Question

Given a short-run production function, Define its average product and marginal product.

Answer #1

A production function exhibits a functional relationship between the inputs used and output produced by the firm. Generally there are two types of inputs or factors used by the firm:variable factor and fixed factor of production. Production function can be given as Q = f(K, L) where K and L are capital and labor inputs.

Average product is total product divided by quantity of input used. Marginal product is the derivative of the total product with respect to the quantity of input used. In other words it is the ratio of change in total product change in quantity of variable input. Assume that production function is Q = L^2 + 2L + 20

Then, marginal product of labour = 2L + 2. Similarly average product of labour = L + 2 + 20/L.

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

Given the short run production function, Q = 3L2 –
0.1L3
( a) Write down the equations for,
(i) the marginal product of labor, MPL
(ii) the average product of labor, APL.
(b) Find the value of Q for which the MPL and APL are
maximized.
(c) Show that the MPL= APL when the APL is at a maximum

Will a firm experience diminishing marginal returns in the short
run if its production function is:
a. q = K+L?
b. q = KL?
C. q = KL^0· 5?

Suppose a firm's short-run production function is given by
Q = 14L +4KL. And, K is fixed at 1. What is the
marginal product of the fourth worker?
4
14
14L
18

Explain the relationship between short run marginal cost and short
run marginal product

If a firm’s production function exhibits constant returns to
scale, its short-run average cost curve must be horizontal. True or
False

1. Is the basic difference
between the short run and the long run that the law of diminishing
returns applies in the long run, but not in the short run?
2. Draw a typical
production function and explain its shape. Below that diagram, draw
an average product schedule and marginal product schedule. Indicate
the relationship between the two diagrams.
##3 Explain why the
marginal product of labour initially increases as more workers are
hired and then eventually...

10. Suppose the short-run production function is q =
L.5
.
If the marginal cost of producing the tenth unit is $5, what is
the wage per unit of labor?
A.$1
B.$0.25
C.$0.5
D.It cannot be determined without more information

How is a firm’s production function related to its marginal
product of labor? How is a firm’s marginal product of labor related
to the value of its marginal product? How is a firm’s value of
marginal product related to its demand for labor? Provide specific
examples to support your answers.

1A.What are the differences between a firm’s production in the
short run and the long run?
B. If the marginal product of labor is 6 and the marginal rate
of technical substitution between labor and capital is 1.5, what is
the marginal product of capital?
C. Find an example of fixed proportion in production.

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