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 ?...

A firm’s production function is Q = 0 + 6L + 5L2 -
.2L3 + 3K+ 2K2- .2K3. The firm is
currently producing output with a fixed amount of capital K =10. It
hires labor with a wage rate of PL = Wage = 120. Suppose
the firm is currently employing 10 units of L along with 10 units
of K. The marginal cost of production is _____. Conduct an analysis
using an Excel Spreadsheet and changing Labor by 1,...

A firm faces the following production function
y = K0.5L0.4
where the rental cost of capital is 20, the wage is 5 and the price
of the output is 25.
(a) In short run, capital cannot be changed and is equal to 25.
What will be the maximum profit of the firm?
(b) What can the firm do when we get to the long run? What is
the optimum level of output and the maximum profit in the
long-run?
(c)...

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

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.

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...

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?

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