Question

A firm has a daily production function q = 2.5L^1/3K^1/3. Currently, the firm rents 8 pieces of equipment. The amount of equipment is fixed in the short run. The unit wage rate is $25 while the rental cost of capital is $100.

Find the short run production function.

Find the number of workers the firm wishes to employ to produce q units (the short run conditional demand for labor).

Find the firm’s short run total cost

Find the firm’s short run marginal cost.

Find the firm’s short run supply function.

The firm can sell its product at $60.

6. What is the profit maximizing output of the firm in the short run?

7. When producing the short run profit maximizing output, does the firm earn a profit, incur a loss or breaks even?

Answer #1

A firm has the following production function:
q=5LK^0.5+2L^2K-L^3K
What is its short-run production function if capital is fixed at
K=9?
What are the firm’s marginal product of labour and average
product of labour in the short run?
Show that the firm’s elasticity of output with respect to labour
in the short run is a function of marginal product of labour and
average product of labour. Calculate the short-run elasticity of
output with respect to labour

If we have a competitive industrial form that has the production
function q=z1^(1/4)*z2^(a)z3^(1/4)
q is the output, z1 z2 z3 is the production inputs and a is
parameter.
Assume that production input 2 (z2) is fixed in the short
run
1) Find the short run conditional input demand functions for the
firm
2) Find the short run cost function for the firm
3) Find the short run supply function for the firm
4) what happens to the conditional input demand,...

Question 1 A firm has a monopoly in the production of
antimacassars. Its factory is located in a town where no other
industry exists and the labour supply is W = 10 + 0.1L, where W is
the daily wage and L is the number of persondays of work performed.
The firm production function is Q = 10L, where L is daily labour
supply and Q is daily output. The demand curve for the good is P =
41 ?...

Suppose that a firm's fixed proportion production function is
given by q = min(2k, 4L), and that the rental rates for capital and
labor are given by v = 1, w = 3.
A) Calculate the firm's long-run total, average, and marginal
cost curves.
B) Graph these curves.
C) Suppose that k is fixed at 10 in the short run. Calculate the
firm's short-run total, average, and marginal cost curves and graph
them.
D) Now suppose in the long run...

1. Suppose a perfectly competitive firm has a cost function
described by TC = 200Q + Q^2 + 225 Each firm’s marginal revenue is
$240. a. Find the profit maximizing level of output. b. Is this a
short-run or long-run situation? How do you know? c. Assuming that
this firm’s total cost curve is the same as all other producers,
find the long-run price for this good.

Consider a firm with the following production technology q =
k0.5l0.5. The market price of the firm’s product is 10, and the
rental rates of capital and wage rate for labor are given,
respectively, by 2 and 3.
(e) If wage rate goes up to 4, what is the new level of profit
maximizing labor?
(f) Find the profit maximizing level

A firm's technology is represented by the production function q
= (KL)1/3
In the short run, K is fixed at 64 = 43
What is the firm's short run production function?
Find the short run conditional factor demand for L.
What is the short run cost function?
What is the shut down price?

A firm produces good Q using inputs L & K. The firm’s
production function is X = 20L^0.5 + 11K. The
price of K is $P_K a unit and the price of L is $P_L a unit, and in
the short‐run, the capital input is
fixed at 3 units.
a. If the firm needs an output of X_1 in the short‐run, what is the
firm’s total cost and marginal
cost of production?
b. What is the firm’s fixed cost and...

6.7 The production function
Q=KaLb where 0≤ a, b≤1 is called a Cobb-Douglas production
function. This function is widely used in economic research. Using
the function, show the following:
a. The production function in Equation 6.7 is a special case of
the Cobb-Douglas.
b. If a+b=1, a doubling of K and L will double q.
c. If a +b < 1, a doubling of K and L will less than double
q.
d. If a +b > 1, a doubling...

The production function for a firm is Q = −0.6L 3 + 18L 2K + 10L
where Q is the amount of output, L is the number of labor hours per
week, and K is the amount of capital.
(a)Use Excel to calculate the total short run output Q(L) for L
= 0, 1, 2...20, given that capital is fixed in the short run at K =
1.
(b) Use Excel to calculate the total long run output Q(L) for...

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