Question

Suppose a monopolist has a production function given by Q = L1/2K1/2. Therefore,MPL = , and MPK = 2/12/12LK2/12/12KLThe monopolist can purchase labor, L at a price w = 16, and capital, K at a price of r = 9. The demand curve facing the monopolist is P = 360 – 2Q.a) (8 points) What is the monopolist’s total cost function? b) (4 points) How much output should the monopolist produce in order to maximize profit?c) (6 points) How much labor should the firm hire to produce this output?d) (4 points) How Much Capital should the firm hire? e) (4 points) What price should the monopolist charge?f) (4 points) What is the deadweight loss?g) (4 points) What is the Price Elasticity of Demand at the profit-maximizing price and quantity?

Answer #1

Suppose a monopolist has a production function given by Q =
(L^1/2)/(K^1/2). Therefore, MPL =( k^1/2) / 2(L^1/2) , and MPK
=(L^1/2) / 2(k ^1/2)The monopolist can purchase labor, L at a price
w = 16, and capital, K at a price of r = 9. The demand curve facing
the monopolist is P = 360 – 2Q.
a) (8 points) What is the monopolist’s total cost function?
b) (4 points) How much output should the monopolist produce in
order...

Suppose a firm’s production function is given by Q = L1/2*K1/2.
The Marginal Product of Labor and the Marginal Product of Capital
are given by:
MPL = (K^1/2)/2L^1/2 & MPK = (L^1/2)/2K^1/2)
a) (12 points) If the price of labor is w = 48, and the price of
capital is r = 12, how much labor and capital should the firm hire
in order to minimize the cost of production if the firm wants to
produce output Q = 10?...

a. A cost minimizing firm’s production is given by Q=L1/2K1/2.
Suppose the desired output is Q=10. Let w=12 and r=4. What is this
firm’s cost minimizing combination of K & L? What it the total
cost of producing this output?
b. Suppose the firm wishes to increase its output to Q=12. In
the short run, the firm’s K is fixed at the amount found in (a),
but L is variable. How much labor will the firm use? What will the...

Answer the following questions about the producer’s production
function: Q = 2K1/2L2
Does the production function display increasing, constant, or
decreasing returns to scale? [Prove your answer by increasing all
inputs by a factor of c in your analysis.]
Find MPL if capital is fixed at K0=9 and
determine whether the production process follows the law of
diminishing returns (LDR) to labor.
If input prices are r=5 and w=4 for capital and labor,
respectively, and suppose MPK=40 and the firm...

Suppose that a firm's production function is Q =
10L1/2K1/2. The cost of a unit of labor (i.e.
the wage) is $20 and the cost of a unit of capital is $80.
a. What are the cost minimizing levels of capital and labor if
the firm wishes to produce 140 units of output?
b. Illustrate your answer for part (a) on a well-labeled diagram
that shows the firm's production isoquant and isocost equation.

Suppose the production function for new iPhones is Q =
17L0.3K0.8 and MPL = 5.1L-0.7K0.8 and MPK = 13.6L0.3K-0.2.
a.What is the equation (in terms of K and L) for the average
product of labor for this production function?
b.What is the equation for the MRTSLK for this production
function? Simplify.
c.If the isocost line for this firm is C = 12L + 8K, what is the
rental rate for capital?
d.If the MRTSLK is 2.33 when output is 276...

2. Suppose the demand function for a monopolist’s product is
given by: Q = 80 – 5P (Total marks = 5) and the cost function is
given by C = 30 + 2Q + 0.5Q2 A) What is the inverse demand function
for this monopoly? B) Calculate the MC. C) Calculate the MR. D)
Determine the profit-maximizing price. E) Determine the
profit-maximizing quantity. F) How much profit will the monopolist
make? G) What is the value of the consumer surplus...

Q1. A monopolist has the following
demand function and marginal cost function P = 120 – Q and MC = 30
+ Q.
i. Derive the monopolist’s marginal revenue function.
ii. Calculate the output the monopolist should produce to
maximize its profit.
ii. (continuation)
iii. What price does the monopolist charge to maximize its
profit?
Now assume that the monopolist above split into two large firms
(Firm A and Firm B) with the same marginal cost as the
monopolist.
Let...

A firm has the production function:
Q = L 1 2 K 1 2
Find the marginal product of labor (MPL), marginal
product of capital (MPK), and marginal rate of technical
substitution (MRTS).
Note: Finding the MRTS is analogous to finding the
MRS from a utility function:
MRTS=-MPL/MPK. Be sure to simplify your
answer as we did with MRS.
A firm has the production function:
Q = L 1 2 K 3 4
Find the marginal product of labor (MPL),...

A firm produces an output with the production function Q=K*L2,
where Q is the number of units of output per hour when the firm
uses K machines and hires L workers each hour. The marginal product
for this production function are MPk =L2 and MPl = 2KL. The factor
price of K is $1 and the factor price of L is $2 per hour.
a. Draw an isoquant curve for Q= 64, identify at least three
points on this curve....

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