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Name____ANSWERS___
Practice Final 2012
(10 pts)1. Suppose that the short-run world demand and supply elasticities for crude oil are
-0.076 and 0.088, respectively. The current price per barrel is $30 and the short-run
equilibrium quantity is 23.84 billion barrels per year. Derive the linear demand and
supply equations.
Answer:
If the demand curve is linear, it is in the form of QD = a + bP Also, we know that
E = b P/Q
b = E (Q/P )= -0.076 (23.84/30)= -0.060.
Rearranging the linear expression for demand allows us to solve for a as follows:
a = QD - bP
a = 23.84 + 0.060(30) = 25.640.
We may now write the linear expression for demand as
QD = 25.640 - 0.060P.
If the supply curve is linear, it is in the form of
QS = c + dP.
Also, we know that E = d (P/Q)
d = E (Q/P) = 0.088 (23.84/30) = 0.070.
Rearranging the linear expression for demand allows us to solve for c as follows:
c = QS - dP
c = 23.84 - 0.070(30) = 21.740.
We may now write the linear expression for supply as
QS = 21.740 + 0.070P.
ECN 100
Final
(15 pts) 2. Janice Doe consumes two goods, X and Y. Janice has a utility function given by the
expression: U = 4X0.5 Y0.5. So, MUX = 2Y0.5/X0.5 and MUY = 2X0.5/Y0.5. The current
prices of X and Y are 25 and 50, respectively. Janice currently has an income of 750 per
time period.
a. Calculate the optimal quantities of X and Y that Janice should choose, given her
budget constraint. Graph your answer.
b. Suppose that the government rations purchases of good X such that Janice is limited
to 10 units of X per time period. Assuming that Janice chooses to spend her entire
income, how much Y will Janice consume? Construct a diagram that shows the
impact of the limited availability of X. Is Janice satisfying the usual conditions of
consumer equilibrium while the restriction is in effect?
Answer:
a.
I = PxX + PyY
750 = 25X + 50Y
Optimal Combination:
MRS =PX/PY
MRS =MUX/MUY= 2/2
(Y0.5/X0.5)/(X0.5/Y0.5)
MRS = Y/X
PX/PY = 25/50= 1/2
Equating MRS to PX/PY: Y/X= 1/2, Y = 1/2X
Janice should buy 1/2 as much Y as X.
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Recall
750 = 25X + 50Y
Substitute
(1/2)X for Y
750 = 25 X + 50(1/2)X
750 = 50X
=> X = 15
Y = (1/2)X
=> Y = 7.5
Janice should consume 7.5 units of Y and 15 units of X.
b.
750 = 25X + 50Y
X = 10
500 = 50Y
=> Y = 10
As indicated in the graph below, at Janice’s optimal bundle with the restriction,
MUX/PX > MUY/PY. This implies Janice should consume more X to increase utility.
However, the ration restriction prevents her from doing so. Given the restriction, this is
the best Janice can do.
(16 pts) 3. Consider a Monopoly with Total Cost function TC = 1000 + 2Q2 facing the following market
demand curve: P = 160 -2Q
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(6 pts) a. Find what the monopoly's price, the monopoly's quantity produced and the monopoly's
profits are in this case:
TR=P*Q= (160 -2Q)Q, MR=160 -4Q=MC=4Q,
Q=20, P=120
Profit= TR-TC=120*20-1000-2*20*20=600
(4 pts)b. In a graph that is carefully labeled, show the Demand Curve, MR Curve, AVC and MC curves
and the price and quantity chosen for the monopoly. Q is measured in pounds/year
(6 pts) c. In the graph above,
i. show the DWL (Deadweight Loss) triangle
ii. compute its area (including what units it is measured in)
Competitive market: P=MC, (160 -2Q)=4Q, Q=80/3, P=320/3。
DWL: 1/2*(120-80)*(80/3-20)=400/3
(6 pts) 4. Explain what a natural monopoly is using a graph. How should a regulatory agency
regulate the price of this monopoly such that the monopoly keeps on operating and the
consumer surplus is maximized?
(5 pts) 5. Use the following diagrams to identify points A, B, C, & D in Edgeworth Box on the
Production Possibilities Frontier curve and call them a, b, c and d Explain your work
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Y/time
capital/time
Isoquant for X
X = 12
Production Possibilities
Frontier
V
z
18
Isoquant for Y
Y = 10
B
Isocost for Y
C
10
A
D
5
Isocost for X
Z
labor/time
v
5
12
17
X/time
Producer of X
in redlined area
(9 pts)
6. In a competitive economy producing two final goods X and Y using two factors of
production L and K, write the efficiency condition in
a. Exchange (consumption good)
MRSxy = MRTxy.
b. Production (allocation of factor inputs)
MRTSLKX = MRTSLKY
c. Production and consumption (output market)
MRSxy = MRTxy.
c. How do we know if any of these conditions actually hold in any economy?
We don’t. When there are government interventions we assume that
they do not hold and when there isn’t we assume that they do.
(5 pts) 7. What is the claim of the first welfare theorem? Under what conditions the claim holds
(just mention a few of the more important assumptions)?
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(4 pts) 8. What are the four major sources of market failure? Just mention their names, no
explanation is required.
Answer)
The four major sources of market failure are market power, incomplete
information, externalities, and public goods.
