Question

2. A firm has the following linear production function:

q = 5L + 2K

a. Does this firm’s production function exhibit diminishing returns to labor?

b. Does this production function exhibit diminishing returns to capital?

c. Graph the isoquant associated with q = 20.

d. What is the firm’s MRTS between K and L?

e. Does this production technology exhibit decreasing, constant, or increasing returns to scale?

Answer #1

1- diminishing returns to labour will be when the mrs is diminishing,

MRSl = Dq/DL = 5, then the mrs will not be diminishing as D(MRSl)/DL = 0

so answer is no

2- same is for capital as done above for labour

3- isoquanti is the curve that shows various combination of two inputs that a sller can use to produce a given amount of output,

so basically 20 = 5L+2K

now this is the equation of straight line, so basically this curve is going to be a downward sloping line with labour on x axis and capital on y axis, with x intercept as 4 and y intercept as 10

c- MRTSkl is the rate at which we are able to substitute one input for other such that the level of production remains the same

it is given by MPl/MPk = 2.5

Suppose a firm’s production function is given by Q = 2K^1/2 *
L^1/2 , where K is capital used and L is labour used in the
production.
(a) Does this production function exhibit increasing returns to
scale, constant returns to scale or decreasing returns to
scale?
(b) Suppose the price of capital is r = 1 and the price of
labour is w = 4. If a firm wants to produce 16 chairs, what
combination of capital and labor will...

3. Suppose that the production of one widget requires that three
units of labor (L) be used in conjunction with two units of capital
(K).
a. Write down the production function q = f(L, K) that
represents this production technology.
b. Graph the isoquant associated with 12 widgets.
c. Does this production technology exhibit decreasing, constant,
or increasing returns to scale?

2. Bridgestone Company has
the following production function for tires: Q = 20 K
0.2 L 0.8, where K represents machine hours
and L represents labor hours. They pay $ 15 per hour to rent their
machines and $ 10 per hour to their workers. They have $ 12,000 to
spend on capital and labor.
A. Does this production function
exhibit constant, increasing, or decreasing returns to scale?
B. Does this production function
exhibit diminishing marginal returns to capital and...

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 output according to the production function.
Q=sqrt(L*K) The
associated marginal products are MPL = .5*sqrt(K/L) and MPK =
.5*sqrt(L/K)
(a) Does this production function have increasing, decreasing, or
constant marginal
returns to labor?
(b) Does this production function have increasing, decreasing or
constant returns to
scale?
(c) Find the firm's short-run total cost function when K=16. The
price of labor is w and
the price of capital is r.
(d) Find the firm's long-run total cost function...

Suppose that you are given the
following production function:
Q =
100K0.6L0.4
For each of the following
production functions, determine whether returns to scale
are decreasing, constant, or increasing when capital and labor
inputs are increased from K = L =
1 to K = L = 2.
a. Q =
25K0.5L0.5
b. Q =
2K + 3L + 4KL

Consider the following production function q
= K2 + L2.
Does this production function exhibit constant, increasing or
decreasing returns to scale?)
Find an expression for the marginal rate of technical
substitution. Does this production function exhibit diminishing
marginal rate of technical substitution? Explain

Suppose that a rm has a production function given by Q=
5L^2/5K^1/5 (a) Show that there is a positive and diminishing
marginal product of labour, and a positive and diminishing marginal
production of capital. (b) Show that increasing K leads to an
increase in the marginal product of labor, and increasing L leads
to an increase in the marginal product of capital.

The production function of good x is as follows: Q =
(L^0.5)(K^0.4)
a. Does this production function have increase, constant or
decreasing returns to scale? _______(Answer either IRS, DRS or
CRS)
b. Calculate the slope of the isoquant when the entrepreneur is
producing efficiently with 10 laborers and 20 units of capital.
Slope = ______(Answer as a fraction or decimal.)
c. If we increase the amount of labor we use in our production
process from 10 to 15 units, how...

Cobb-Douglas Production Function & Cost of
Production
A firm’s production function is given as –
q =
2K0.4N0.6
What kind of returns to scale does this production technology
exhibit? Justify your answer.
Find out the expression for the marginal product of labor.
Find out the expression for the marginal product of
capital.
Find out the expression for MRTS.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 21 minutes ago

asked 29 minutes ago

asked 31 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago