Q2). Assume that both ﬁrms can produce costlessly.
Derive each ﬁrm’s optimal quantity, the market price, and the proﬁt received by each
ﬁrm. 0) Now suppose that three ﬁrms (a “triopoly”) face this market demand. All ﬁrms choose
quantity simultaneously, and then price adjusts to clear the market given the total quantity
produced (Q = Q1 + Q2 + Q3). Assume that all ﬁrms produce costlessly. Derive each
ﬁrm’s optimal quantity, the market price, and the proﬁt received by each ﬁrm. [HINT:
You should ﬁrst derive the reaction function for one ﬁrm, viewing the quantities chosen
by other ﬁrms as constants. Deriving all 3 reaction functions, you would have a system
of 3 equations with 3 unknowns. But recognizing the symmetry of the problem (which
implies that all ﬁrms will choose the same quantity in equilibrium), you could simply use
any one reaction function along with the condition that Q = Q2 = Q3 = (1/3)Q.] d) Intuitively, what happens to each ﬁrm’s optimal quantity, the market price, and the
proﬁt received by each ﬁrm as the number of ﬁrms becomes very large? 3. [18 points] Political scientists sometimes view rulers (e. g., kings or dictators) as
revenue maximizers who attempt to extract as much wealth as possible from their
subjects. In a country governed by this kind of ruler, suppose that an entrepreneur can
decide either to undertake or not undertake a new business venture. If the entrepreneur
does undertake this venture, she would earn revenue = 4 and incur cost = 1. If she does
not, she earns revenue = 0 and incurs cost = 0. Further suppose that, after the
entrepreneur makes her choice, the ruler can either conﬁscate all of the entrepreneur’s
revenue or else conﬁscate half of the entrepreneur’s revenue. The entrepreneur’s payoff
is equal to the amount of revenue not conﬁscated by the ruler, minus any cost incurred.
The ruler’s payoff is equal to the amount of revenue conﬁscated from the entrepreneur. a) Use a gametree diagram to show the possible sequences of actions and the resulting
payoffs for each player. [Payoffs should be written in the form (payoff for entrepreneur,
payoff for ruler).] Using backward induction (“rollback”), explain what outcome will
occur in this game. Further explain how the outcome could be more efﬁcient if the
players were able to make credible commitments to take (or not to take) some actions. b) Conceptually, how and why might the outcome of the game (without commitment)
change if there was (inﬁnitely) repeated interaction between the ruler and entrepreneur? 4. [20 points] An insurance company is deciding whether to offer dental insurance to
6000 university employees, and if so, the yearly price (p) at which the company should
offer the insurance. Suppose there are three types of employees: 1000 “high use”
employees who would each be willing to buy insurance if p S $1,500, and would each
generate expected costs of $1,300 for the insurance company; 3000 “medium use”
employees who would each be willing to buy insurance if p .<. $1,000, and would each
generate expected costs of $800for the company; 2000 “low use” employees who would
each be willing to buy insurance if p 5 $500, and would each generate expected costs of
$400 for the company. While the insurance company might be able to distinguish
between these different types of employees (perhaps by requiring dental exams before
issuing policies), the company has been told by the university that it cannot charge
different prices to different employees. Thus, if the company offers insurance at all,
every employee must be offered insurance at the same price p. Each employee would
then decide for themselves whether or not to buy at this price. For each price p that the company might set, determine the company’s expected cost per
policyholder. What price maximizes proﬁt (= price — expected cost) per policyholder?
What price maximizes total proﬁt (= expected proﬁt per policyholder X number of
policyholders)? Should the ﬁrm offer insurance? At what price? Which employees
beneﬁted from the university’s rule that the company could not set different prices?
