Question

If we have a competitive industrial form that has the production function q=z1^(1/4)*z2^(a)z3^(1/4)

q is the output, z1 z2 z3 is the production inputs and a is parameter.

Assume that production input 2 (z2) is fixed in the short run

1) Find the short run conditional input demand functions for the firm

2) Find the short run cost function for the firm

3) Find the short run supply function for the firm

4) what happens to the conditional input demand, the cost of production, and supply in short-run if there is a decrease in a?

Answer #1

Consider a firm whose production technology can be represented
by a production function of the form q = f(x1, x2) = x α 1 x 1−α 2
. Suppose that this firm is a price taker in both input markets,
with the price of input one being w1 per unit and the price of
input two being w2 per unit. 1. Does this production technology
display increasing returns to scale, constant returns to scale,
decreasing returns to scale, or variable...

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...

1. Acme Inc. produces widgets. Its production function
is ? = ? 1/3 (? − 1) 1/3 , for ? ≥ 0 and ? ≥ 1, where ? denotes
units of capital input, ? denotes units of labor input, and ?
denotes units of output. (Note that ? = 0 for all ? < 1.) The
price of a unit of capital input is ? and the price of a unit of
labor input is ?.
a. Find Acme’s ???...

A firm has the following production function: ?(?, ?) = ?
3/4?1/4 .
A) What is the firm’s Technical Rate of Substitution?
B) What is the optimality condition that determines the firm’s
optimal level of inputs?
C) Suppose the firm wants to produce exactly ? units and that
input ? costs $?? per unit and input ? costs $?? per unit. What are
the firm’s conditional input demand functions? D) Using the
information from part C, write down the firm’s...

Pinnacle Inc. produces industrial pins. Its production
function is ? = ?? 1/2 ? 1/2 , for ? ≥ 0 and ? ≥ 0, where ? denotes
units of capital input, ? denotes units of labor input, and ?
denotes units of output. The price of a unit of capital input is ?
and the price of a unit of labor input is ?.
a. Find Pinnacle’s ??? and ??? functions.
b. Find Pinnacle’s ??? function.
c. Find Pinnacle’s long...

A firm's technology is represented by the production function q
= (KL)1/3
In the short run, K is fixed at 64 = 43
What is the firm's short run production function?
Find the short run conditional factor demand for L.
What is the short run cost function?
What is the shut down price?

Every firm in a competitive market has the production
function
Q =
K.5L.5and it is observed
that long-run total market supply is described by the function P =
.025Q. These facts suggest that
This is a decreasing cost industry
This is an increasing cost industry.
The price of at least one input increases as market demand for
this good increases.
Some owners of resources used in the production of this product
earn economic rents.
None of the above.
If the...

A competitive firm has the production technology ?(ℓ, ?) = ℓ
0.2? 0.4 , where ℓ is labour and ? is
capital. The firm obtains labour and capital from competitive
markets with wage rate ? and capital rent rate ?, respectively.
Calculate the long-run conditional demand functions for labour
and capital; the longrun total, marginal, and average cost
functions; and the supply function for this firm taking ? = ? =
£1.

The long run cost function for each (identical) firm in a
perfectly competitive market is C(q) =
q1.5 + 16q0.5 with long run
marginal cost given by LMC = 1.5q0.5 +
8q-0.5, where q is a firm’s
output. The market demand curve is Q = 1600 –
2p, where Q is the total output of all
firms and p is the price of output.
(a) Find the long run average cost curve for the firm. Find the
price of output and the amount of output...

3: For each (identical) firm in a perfectly competitive market
the long-run cost function is C(q) = q1.5 + 16q0.5 with long run
marginal cost being LMC = 1.5q0.5 + 8q-0.5, where q = firm’s
output. Market demand curve: Q = 1600 – 2p, where Q = total output
of all firms, and p = price of output. (a) For the firm find the
long run average cost curve , as well as the price of output and
the amount...

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