Question

6. What do we mean by an isoquant? Why is it downward sloping? Why is it convex?

(a) Find the equation for an isoquant with Q= 48 for the
production function Q= 24 L^{1/4} K^{1/4} :

Prove that it is downward sloping and convex.

(b) What kind of returns to scale does the production function given above exhibit? What do we mean by that? What would the long-run average total cost look like?

(c) Suppose price of labor

(w) = 1 and price of capital (r) = 2. The market price for the output produced is P= 12.

For the production fumction given above,

i. find out the short-run cost function C (Q) I_{k=81} ,
and

ii. the profit maximizing choice of output and labor in the short-run. How much is the profit?

Answer #1

8.) What is the Phillips Curve? Why is it downward sloping in
the short-run if wages are stickier
than the prices of other goods and services? Why is it vertical
in the long-run?

A firm produces output (y), using capital (K) and labor (L). The
per-unit price of capital is r, and the per-unit price of labor is
w. The firm’s production function is given by, y=Af(L,K), where A
> 0 is a parameter reflecting the firm’s efficiency.
(a) Let p denote the price of output. In the short run, the
level of capital is fixed at K. Assume that the marginal product of
labor is diminishing. Using comparative statics analysis, show that...

1. Why is the MRP curve downward sloping? What factors cause it
to shift? Answer with respect to the MRP for each of the factors of
production.
2. Under what conditions is the labor supply curve upward
sloping? When is it backward bending? What factors cause the labor
supply curve to shift?
Thank you!!

Consider a firm that used only two inputs, capital (K) and labor
(L), to produce output. The production function is given by: Q =
60L^(2/3)K^(1/3) .
a.Find the returns to scale of this production function.
b. Derive the Marginal Rate of Technical Substitutions (MRTS)
between capital and labor. Does the law of diminishing MRTS hold?
Why? Derive the equation for a sample isoquant (Q=120) and draw the
isoquant. Be sure to label as many points as you can.
c. Compute...

Consider a firm using quantities L1 and L2 of two kinds of
labour as its only inputs in order to produce output Q=L1+L2. Thus,
each unit of labour produces one unit of
output. Suppose that we also have two segmented labor markets,
with the following inverse labor supply functions.
w1=α1+β1L1
w2=α2+β2L2
which shows the wage that must be paid to attract a given labor
supply. Assume that the firm is competitive and take price of
output P as given. (α1,...

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...

Consider a firm using the production technology given by q =
f(K, L) = ln(L^K)
If capital is fixed at K = 2 units in the short run, then what
is the profit maximizing allocation of output if the price of
output and respective input prices of labor and capital are given
by (p, w, r) = (2, 1, 5)?

In the short-run, we assume that capital is a fixed input and
labor is a variable input, so the firm can increase output only by
increasing the amount of labor it uses. In the short-run, the
firm's production function is
q = f(L, K),
where q is output, L is workers, and
K
is the fixed number of units of capital.
A specific equation for the production function is given
by:
q = 8LK + 5L2 − 13L3
or ,...

1.
True/False/Uncertain
Answer each of the following statements True/False/Uncertain.
Give a full explanation of your answer including graphs where
appropriate. (When in doubt, always include a fully labeled
graph.)
A) Firms typically make investment choices over a small time
horizon when profit maximizing.
B) The Cobb-Douglas production function can exhibit increasing,
decreasing, or constant returns to scale.
C) An isoquant represents every point of economically efficient
production for a given quantity.
D) In the short-run, the marginal product of labor...

1. In the short run, the firm ________ change the number of
workers it employs but ________ change the size of its plant.
A) can; can B) can; cannot C) cannot; can D) cannot; cannot
2.Jill runs a factory that makes lie detectors in Little Rock,
Arkansas. This month, Jill's 34 workers produced 690 machines.
Suppose Jill adds one more worker and, as a result, her factory's
output increases to 700. Jill's marginal product of labor from the
last worker...

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