Question

Consider a firm using a 3-dimensional technology with long-run marginal cost function given by MC(q, w, r)

If d/dq[MC(q,w,r)] = 1/2 & MC(0,w,r) = 0

What is the elasticity of the quantity supplied with respect to the output price in the profit maximizing solution?

Answer #1

Consider a firm using the production technology given by q =
f(K, L) = ln(L^K)
If capital is fixed at K = 2 units in the short run, then what
is the profit maximizing allocation of output if the price of
output and respective input prices of labor and capital are given
by (p, w, r) = (2, 1, 5)?

Consider the following total cost function for an individual
firm:
C(q) = 10+ q + (1/4)q^2
The industry demand is estimated to be:
Q = 100 - P
1) Now suppose there is a monopolist facing the industry demand.
Write down the monopolist's pro t function.
2) What is the equation of the monopolists marginal revenue
function? Also, explain how the monopolist's marginal revenue
function differs from the marginal revenue function of a firm in a
long-run perfectly competitive market....

1. Consider a firm whose demand curve is given by Q =
300 – 2P and whose marginal cost is given
by MC = 70 + 3Q .
a. determine the profit-maximizing output.
b. determine the profit-maximizing price.
c. suppose that demand increases to Q = 500 –
2P , while marginal cost remains the same.
what happens to the firm’s profit-maximizing
price and output? (show your work)
d. is this result similar to what would happen...

A perfectly competitive firm in the short run has Total Cost and
Marginal Cost functions given by TC(Q)=9+Q+Q2 and
MC(Q)=1+2Q, respectively. The firm faces a price of P=$17.
Determine the output that the firm will produce and the profit.
Show the solution graphically.

a) Assume the firm operates in the monopoly market in the long
run with the demand function P = 100-Q and TC = 640 + 20Q with TC
showing the total cost of production, Q and P respectively of
output quantity and price. Using the information above,
publish
i) Total revenue function (TR)
ii) Marginal revenue (MR)
iii) Marginal cost function (MC)
iv) Determine the level of price and quantity of production that
maximizes profit
v) Determine the amount of...

The demand for product Q is given by Q = 136 -.4P and
the total cost of Q by:
STC = 3000 + 40Q - 5Q^2 + 1/3Q^3
A. Find the price function and then the TR function. See
Assignment 3 or 4 for an example.
B. Write the MR and MC functions below. Remember: MR =
dTR/dQ and MC = dSTC/dQ. See Assignment 5 for a review of
derivatives.
C.What positive value of Q will maximize total
profit? Remember, letting...

A resource firm faces the following demand function: P = 60 –
10Q. The marginal cost of extraction is $20. (MC = $20).
Using the Inverse Elasticity Pricing Rule, calculate the profit
maximizing output level and price.

The long run cost function for each (identical) firm in a
perfectly competitive market is C(q) =
q1.5 + 16q0.5 with long run
marginal cost given by LMC = 1.5q0.5 +
8q-0.5, where q is a firm’s
output. The market demand curve is Q = 1600 –
2p, where Q is the total output of all
firms and p is the price of output.
(a) Find the long run average cost curve for the firm. Find the
price of output and the amount of output...

3: For each (identical) firm in a perfectly competitive market
the long-run cost function is C(q) = q1.5 + 16q0.5 with long run
marginal cost being LMC = 1.5q0.5 + 8q-0.5, where q = firm’s
output. Market demand curve: Q = 1600 – 2p, where Q = total output
of all firms, and p = price of output. (a) For the firm find the
long run average cost curve , as well as the price of output and
the amount...

Suppose a firm’s long-run production function is given by
Q=K^0.25 L^0.25 ,where K is measured in machine-hours per year and
L is measured in hours of labor per year. The cost of capital
(rental rate denoted by r) is $1200 per machine-hour and the cost
of labor (wage rate denoted by w) is $12 per hour.
Hint: if you don’t calculate the
exponential terms (or keep all the decimals when you do), you will
end up with nice numbers on...

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