In: Economics

Consider a firm for which production depends on two normal inputs, labour and capital, with prices w and r, respectively. Initially the firm faces market prices of w = 6 and r = 4. The price of capital (r) then shifts to r = 6 while w remains the same. Use isocost-isoquant analysis to show and explain the following. A. In which direction will the substitution effect change the firm’s employment and capital stock? B. In which direction will the scale effect change the firm’s employment and capital stock? C. Can we say conclusively whether the firm will use more or less labour and more or less capital?

A firm uses two inputs in production: capital and labour. In the
short run, the firm cannot adjust the amount of capital it is
using, but it can adjust the size of its workforce. What happens to
the firm’s average-total-cost curve, the average-variable-cost
curve, and the marginal-cost curve when the cost of renting capital
increases?
The average-total-cost curve (shifts up/shifts
down/do not change) .
The average-variable-cost curve (shifts
up/shifts down/do not change) .
The marginal-cost curve (shifts up/shifts
down/do not change) ....

Consider a producer making choices over two inputs, labour (l)
and capital (k) with prices w = 3 and r = 1. The production
technology is f(l, k) = l + 3k.
What is the marginal rate of technical substitution (MRTS)? Is
there diminishing MRTS?
Find the input demands in long-run (as a function of output
level)?
Find the long-run total cost, marginal cost, and average cost
functions?
Do the properties of a typical cost function hold for the long...

A firm produces output y using two factors of production
(inputs), labour L and capital K. The firm’s production function is
?(?,?)=√?+√?=?12+?12. The wage rate w = 6 and the rental price of
capital r = 2 are taken as parameters (fixed) by the firm. a. Show
whether this firm’s technology exhibits decreasing, constant, or
increasing returns to scale. b. Solve the firm’s long run cost
minimization problem (minimize long run costs subject to the output
constraint) to derive this...

A competitive firm uses two inputs, capital (?) and labour (?),
to produce one output, (?). The price of capital, ??, is $1 per
unit and the price of labor, ?? , is $1 per unit. The firm operates
in competitive markets for outputs and inputs, so takes the prices
as given. The production function is ?(?, ?) = 3? 0.25? 0.25. The
maximum amount of output produced for a given amount of inputs is ?
= ?(?, ?) units....

A firm uses two inputs in production: capital and labor. In the
short run, the firm cannot adjust the amount of capital it is
using, but it can adjust the size of its workforce.
--
If the cost of renting capital increases, which of the following
curves will be affected? (Check all answers that apply).
--
Average variable cost
Marginal cost
Average fixed cost
Average total cost
2 points
QUESTION 2
If the cost of hiring workers increases, which...

Suppose there are two inputs in the production function, labor
and capital, and these two inputs are perfect substitutes. The
existing technology permits 5 machines to do the work of 2 workers.
So the production function is f(E, K) = 2K + 5E. The firm wants to
produce q units of output, where q > 0 is some number. Suppose
the price of capital is $10 per machine per hour. What combination
of inputs will the firm use if the...

Suppose there are two inputs in the production function, labor
and capital, which are substitutes. The current wage is $10 per
hour and the current price of capital is $25 per hour.
Given the following information on the marginal product of
labor and the marginal product of capital, find the firm’s
profit-maximizing input mix (i.e. number of workers and units of
capital) in the long-run. Show your work and explain.
L
MPL
K
MPK
1
125
1
130
2
100...

Consider a production function of two inputs, labor and capital,
given by Q = (√L + √K)2. Let w = 2 and r = 1. The marginal products
associated with this production function are as follows:MPL=(√L +
√K)L-1/2MPK=(√L + √K)K-1/2
a) Suppose the firm is required to produce Q units of output.
Show how the cost-minimizing quantity of labor depends on the
quantity Q. Show how the cost-minimizing quantity of capital
depends on the quantity Q.
b) Find the equation...

3. A perfectly competitive firm produces output y using two
factors of production (inputs), labour L and capital K. The firm’s
production function is ?(?, ?) = (?^1/2 + ?^1/2) ^2. The wage rate
is w = 9 and the rental price of capital is r = 1.
a. Find the long run equilibrium price p in this market.
b. Suppose in the short run, capital is fixed at K = 1. The
output price in the short run is...

Consider a firm producing one output using two inputs, capital
and labor. If the weak axiom of revealed profit maximization holds,
which of the conditions below describes the constraint implied by
profit maximizing behavior across any two periods?
1. delta(p)delta(q) >= delta(w)delta(L) -
delta(r)delta(K)
2. delta(p)delta(q) <= delta(w)delta(L) +
delta(r)delta(K)
3. delta(p)delta(q) >= delta(w)delta(L) +
delta(r)delta(K)
4. delta(p)delta(q) <= - delta(w)delta(L) +
delta(r)delta(K)

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