Question

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

Answer #1

An electronics plant’s production function is Q = L 2K, where Q
is its output rate, L is the amount of labour it uses per period,
and K is the amount of capital it uses per period.
(a) Calculate the marginal product of labour (MPL) and the
marginal product of capital (MPK) for this production function.
Hint: MPK = dQ/dK. When taking the derivative with respect to K,
treat L as constant. For example when Q = L 3K2 ,...

A firm produces good Q using inputs L & K. The firm’s
production function is X = 20L^0.5 + 11K. The
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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
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b. What is the firm’s fixed cost and...

The production function for a firm is Q = −0.6L 3 + 18L 2K + 10L
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(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...

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...

(2) Consider the production function f(L, K) = 2K √ L. The
marginal products of labor and capital for this function are given
by MPL = K √ L , MPK = 2√ L. Prices of inputs are w = 1 per hour of
labor and r = 4 per machine hour. For the following questions
suppose that the firm currently uses K = 2 machine hours, and that
this can’t be changed in the short–run.
(e) What is the...

1. Suppose a short-run production function is described as Q =
2L – (1/800)L^2 where L is the number of labors used each hour. The
firm’s cost of hiring (additional) labor is $20 per hour, which
includes all labor costs. The finished product is sold at a
constant price of $40 per unit of Q.
a. How many labor units (L) should the firm employ per hour
b. Given your answer in a, what is the output (Q) per hour...

The production function for a firm is given by q = L0.75 K0.3
where q denotes output; L and K labor and capital inputs
. (a) Determine marginal product of labor. Show whether or not
the above production function exhibits diminishing marginal
productivity of labor.
(b) Calculate the output (or production) elasticity with respect
to labor.
c) Determine the nature of the Return to Scale as exhibited by
the above production function. Show and explain all
calculations

A firm uses two inputs, capital K and labor L, to produce output
Q that can be sold at a price of $10. The production function is
given by Q = F(K, L) = K1/2L1/2 In the short run, capital is fixed
at 4 units and the wage rate is $5, 1. What type of production
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1. Suppose a short-run production function is described as Q =
2L – (1/800)L2 where L is the number of labors used each hour. The
firm’s cost of hiring (additional) labor is $20 per hour, which
includes all labor costs. The finished product is sold at a
constant price of $40 per unit of Q.
a. How many labor units (L) should the firm employ per hour:
b. Given your answer in a, what is the output (Q) per hour:...

A firm produces good X and has a production function X =
2L^0.25K^0.25, where L and K are the inputs.
Assume that the price of L is $6 and the price of capital is $12.
Let the firm have a target output
of X1 units.
a. Find the firm’s conditional demand for labor and capital.
b. Find the firm’s total cost function.
c. What is the firm’s marginal cost?

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