Question

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 cost of producing Q = 20 units of output. To get this total cost, you must use the total cost function from part a). For the isocost line, clearly identify the vertical and horizontal intercepts. For the isoquant, clearly identify 4 combinations of labor and capital that will produce Q = 20.... include the bundle that minimizes the firm’s cost of production.

Answer #1

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,...

Suppose that a firm's production function is Q =
10L1/2K1/2. The cost of a unit of labor (i.e.
the wage) is $20 and the cost of a unit of capital is $80.
a. What are the cost minimizing levels of capital and labor if
the firm wishes to produce 140 units of output?
b. Illustrate your answer for part (a) on a well-labeled diagram
that shows the firm's production isoquant and isocost equation.

3. A firm’s production function is Q=min(K, 3L ). Input prices a
re as follows: w=$ 2 and r=$1.
On the optimal choice diagram below, draw the isoquant for Q=12.
Calculate the optimal choice of K and L for this level of output as
well as the total cost.
Then, draw in (with a dotted line) the isocost line consistent
with your Total Cost value.
It won't let me copy the graph template but it is a simple graph
with...

Suppose a firm’s production function is given by Q = L1/2*K1/2.
The Marginal Product of Labor and the Marginal Product of Capital
are given by:
MPL = (K^1/2)/2L^1/2 & MPK = (L^1/2)/2K^1/2)
a) (12 points) If the price of labor is w = 48, and the price of
capital is r = 12, how much labor and capital should the firm hire
in order to minimize the cost of production if the firm wants to
produce output Q = 10?...

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...

A firm’s production function is Q(L,K) = K^1/2 + L. The firm
faces a price of labor, w, and a price of capital services, r.
a. Derive the long-run input demand functions for L and K,
assuming an interior solution. If the firm must produce 100 units
of output, what must be true of the relative price of labor in
terms of capital (i.e. w/r) in order for the firm to use a positive
amount of labor? Graphically depict this...

1. (a) Based on the production function: Q = 2K1/2L1/2, please
draw the isoquant with Q=10.
(b) Given r=1; w=2, please draw the isocost with TC=27, on the
same graph.
(c) Based on the isoquant and isocost curves you drew, is TC=27
the cheapest cost of producing Q=10? Is Q=10 the maximum quantity
given TC=27? Explain.

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...

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. A cost minimizing firm’s production is given by
Q=L^(1/2)K^(1/2)
. Suppose the desired output is
Q=10. Let w=12 and r=4. What is this firm’s cost minimizing
combination of K & L? What it the
total cost of producing this output?
b. Suppose the firm wishes to increase its output to Q=12. In
the short run, the firm’s K is fixed
at the amount found in (a), but L is variable. How much labor
will the firm use? What will...

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