Which employees were hurt? 5. [12 points] The city council has recently debated whether to outlaw smoking in all bars
and restaurants. Some proponents have argued that regulation is necessary because
restaurant workers are harmed by second—hand smoke. What alternative solution would
be suggested by the Coase Theorem? Why is (or isn’t) this solution viable? Econ 111 Exam 2 Fall 2004 Solutions 1) Note that monopsony is discussed in the appendix to Chapter 12, and that this question
could be answered directly from that discussion. a) [12 pts] marginal cost of labor
w (wage) labor supply labor demand
L* Lc L (number of nurses) The hospital will hire nurses until the marginal cost of labor is equal to the value of the
marginal product of labor. Graphically, this point is determined by the intersection of the
marginal cost of labor curve and the labor demand curve. Thus, the hospital hires L*
nurses and pays the wage w*. As shown on the diagram, the marginal cost of labor curve
is above the labor supply curve. Intuitively, to hire an additional nurse, the hospital must
not only pay that additional nurse, but also pay more to all the other nurses hired. [Note
the analogy to the monopolist’s problem: the marginal revenue curve is below the
demand curve because, in order to sell an additional unit, the ﬁrm must cut the price sold
on all previous units.] b) [6 pts] In a competitive market, price and quantity are determined by the intersection
of the supply and demand curves. Using the graph above, the wage would be w° and the
quantity of labor supplied would be LC. Thus, both the wage and the quantity of labor
supplied is lower under monopsony: w* < wc and L* < LC. Total surplus is also lower
under monopsony, since there is deadweight loss equal to the area of the triangle bounded
by the demand curve, the supply curve, and the (dotted) horizontal line at L*. 2a) [9 pts] The monopolist would set quantity Q so that MR(Q) = MC(Q) which implies
360 — 6Q = 0 and hence Q = 60
p= 360—3Q = 360—3(60) = 180
n = pQ = (180)(60) = 10,800 b) [10 pts] Taking ﬁrm 2’s quantity Q2 as constant, the residual demand curve facing
ﬁrm 1 is given by p = 360 — 3Q1 — 3Q2. Thus, ﬁrm 1’s marginal revenue is equal to
MR1 = 360 — 3Q2 — 6Q1. Firm 1 chooses quantity by setting MR1(Q1) = MC1(Q1) which
becomes 360 — 3Q2 — 6Q1 = 0. Rewriting this equation, we obtain ﬁrm 1’s reaction
function: Q, = 60 — (1/2)Q2. In the same way, we can derive ﬁrm 2’s reaction function: Q2 = 60  (1/2)Q1. The Nash equilibrium is determined by the intersection of the two reaction functions. Algebraically, we can substitute one reaction function into the other, obtaining
Q = 60 — (1/2)[60 — (1/2)Q1] which implies Q1 = 40 and hence Q2 = 60—(1/2)(40) = 40. Price p = 360—3(40+40) = 120, and proﬁt for each ﬁrm is 1: = (120)(40) = 4,800. c) [10 pts] Taking the outputs of ﬁrms 2 and 3 as constant, the residual demand curve
facing ﬁrm 1 is p = 360 — 3Q1 — 3Q2 — 3Q3, and thus ﬁrm 1’s marginal revenue is equal
to MR1 = — 3Q2  3Q} — 1 sets Q1 SO that = MC1(Q1), 360 — 3Q2 — 3Q3 — 6Q1 = 0. Rewriting this equation, we obtain ﬁrm 1’s reaction
function: Q = 60 — (1/2)Q2 — (1/2)Q3. There are now several ways to solve for the Nash equilibrium. One strategy is to solve
for the other two reaction functions. You would then have a simultaneous equation
system with 3 equations and 3 unknowns that could be solved to ﬁnd the Qi’s.
Alternatively, given the symmetry of this problem, it is clear that every ﬁrm will choose
the same quantity in equilibrium. Thus, given Q1 = Q2 = Q3 = (l/3)Q, substitution into
ﬁrm 1’s reaction ﬁmction yields (1/3)Q = 60 — (1/2)(1/3)Q — (1/2)(1/3)Q
which implies Q = 90 and hence Q1 = Q2 = Q3 = 30.
Thus, p = 360 — 3(90) = 90, and proﬁt for each ﬁrm is 1t = (90)(30) = 2700. d) [3 pts] As the number of ﬁrms continues to rise, the quantity per ﬁrm, price, and proﬁt
per ﬁrm will fall to 0, while total quantity will rise toward 120. Intuitively, this is the
outcome that would be generated by a perfectly competitive market (given the assumed
market demand curve, and inﬁnitely elastic supply at price p = 0). [Formally, given Coumot competition with n ﬁrms, ﬁrm 1’s reaction function becomes
Q = 60 — (1/2)(Q2+Q3+. . .+Qn). Given the symmetry of the problem, each of the Qi’s
will equal Q/n in equilibrium. Substituting into ﬁrm 1’s reaction ﬁmction, we obtain
Q/n = 60 — (1/2)(n1)(Q/n) which implies total quantity = Q = (120)[n/(n+1)]
market price = p = 360 — 3Q = 360/(n+1)
proﬁt per ﬁrm = n = 43200/(n+1)2 ] 3a) [12 pts] entrepreneur 0,0 Solving this sequential game using backward induction (“rollback”), we ﬁrst consider
what would happen if the entrepreneur does undertake the new venture. Because he
would prefer 4 rather than 2, the ruler would conﬁscate all of the entrepreneur’s revenue.
