Question

Suppose the production function is given by formula Q = KL.

A) Draw the isoquant curve for Q = 128. (Draw K on the vertical axis and L on the horizontal axis.)

B) Suppose K = 4. How many units of labor should the firm use if it wants to produce 128 units of output? Label it point X on the isoquant curve.

C) Suppose K = 8.How many units of labor should the firm use if it wants to produce 128 units of output? Label it point Y on the isoquant curve.

D) What is the marginal rate of technical substitution between points X and Y? Explain.

Answer #1

Suppose a business estimates his production function to be ?? =
?? ^0.25?? ^0.75 where Q is the output, K amount of capital and L
is amount of labor. Price of labor (wage rate) is $10 and price of
capital is $15.
(a) Calculate the slope of isoquant curve.
(b) Calculate the slope of isocost curve.
(c) Suppose the firm wants to produce 100 units of output. Find
the optimal combination of labor and capital.

A firm’s production function is Q = min(K , 2L), where Q
is the number of units of output produced using K units of capital
and L units of labor. The factor prices are w = 4 (for labor) and r
= 1 (for capital). On an optimal choice diagram with L on the
horizontal axis and K on the vertical axis, draw the isoquant for Q
= 12, indicate the optimal choices of K and L on that isoquant,...

A firm produces an output with the production function Q=K*L2,
where Q is the number of units of output per hour when the firm
uses K machines and hires L workers each hour. The marginal product
for this production function are MPk =L2 and MPl = 2KL. The factor
price of K is $1 and the factor price of L is $2 per hour.
a. Draw an isoquant curve for Q= 64, identify at least three
points on this curve....

Suppose a firm’s production function is given by Q = L 1/2 , K
1/2.
a) Suppose the firm has a fixed cost FC=6, the price
of labor is w = 64 and the price of capital is r = 4. Derive the
firm’s total cost function, TC(Q).
b) What is the firm’s marginal cost?
c) Graph the firm’s isoquant for Q = 20 units of
output. On the same graph, sketch the firm’s isocost line
associated with the total...

Suppose the production function for widgets is given by
q = kl -0.8k2- 0.2l2,
where q represents the annual quantity
of widgets produced, k represents annual capital input, and l
represents annual labor input.
Suppose k = 10; graph the total and average productivity of
labor curves. At what level of labor input does this average
productivity reach maximum? How many widgets are produced at that
point?
Again, assuming that k = 10, graph the MPL curve. At
what...

A firm produces an output with the production function Q = KL,
where Q is the number of units of output per hour when the firm
uses K machines and hires L workers each hour. The marginal
products for this production function are MPK= L and MPL= K. The
factor price of K is 4 and the factor price of L is 2. The firm is
currently using K = 16 and just enough L to produce Q = 32....

A firm’s production function is given by Q = 5K1/3 +
10L1/3, where K and L denote quantities of capital and
labor, respectively.
Derive expressions (formulas) for the marginal product of each
input.
Does more of each input increase output?
Does each input exhibit diminishing marginal returns?
Prove.
Derive an expression for the marginal rate of technical
substitution (MRTS) of labor for capital.
Suppose the price of capital, r = 1, and the price of labor, w
= 1. The...

Draw a graph showing the effect of a decrease in the price of
capital on the combination of capital and labor that the firm
selects, holding output constant at 10. Capital is on the y-axis
(vertical axis) and labor on the x-axis (horizontal axis). Suppose
that the production function is given by Q=min{K,5L}. Identify the
amount of capital and labor that will be used to produce 10 units
given the original price and label it A. Identify the amount of...

Draw isoquant curve for the following production functions.
Here ?Kdenotes quantity of capital input and ?Ldenotes the
quantity of labor input.
In the graph, let ?Kbe on the vertical axis and ?Lbe on the
horizontal axis.
(a) ?(?,?)=?⋅?=?¯,F(K,L)=K⋅L=Q¯,where
(1) ?¯=100,Q¯=100,
(2) ?¯=200,Q¯=200,
(3) ?¯=300.Q¯=300.
This production function is an example of Cobb-Douglas
production technology.
(b) ?(?,?)=2?+5?=?¯,F(K,L)=2K+5L=Q¯,where
(1) ?¯=100,Q¯=100,
(2) ?¯=200,Q¯=200,
(3) ?¯=300.Q¯=300.
This production function is an example of perfect substitutes
production technology.
(c) ?(?,?)=min{2?,5?}=?¯,F(K,L)=min{2K,5L}=Q¯,where
(1) ?¯=100,Q¯=100,
(2) ?¯=200,Q¯=200,
(3)...

Draw isoquant curve for the following production functions.
Here ?Kdenotes quantity of capital input and ?Ldenotes the
quantity of labor input.
In the graph, let ?Kbe on the vertical axis and ?Lbe on the
horizontal axis.
(a) ?(?,?)=?⋅?=?¯,F(K,L)=K⋅L=Q¯,where
(1) ?¯=100,Q¯=100,
(2) ?¯=200,Q¯=200,
(3) ?¯=300.Q¯=300.
This production function is an example of Cobb-Douglas
production technology.
(b) ?(?,?)=2?+5?=?¯,F(K,L)=2K+5L=Q¯,where
(1) ?¯=100,Q¯=100,
(2) ?¯=200,Q¯=200,
(3) ?¯=300.Q¯=300.
This production function is an example of perfect substitutes
production technology.
(c) ?(?,?)=min{2?,5?}=?¯,F(K,L)=min{2K,5L}=Q¯,where
(1) ?¯=100,Q¯=100,
(2) ?¯=200,Q¯=200,
(3)...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 23 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

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago