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Price Theory Study Questions: Set #5
1.
Consider the following two workers.
A’s utility function is U = L
0.9
I
0.1
and B’s utility function
is U = L
0.1
I
0.9
where L = leisure and I = consumption of all other goods.
a. Calculate the MRS for each worker.
b. At the bundle L = 10 and I=$10 which consumer places a
relatively
higher value on leisure? Draw
representative indifference curves through this bundle.
2. Assume the following (unless told otherwise) for this question: U = L
0.8
I
0.2
, w = $4/hour, N = $6 and T=
16 hours/day.
a. What is “fullincome”? Write the equation for the budget line.
b. Find the optimal bundle. Show answer on a graph.
c. Derive this worker’s leisure demand function and labor supply function.
d. At what wage rate would this worker be indifferent between working and not working? (That is, at what
wage rate would the optimal L be 16?). Show answer on a graph.
e. At level of nonlabor income would this worker be indifferent between working and not working? (That
is, at what wage rate would the optimal L be 16?). Show answer on a graph.
f. Suppose the wage rate fell to $3 per hour. What would N have to be to leave this worker just as well as
before the decrease in the wage rate?
Do hours worked change? Why?
Show your answer on a graph.
g. Suppose the above job required the worker to work at least three hours. Would the worker still work?
Show your answer on a graph.
LABOR DEMAND
1. Assume Q = K
0.5
L
0.5
with K fixed at 16 units. The output price facing the firm is $50 and the going wage
rate is $10.
a. Find the MRP
L
function.
b. Find the profitmaximizing level of employment (L) and the corresponding output level (Q).
c. Find the firm’s
inverse shortrun demand function and the shortrun firm demand function for labor.
2. Firm is a monopoly in the output market but a price taker in the input market.
Market demand for
the product is P = 27 – 0.5Q. The wage rate is $10 per unit of labor. The firm’s
production function is Q = K
0.5
L
0.5
with K fixed at 16 units.
a. Find the MRP
L
function.
b. Find the profitmaximizing level of employment (L) and the corresponding output level (Q).
c. Find the firm’s
inverse shortrun demand function and the shortrun firm demand function for labor.
d. How does the L and Q found in part (b) compare with the level of employment and output in a
competitive output market?
3. Evaluate: “In
competitive output and input markets, the industry shortrun labor demand curve is
derived by simply horizontally summing up all individual firm’s MRP
L
curves. “
4. Assume that a firm desires to produce Q
1
using the two inputs labor and capital. Now suppose the price
of labor rises. On a clearly drawn graph, show the substitution and scale effects of the change in the price
of labor. Directly below this graph
sketch in the conditional and unconditional L demand curves.
5.. Suppose a firm has monopsony power and faces two types of labor given by the following inverse labor
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 Spring '10
 Jeong
 Utility

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