Thus, the entrepreneur realizes that, if she undertakes the venture, she will receive —1.
Because this is worse than 0, the entrepreneur will choose to not undertake the new
venture, and both players will receive payoffs of zero. Both players could obtain better
outcomes if the ruler could commit to take only half (or, equivalently, if the ruler could
commit not to take all) of the entrepreneur’s revenue. Perhaps counterintuitively, the
ruler would be better off in this game if he was less powerful — if he was not able to seize
all of the revenues for himself. b) [6 pts] If this game was repeated indeﬁnitely, the two players might be able to sustain
the good outcome (i.e., entrepreneur undertakes new venture, then ruler conﬁscates only
half). Suppose the entrepreneur undertakes the ﬁrst new venture, and then continues to
undertake new ventures if and only if the ruler has never conﬁscated all of the revenue on
previous ventures. Given that the entrepreneur is following this type of “trigger
strategy,” the ruler will prefer to conﬁscate only half if the present value of his stream of
future beneﬁts (= 2 + B2 + [322 + [332 + ...) exceeds the value of conﬁscating everything
today and then receiving no future beneﬁts (= 4). This will occur when the ruler places enough weight on future outcomes — when his discount factor ([3) is close enough to 1. 4) [20 pts] If the company sets p > 1500, no employees will buy insurance. If the
company sets price between 1000 and 1500 (i.e., 1000 < p S 1500), only “high use”
employees will buy, and expected costs per policyholder will be $1300. If the company
sets price between 500 and 1000 (i.e., 500 < p S 1000), both “high” and “medium”
employees will buy, and expected coSts per policyholder will be (1000/4000)(1300) +
(3 000/4000)(800) = $925. (Note that the expected costs are weighted by the proportion
of each type of employee among all employees who will buy.) If the company sets p S
500, all employees will buy, and expected costs per policyholder will be
(1000/6000)(1300) + (3000/6000)(800) + (2000/6000)(400) = $750. (Again, expected
costs are weighted by the proportion of each type of policyholder.) For each price p, the company’s expected proﬁt per policyholder would be p—Ec(p)
where Ec(p) is expected cost given price p (as derived above). Thus, p=500 —) p—Ec(p) = 500—750= —250
I): 1000 —) p—Ec(p) = 1000—925=75
P: 1500 —) p—Ec(p) = 1500—1300=200 Total proﬁt = (proﬁt per policyholder x number of policyholders). Thus, p = 500 —> —250 x 6000 = —1,500,000
p = 1000 —) 75 x 4000 = 300,000
p = 1500 —> 200 x 1000 = 200,000 Yes, the ﬁrm should offer insurance at price p = 1000. If allowed to set different prices
for different types of consumers, the company would have charged 1500 to highuse
employees, 1000 to mediumuse employees, and 500 to lowuse employees. Thus, the
university’s rule beneﬁts highuse employees (increasing each employee’s consumer
surplus by 500). [Lowuse employees will not buy insurance at price 1000, but aren’t
really hurt by the university’s rule, given that the (monopolist) insurance company would
have charged them their full willingness to pay.] 5) [12 pts] The Coase Theorem suggests that government regulation is not needed to
solve externality problems. Assuming that bargaining is costless, the government merely
assigns property rights, and then the parties themselves negotiate an efﬁcient solution. In
the present example, smoking by restaurant customers generates negative extemalities for
restaurant workers (and for other customers). But rather than simply outlaw smoking in
restaurants, the city council might assign property rights to the customers or to the
workers (or to the restaurant owners). For instance, if property rights were assigned to
workers, the customers would have to pay workers for the right to smoke. Conversely, if
the rights were assigned to customers, the workers would have to pay the customers not
to smoke. After negotiation, smoking would occur if and only if the disutility to workers
is less than the utility to customers. Trying to imagine how this propertyrights solution would work in practice, critics of the
Coase Theorem might argue that bargaining costs would be prohibitive. Obviously, it
would be difﬁcult and timeconsuming for customers to negotiate with workers every
time they went out to eat. Even more crucially, if smoking affects every customer and
worker in the restaurant, any negotiation would need to include all of these parties. On the other hand, if property rights are assigned to restaurant owners (which is
essentially the situation before regulation), a “market solution” to the extemality problem
may seem more Viable. Each owner could choose whether to allow smoking, adjusting
prices and wages accordingly, without need for costly bargaining. (Presumably, owners
who allow smoking will need to pay higher wages to attract workers and will thus set
higher prices for customers. Given free entry in the restaurant market, customers could
choose their preferred combination of smoking/nonsmoking and price.) Some
economists would argue that government regulation in this case would be overly
“paternalistic” because some workers might (rationally?) be willing to inhale second
hand smoke in exchange for higher wages. Economics 111 Fall 2004 Exam 3 Prof Montgomery
Answer all questions. 1 00 points possible. Explanations can be brief 1) [15 points] A small economy has three industries producing goods X, Y, and Z. Some
of the output of each industry is sold to other industries (as intermediate goods) while the
remainder is sold to ﬁnal consumers. In addition to purchasing goods from other
industries, ﬁrms in each industry also pay wages to workers. Any proﬁts are paid out to
shareholders. The following table lists revenues and costs for each industry. [HINT:
Note that purchases are reported in dollars, not units of output] industry X industry Y industry Z revenues: $ 2200 $ 3100 $ 1800
costs:
purchases of X $ 500 $ 100
purchases of Y $ 200 $ 600
purchases of Z $ 900
wages $ 1500 $ 400 $ 500 Compute the Gross Domestic Product (GDP) for this economy using (a) the ﬁnal goods approach,
(b) the valueadded approach, and
(c) the income approach. [HINT: You must give the details of each computation to receive credit for this problem,
labeling terms to demonstrate that you understand each approach] 2) [18 points] Deﬁne the federal funds rate and the discount rate. Which rate does the
Fed set directly? For which rate does the Fed set a target? What action would the Fed
take if this rate began to move above the Fed’s target? Explain how this action would
affect the rate, using the relevant supply—anddemand graph. 3) [18 points] Consider the full employment model for an open economy. Suppose that an improvement in technology causes the fullemployment output level (I7 ) to rise. List
the changes (if any) that would occur in macroeconomic ﬂows (given by the edges of the
circular ﬂow diagram), the interest rate (r), and the exchange rate (e). Brieﬂy discuss,
using the relevant supply—anddemand graphs for the capital and/or foreignexchange
markets. [HINT: Assume that imports depend only on e, while domestic consumption
depends positively on Y and negatively on e.] 4) [12 points] Brieﬂy discuss “efﬁciency wage” models, and then brieﬂy explain why
these models are relevant for macroeconomics. 5) [25 points] Consider the unemployment model for a closed economy. Suppose that consumption is C = 15 + (.75)(1'c)Y
private savings are Sp = —15 + (.25)(lt)Y
tax revenue is T = TY investment is I = 40 government spending is G = 90 where T is the tax rate and Y is income. a) Assuming T = .25, solve for the equilibrium level of income. Is the government
running a budget surplus or budget deﬁcit? How large is this surplus or deﬁcit? b) Suppose that the government decides to balance its budget by altering its spending (G)
while holding the tax rate constant at r = .25. Find the new equilibrium level of income,
and the new level of government spending. 0) To balance its budget in a different way, the government might have altered the tax
rate (I) while holding its spending constant at G = 80. If the government had balanced its
budget in that way, what would have been the equilibrium level of income? What would
have been the new tax rate? 6) [12 points] Suppose that the President is more likely to be reelected when both
unemployment is low and inﬂation is low. Further suppose that voters merely consider
current unemployment and inﬂation, ignoring longerrun impacts of current monetary
policy. Using the ADIAS framework, explain why the Federal Reserve should not be
placed under direct presidential control. If the Fed was under the President’s direct
control, what actions would you expect a President to take in the short run (while running
for re—election) and the long run (after winning reelection, assuming that he wants his party to win the next election)? Econ 111 Exam 3 Fall 2004 Solutions Note: I added 1 extra point to each part of Q1 , so the exam was worth 103 points total. 1a) [6 pts] GDP = sum of value of ﬁnal goods produced by each industry
= (2200600) + (3100800) + (1800900)
= 1600 + 2300 + 900
= 4800 b) [6 pts] GDP = sum of valueadded by each industry
= (2200200) + (31001400) + (1800700)
= 2000 +1700 +1100
= 4800 c) [6 pts] GDP = sum of wages and proﬁts* paid by each industry
= (1500 + 500) + (400 + 1300) + (500 + 600)
= 2000 +1700 +1100
= 4800 (*recall that proﬁt = revenues  costs) 2) [18 pts] The federal funds rate is the interest rate that banks charge each other for
borrowing reserves. The discount rate is the interest rate that the Fed charges when it
loans reserves to banks. The Fed sets the discount rate directly, and sets a target for the
federal funds rate (currently, in Dec 2004, the target is at 2%). If the federal funds rate
