Question

1. Schmutz Auto Wash provides car washes. Its production
function is ? = 2?^{1/2}(? - 1)^{1/2}

where ? is cars washed per day, ? is daily hours of labor input,
and ? is daily usage of capital inputs. The price of a unit of
capital input is $48. The price of a unit of labor input is $16. In
the short run, Schmutz has one unit of capital input installed (so
? = 1).

a). Find Schmutz’s short run daily total cost function, short run daily variable cost function, and short run daily fixed costs.

b). Find Schmutz’s short run marginal cost function, short run average variable cost function, and short run total cost function.

c). Suppose that the market for car washes is perfectly competitive and the going market price of a car wash is ?. Find Schmutz’s short run daily supply function, including its shutdown price.

d). Find Schmutz’s short run daily quantity supplied, producer surplus, and profit if ? = 40.

Answer #1

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 ???...

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...

1. Consider the Cobb-Douglas production function Q = 6 L^½ K^½
and cost function C = 3L + 12K. (For some reason variable "w" is
not provided)
a. Optimize labor usage in the short run if the firm has 9 units
of capital and the product price is $3.
b. Show how you can calculate the short run average total cost
for this level of labor usage?
c. Determine “MP per dollar” for each input and explain what the
comparative...

The production function is q = (10KL)/(K+L)
where L = labor, K= capital
The cost function is C = wL + vK where w = wages and v = cost of
capital
Assume K is fixed in the short run at K = 20
a.) Find the short run cost function. Find also the short run
average and marginal costs.
b.) The shut-down price is defined as the minimum of average
variable cost. For this cost function, what is the...

A car wash firm calculates that its daily production (in number
of cars washed) depends on the number n of workers it employs
according to the formula P=40n-0.05n^2 cars. Calculate the marginal
product of labor for the 51st worker and interpret the answer in
context

A firm produces good Q using inputs L & K. The firm’s
production function is X = 20L^0.5 + 11K. The
price of K is $P_K a unit and the price of L is $P_L a unit, and in
the short‐run, the capital input is
fixed at 3 units.
a. If the firm needs an output of X_1 in the short‐run, what is the
firm’s total cost and marginal
cost of production?
b. What is the firm’s fixed cost and...

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,...

A firm produces a product with labor and capital. Its production
function is described by Q = min(L, K). Let w and r be the prices
of labor and capital, respectively.
a) Find the equation for the firm’s long-run total cost curve as
a function of quantity Q and input prices, w and r.
b) Find the solution to the firm’s short-run cost minimization
problem when capital is fixed at a quantity of 5 units (i.e., K =
5). Derive...

(2) Consider the production function f(L, K) = 2K √ L. The
marginal products of labor and capital for this function are given
by MPL = K √ L , MPK = 2√ L. Prices of inputs are w = 1 per hour of
labor and r = 4 per machine hour. For the following questions
suppose that the firm currently uses K = 2 machine hours, and that
this can’t be changed in the short–run.
(e) What is the...

The production of sunglasses is characterized by the production
function Q(L,K)= 4L^1/2K^1/2.
Suppose that the price of labor is $10 per unit and the price of
capital is $90 per unit. In the short-run, capital is fixed at
2,500. The firm must produce 36,000 sunglasses. How much money is
it sacrificing by not having the ability to choose its level of
capital optimally? That is, how much more does it cost to produce
36,000 sunglasses the short-run compared to the...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 14 minutes ago

asked 23 minutes ago

asked 32 minutes ago

asked 47 minutes ago

asked 50 minutes ago

asked 50 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago