Question
In: Economics
3. A perfectly competitive firm produces output y using two factors of production (inputs), labour L...
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 p = 3. Find the firm’s profit maximizing output in the short run.
Solutions
Rahul Sunny answered 2 years agoRelated Solutions
A firm produces output y using two factors of production (inputs), labour L and capital K....
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, (?)....
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....
Consider a perfectly competitive firm that produces output using a wellbehaved production function y = f(x1,x2)....
Consider a perfectly competitive firm that produces output using
a wellbehaved production function y = f(x1,x2). Let the price of
output be denoted by p, the price of input 1 be denoted by w1, and
the price of input 2 be denoted by w2.
(a) State the firm’s cost-minimization problem, and draw the
solution to the cost minimization problem on a graph.
(b) What are the solutions to the cost-minimization problem? What
are these solutions called? Which variables are these...
Consider a perfectly competitive firm that produces output using a wellbehaved production function y = f(x1,x2)....
Consider a perfectly competitive firm that produces output using
a wellbehaved production function y = f(x1,x2). Let the price of
output be denoted by p, the price of input 1 be denoted by w1, and
the price of input 2 be denoted by w2.
j) Suppose x2 is fixed at some level x2. Graph the
solution to the profit maximization problem where profit is maximized
by choosing x1. [Note that this profit maximization problem is the
short-run version of the profit...
In the short run, a perfectly competitive firm produces output using capital services (a fixed input) and labour services (a variable input).
In the short run, a perfectly competitive firm produces output
using capital services (a fixed input) and labour services (a
variable input). At its profit-maximizing level of output, the
marginal product of labour is equal to the average product of
labour.a. What is the relationship between this firm’s average variable
cost and its marginal cost?b. If the firm has 5 units of capital and the rental price of
each unit is €9/day, what will be the firm’s profit? Should it...
A firm uses two inputs in production: capital and labour. In the short run, the firm...
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) ....
The Production Function of a perfectly competitive firm is Q = 80L +12L2 -0.5L3, where Q = Output and L = labor input
The Production Function of a perfectly competitive firm is Q = 80L +12L2 -0.5L3, where Q = Output and L = labor input
a. At what value of L will Diminishing Returns take effect?
b. Calculate the range of values for labor over which stages I, II, and III occur?
c. Suppose that the wage rate is $30 and the price of output is $2 per unit. How many workers should the firm hire?
d. At what value of...
A perfectly competitive firm faces a price of $40 for the output it produces. Average Variable...
A perfectly competitive firm faces a price of $40 for the output
it produces. Average Variable Cost for the firm is equal to $30 per
unit and the firm's average fixed cost is equal to $20 per unit.
Determine if the following statement is either True or False. The
firm earns negative profits and should should shut down.
A firm produces a single output using two variable inputs (denoted ?1 and ?2). The firmproduction...
A firm produces a single output using two variable inputs
(denoted ?1 and ?2). The firmproduction function is given by ? =
Φ(?1, ?2) = (?1?2) ^0.5. The firm can employ as much of either
input it desires by incurring constant (and respectively denoted)
per-unit input costs of ?1 and ?2. Assume throughout that all
prices and quantities are positive and infinitely divisible.
Finally, let ?0 denote the “target” level of output that the firm
envisions producing when deciding how...
Consider a firm for which production depends on two normal inputs, labour and capital, with prices...
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...
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