began to move above this target, the Fed would increase the supply of reserves by
purchasing Tbills. By increasing the supply of reserves, the Fed would cause the federal
funds rate to fall back toward the target level. Graphically, an initial increase in the
demand for reserves (from Do to D1) would increase the equilibrium federal funds rate
above the target level (say 2%); the Fed would increase the supply of reserves (from Soto
S1) to decrease the rate back to the target level. federal
funds
rate 2% ....................................................................... .. quantity of reserves 3) [18 pts] It may be helpful to refer to the circular ﬂow diagram as you solve this problem. An increase in 7 would increase disposable income, and hence cause domestic
consumption (Cd) and private savings (Sp) and tax revenue (T) to rise. [By the
assumption given in the hint, imports (M) do not depend on Y.] The increase in T would
cause government savings (Sg) to rise. The increases in both Sp and Sg would shift the
supply of savings to the right and hence cause the equilibrium interest rate (r) to fall. r sp 4 5g + NCF(r)
——>
capital market
1(r)
—___—_____—_._————>
8,1 The decrease in the equilibrium interest rate would cause net capital ﬂows (N CF) to
decrease, shifting the demand for dollars to the left, thus decreasing the equilibrium exchange rate (6). M(e) foreign exchange
market X(e) + NCF(r) $ This decrease in the exchange rate would cause imports (M) to fall and exports (X) to
rise. (By the assumption given in the hint, it would also cause Cd to rise further.) 4) [12 pts] Efﬁciencywage models assume that worker productivity is an increasing
function of the wage. This effect might occur for several reasons: ﬁrms paying higher
wages may have lower turnover, be more likely to retain hi gher—ability workers, might
provide more incentive to keep workers from “shirking,” or might induce greater
employee morale (if worker effort depends on the perceived “fairness” of the wage). If
productivity depends on the wage, then the optimal wage paid by the ﬁrm may not be
very responsive to labormarket conditions. Thus, efﬁciencywage model may help explain why wages are “sticky,” failing to fall during recessions when unemployment is
high. ' 5a) [9 pts] Equilibrium Y is determined by the equation Y = c + 1+ G Y =15 + (.75)(1.25)Y + 40 + 90 Y = [1/(1—(.75)(1.25))][15 + 40 + 90]
Y= 331.43 Tax revenue is thus T = (.25)(331.43) = 82.86, and the government has a budget deﬁcit
equal to G — T = 90 — 82.86 = 7.14. b) [8 pts] A balanced budget requires G = TY. Holding the tax rate ﬁxed at T = .25, the
government obtains a balanced budget by setting G = (.25)Y. Equilibrium Y is '
determined by the equation Y = c + I + G Y = 15 + (.75)(1.25)Y + 40 + (.25)Y
Y = [1/(1 — (.75)(1.25) — .25)][15 + 40]
Y = 293.33 In equilibrium, G = 1: Y = (.25)(293.33) = 73.33 c) [8 pts] Again, a balanced budget requires G = TY. Holding spending ﬁxed at G = 90,
the government obtains a balanced budget by setting I = 90/Y. Equilibrium Y is
determined by the equation Y = C + I + G Y = 15 + (.75)[1(90/Y)]Y + 40 + 90 Y = 15 + (.75)(Y—90) + 40 + 90 Y = [1/(1—.75)][15  (.75)(90) + 40 + 90]
Y= 310 In equilibrium, T = 90/310 = .29 6) [12 pts] Suppose that the Fed was under direct Presidential control. By adopting a
“looser” monetary policy (shifting the Fed’s monetary policy rule downwards), the
President could cause the ADI curve to shift to the right. In the very short run, this would
cause output to rise (and unemployment to fall) without any immediate effect on
inﬂation. Graphically, on the ADIAS diagram, the economy moves from point A to
point B. Voters (who, by assumption, care only about current inﬂation and
unemployment) would feel better off, and would thus be more likely to reelect the
incumbent President. However, in the longer run (following the election), inﬂation
would begin to rise. Graphically, the economy begins moving up the ADI to point C. To
bring inﬂation back down to its original level, the President would need return to the
original “tighter” monetary policy (shifting the Fed’s policy rule back upwards), causing
the ADI curve to shift back to the left. This would move the economy from point C to
point D. By temporarily inducing a recession (with income below the fullemployment
level), this tighter monetary policy would gradually bring inﬂation back down to its
original level (hopefully in time for the next election). Thus, direct presidential control of
the Fed might lead to “political business cycles” with booms just before elections and recessions during the midterm. TC TC
Z
7T Fed’s rule (tighter) r equilibrium Y given r
% (looser) ...
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 Spring '08
 MONTGOMERY
 Economics, Supply And Demand, Federal Reserve, ........., Factory

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