Download Name: ______ Student No.: ______ Quiz #3 Microeconomics

Name: _____________
Student No.: _____________
Quiz #3
Microeconomics (I), Fall 2010
Due day: 06 Jan., 2011
Part I. Multiple Choice: 40% (5% each)
Please fill your answers in below blanks, only one correct answer for each question.
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1. Economic costs of an input include:
A. only implicit costs.
B. only explicit costs.
C. both implicit and explicit costs.
D. whatever management wishes to report to the shareholders.
2. There are 10 identical internet service providers (ISPs) in a city serving a
market demand with an elasticity of -1.5. The elasticity of supply for each
firm is 3.0. The elasticity of demand faced by an individual ISP provider
is:
A. -42
B. -15
C. -1.5
D. -27
3. Sarah and David both have linear demand curves for lemonade. Sarah's
demand curve for lemonade intersects David's demand curve at a price
of 50 cents per glass. Sarah's demand curve is more inelastic than
David's. A change in the price of lemonade from 50 cents to 25 cents per
glass will:
A. decrease Sarah's consumer surplus more than David's.
B. decrease David's consumer surplus more than Sarah's.
C. increase Sarah's consumer surplus more than David's.
D. increase David's consumer surplus more than Sarah's.
4. A quota will reduce consumer welfare when:
A. the quota is less than the amount purchased without the quota.
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B. the quota is greater than the amount purchased without the quota.
C. the quota is on a good with high income elasticity.
D. quotas always reduce consumer welfare.
5. Homer's Donut Shoppe has the production function q=10L +20L2- 5L3.
The marginal product (MP) and average product (AP) of labor is :
A. MP=10 + 40L -15L2; AP=10 + 20L -5L2
B. AP=10 + 40L -15L2; MP=10 + 20L -5L2
C. MP=10L; AP=10
D. MP = 10 + 20L; AP=10+20L
6. If the marginal productivity of labor is constant for all levels of output,
then the average productivity of labor:
A. is constant.
B. equals the marginal productivity of labor.
C. Both A and B above.
D. Neither A or B.
7. Suppose the cost of producing two goods, x and y, can be represented as
C = ax + by + cxy. If there are economies of scope, then which of the
following must be true?
A. c > 0
B. c < 0
C. c = 0
D. a + b = -c
8. Suppose MPL = 0.5 (q/L) and MPK = 0.5 (q/K). In the long run, the firm
will hire equal amounts of capital and labor:
A. all of the time
B. only when w = r
C. only when w = 0.5r
D. no chance to happen.
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Part II. Problems: 60%
1. Carmela’s pasta factory employs workers and pasta machines according
to the following production function:
Q = F(L,K) = L0.5K0.5
The unit cost of capital (r) is $10 and the unit cost of workers (w) is $40.
(a) Write out the Lagrangian for the cost-minimization problem
and derive the optimal ratio of capital to labor (K/L). (20%)
(b) Suppose Carmela wishes to produce 1,000 units of pasta, and
assume it is in the short run, and capital fixed at 400 units.
How much labor should she employ? (10%)
(c) If Carmela wants to produce 2,000 units of pasta in the long
run, how much is the total cost? (30%)
Ans:
(a) The Lagrangian is:
L = 40L + 10K + λ[q – L0.5K0.5]
The first-order conditions from the Lagrangian are:
LL = 40 – 0.5L-0.5K0.5 = 0
LK = 40 – 0.5L0.5K-0.5 = 0
Combining these we get:
K/L = 4
(b) Cause of K fixed at 400 units, therefore the production function can
rewrite as: Q = L0.5(400)0.5 = 20(L0.5)
Plug Q = 1000 into the rewrote production function:
1000 = 20(L0.5)  L = 2500
Therefore Carmela needs to employ 2500 units of labor.
(c) ∵ K = 4L and Q = 2000, plug it into production function: 2000 = 2L
∴ L = 1000, K = 4000
Plug optimal L and K into cost function:
Total cost = 40*1000 + 10*4000 = 80,000
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