Download Name: ______ Student No.: ______ Quiz #2 Microeconomics

Name: _____________
Student No.: _____________
Quiz #2
Microeconomics (I), Fall 2010
Due day: 28 Dec., 2010
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. Returns to scale refers to the change in output when:
A. all inputs increase proportionately.
B. labor increases holding all other inputs fixed.
C. capital equipment is doubled.
D. specialization improves.
2. The above figure shows the market demand curve for telecommunication
while driving one's car (time spent on the car phone). The current price
is 35¢ per minute. If the price were to increase by ten cents per minute,
consumer surplus would:
A. fall to $820.
B. fall by $84
C. fall by $58
D. fall to $369
3. The long run average cost curve may initially slope downward due to:
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A. economies of scale.
B. decreasing average fixed costs.
C. increasing marginal returns.
D. All of the above.
4. In response to an increase in the wage rate, the income effect will usually
cause a person to:
A. have a horizontal labor supply curve.
B. supply the same hours of labor.
C. supply more hours of labor.
D. supply fewer hours of labor.
5. The marginal rate of technical substitution always equals:
A. the slope of the total product curve.
B. the change in output due to a change in the amount of one input.
C. the ratio of the marginal products of inputs.
D. the distance between two isoquants.
6. The total cost of producing one unit is $50. The total cost of producing
two units is $75. At a production level of two units, the cost function
exhibits:
A. constant returns to scale.
B. increasing marginal costs.
C. rising average costs.
D. economies of scale.
7. In the short run, the expansion path is:
A. horizontal.
B. vertical.
C. diagonal.
D. cannot be determined.
8. Many universities have either a top football program OR a top basketball
program. Very few have both. These results suggest the presence of:
A. economies of scope.
B. diseconomies of scope.
C. returns to scale.
D. the law of diminishing marginal returns.
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Part II. Problems: 60%
1. This question has you determine the effect of a tax on labor on the
long-run cost function.
Consider a firm with the production function
f(L,K) = LK. The wage rate and rental rate on capital are w and r,
respectively.
(a) Try to derive the long-run cost function for this firm. (30%)
(b) Suppose the government taxes labor at by an amount t per unit
of labor. Rewrite the long-run cost function including the tax.
(Hint: the effective wage rate is now w+t.) (10%)
(c) Compute the marginal effect of the tax on the long-run cost
function. Does an increase in the tax increase the cost linearly?
(Hint: compute the partial derivative of the cost function with
respect to t.) (20%)
Ans:
(a). The Lagrangian is L = wL +rK + λ[q – LK]
The first-order conditions are
L L = w – λK = 0
LK = r – λL = 0
Lλ = q - LK
Combining the first two conditions:
w/r = K/L
Rearranging yields
K = wL/r
Substituting into the third condition:
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q = wL /r
Solving for L and K:
L = (qr/w)
1/2
K = (qw/r)
1/2
The cost function is
C(w,r,q) = w(qr/w)
1/2
+ r(qw/r)
1/2
= 2(qwr)
1/2
(b.) Replace ‘w’ with ‘w+t’ in the cost function above.
C(w+t,r,q) = 2[q(w+t)r]
(c.)
1/2
The derivative is:
Ct = (qr)
1/2
(w+t)
-1/2
The tax does not increase the costs linearly in q.
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