National Chung Cheng University
Department of Economics
MICROECONOMICS 2025
Problem Set 3 (Chapters 5-6)
1.
(Quiz3 暫時不考) A firm has the production function q = √
. The MRTSLK = K/L. The
wage rate is $10 per unit of labor and the rental rate is $5 per unit of capital and the firm
is going to spend $1000 on production.
(i). Assuming that the firm is free to choose any level of K and L to employ, how much
of each should it employ? How much output will they produce?
(ii). Now assume that once the firm has chosen its level of L and K, the level of K
becomes fixed. If the price of K increases to $8 per unit, how many units of output can
the firm now produce if it spends the same amount?
(iii). Once the firm reaches the long run again and is able to vary its level of K, how much
should L and K should it employ in order to achieve its original level of output? How
much will that level of production cost?
2. Suppose that you hire workers to address and stamp envelopes. Each worker earns $5 per
hour and produces 50 addressed, stamped envelopes per hour. You have unlimited free
office space and can therefore add as many workers as you want to with no fall-off in
productivity. You have no expenses other than paying workers.
Calculate and draw the
total product, marginal product, average product, total cost, average cost, average variable
cost, and marginal cost curves.
3
Marvin has a Cobb-Douglas utility function, U =
.
.
, his income is Y = 100, and,
initially he faces prices of p1 = 1 and p2 = 2. If p1 increases to 2, what are his CV, ∆CS,
and EV? (Hint: See Solved Problems 5.1 and 5.2.)
4. Kwabena’s utility function is U(q1, q2) = min (q1, q2). The price of each good is $1, and his
monthly income is $4,000. His firm wants him to relocate to another city where the price
of q2 is $3, but the price of q1 and his income remain constant. Obviously, he would be
worse off due to the move. What would be his equivalent variation and compensating
variation?
5. Originally when he could work as many hours as he wanted at a wage w, Roy chose to
work seven hours a day. The employer now offers him w for the first eight hours in a day
and an overtime wage of 1.5w for every hour he works beyond a minimum of eight hours.
Show how his budget constraint changes. Will he necessarily choose to work more than
seven hours a day? Would your answer be different if he originally chose to work eight
hours?
6. Derive Sarah’s labor supply function given that she has a quasilinear utility function, U =
Y0.5 + 2N, and her income is Y = wH. What is the slope of her labor supply curve with
respect to a change in the wage? (Hint: See Solved Problem 5.3.)
7. Suppose that the Cobb-Douglas production function is q = L0.75K0.25.
a. What is the average product of labor, holding capital fixed?
b. What is the marginal product of labor?
c. What are the APL and MPL when K = 16? (See Solved Problem 6.1).
8 If the Cobb-Douglas production function is q = L0.75K0.25, and
of output with respect to labor?
= 16, what is the elasticity