(12 pts) 9. The local swimming pool charges nonmembers $10 per visit. If you join the pool,
you can swim for $5 per visit, but you have to pay an annual fee of $F.
a) Use an indifference curve diagram to find the value of F that would make it just
worthwhile for you to join the pool.
b) Suppose that the pool charged you exactly that value. Would you swim more or less
than you did before joining? Use income and substitution effects to explain your answer.
a) Budget constraint BC1 is the budget constraint when the pool costs $10 per visit.
Budget constraint BC2 is when the pool costs $5 per visit with no membership fee,
and budget constraint BC3 is the budget constraint with $5 visits and a
membership fee of $(Y-Z) (=F). The value of F that would make it just
worthwhile for you to join the pool is the compensating variation $(Y-Z).
AOG
Y
F=CV
=
Z
A
B
C
BC1
S1
S2
SE
BC2
BC3
S3
Swimming
IE
b) If the pool charged you exactly $F then you would swim more than you did before
joining because the substitution effect would increase the quantity demanded from
S1 to S2.
(9 pts) 10. a Show that emission fee can be superior to emission standards.
b. Under what condition emission standard is superior to emission fee?
c. What is Cap and Trade and why it is desirable?
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(24 pts) 11. Widgets are produced according to the production-function Q = 4K0.5L0.5.
(6 pts) (a) Find the formulas for cost-minimizing level of labor and capital in terms of
output level Q and factor prices w and r.
Use the tangency condition: MRTS = w/r
MRTS = MPL/MPK => MRTS=K/L
MRTS = w/r =>K/L = w/r => L = (r/w)K
Substitute for L in the production constraint and solve for K:
4K0.5 [(r/w)K] 0.5 =Q so
KReq = (Q/4)(w/r) 0.5 and LReq = (Q/4)(r/w) 0.5
(6 pts) (b) Find the formulas for the long-run total cost, marginal cost and average cost
functions.
TC= wLReq + rKReq = w(Q/4)(r/w)0.5 + r(Q/4)(w/r) 0.5
TC = (r.w) 0.5 Q/2
MC = 0.5(r.w) 0.5 and AC = 0.5(r.w) 0.5
(12 pts) (c) For a fixed capital level of 16 units find the formula for short run factor
demand for labor (in terms of w, r and the product price p). Find a formula for (i) labor
required in the short run, (ii) variable cost, (iii) marginal cost, and (iv) short-run supply
curve in terms of w, r and p.
(i) Q = 4K0.5L0.5 => Q= 4(16)0.5L0.5 => Q2= 16(16)L => LReq = (Q/16)2
(ii) Variable cost =w.L = w(Q/16)2
(iii) MC = 2w Q/(16)2
(iv) p=MC => p= 2w Q/(16)2 Solve for P
SR- Supply: P =2w Q/(16)2
12) Suppose an industry has no fixed costs. Draw two graphs side by side for the industry.
In the left graph draw a U-shaped average cost curve and the corresponding marginal cost
curve. In the right graph, draw a downward-sloping market demand curve. Also in the
right graph, draw a short-run supply curve that would generate positive profit, and the
long-run supply curve that would result.
Answer:
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13) The above below shows the cost curves for a typical firm in a competitive market
a) From the graph, estimate the firm's profits when price equals $10 per unit.
b) If there are 200 identical firms, estimate the market quantity supplied when p = 4,
8, and 10.
Answer)
a) When price = 10, p = MC when q = 60. TR = 600. The AC is just above 8.5, say
8.6. This yields TC = 516. The firm's profit is estimated to be around $84.
b) When p = 4, p < AVC so no firms will produce. At p = 8, each firm produces 50
units at a loss. At p = 10, each firm produces 60 units. The market quantity
supplied at each price is:
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(9 pts) 14. Take a look at the following list of goods and services: Apples, Open-heart surgery,
Cable television, Farm-raised salmon, Yosemite National Park Central Park, New York,
The Chinese language, The idea of calculus, Estrogen in Caspian Sea, The ozone layer
a. Is each item on the list excludable or nonexcludable? Sometimes the border is a little
fuzzy, but justify your answer if you think there’s any ambiguity.
b. Rival or nonrival?
c. Based on your answers to parts a and b, sort each good or service into one of the four
categories Rival-Nonrival and Excludable-Nonexcludable.
Excludable
Nonexcludable
Rival
Nonrival
Answer)
a. The first five are all excludable: Apples, open-heart surgery, cable TV, farm-raised
salmon, and Yosemite. The rest (Central Park, the Chinese language, and the idea of
calculus) are nonexcludable.
b. Apples, surgery, and salmon are all rival. Cable TV, Yosemite, Central Park, Chinese,
and calculus are nonrival.
c. Apples, open-heart surgery, and salmon are all private goods. Cable TV and Yosemite
are nonrival private goods (also known as “club goods,”). Estrogen in Caspian sea and
the ozone layer are common resources. Central Park, Chinese, and calculus are all public
goods. They are nonrival and nonexcludable. Of course, if Central Park gets very
crowded it turns into a common resource: Too many users will reduce the amount of
“park” available to others.
Excludable
Nonexcludable
Rival
Private goods
Common resources
Apples,
Estrogen
open-heart surgery,
ozone layer
salmon
Nonrival
Nonrival private goods or
Public goods
Central Park,
“club goods,”
Cable TV,
Chinese,
Yosemite
calculus
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15. The figure below shows supply and demand curves for apartment units in a large city.
If the city government passes a law that establishes $350 per month as the legal maximum
rent.
a)
b)
c)
d)
e)
what is social welfare loss
Why deadweight loss occurs?
What is the consumer loss?
How much the producer surplus change?
What is the Producer surplus?