Log in
Economics
2
answers
0
watching
329
views

Consider a profit-maximizing firm with the following production function: f(x1,x2) = ½x1x2.

The prices of the two inputs are equal to w1= 4 and w2= ½ 2, respectively

.a) What are the returns-to-scale properties of the firm’s production technology. Prove your answer.

.b) What input combination should the firm use to produce Q units of output?

.c) What is the firm's total cost of production as a function of the amount of output, Q?

.d) What is its marginal and average cost of production?

.e) Suppose the price of the first input falls to $2. What input combination should the firm use

now to produce Q units of output? What is its total, marginal, and average cost of production?

Watch
2
answers
0
watching
329
views

For unlimited access to Homework Help, a Homework+ subscription is required.

Unlock all answers

Get 1 free homework help answer.
Already have an account? Log in
Share
Chika Ilonah
Chika IlonahLv10
28 Sep 2019
Already have an account? Log in
Share

Related textbook solutions

Principles of Economics
2nd Edition, 2017
Openstax
ISBN: 9781947172364
Principles of Macroeconomics
2 Edition,
Openstax
ISBN: 9781947172388
Principles of Microeconomics
2 Edition,
Openstax
ISBN: 9781947172340

Related questions

A firm produces output using two factors of production according to technology f(x1, x2) = X1^1/2*X2^1/4. The price of output is 4. Factors 1 and 2 costs to the firm w1 and w2 per unit, respectively.

(i) Write an expression for the firm's profit.

(ii) Write an equation having on the left-hand side the marginal product of input 1 times the price of output and on the right-hand side its wage (w1). Do the same for input 2.

(iii) Solve the two equations you found in (ii) in the two unknowns, x1 and x2. (This will give the amounts of factors 1 and 2 that maximize the firm's profits.)

(iv) If w1 = 2 and w2 = 1, how many units of factors 1 and 2 will the firm demand? How much output will it produce? How much profit will it make?

- Essay Question:

Assume a firm uses two inputs in its production process: labour and capital. Using isocost and isoquant analysis, examine the possible effects of an increase in wage on the firm’s

(a) use of labour and capital

(b) long-run total and average costs.

- Problem Question:

a) Derive the cost minimizing input demands and the long-run total cost function for the following production functions assuming input prices w1 and w2:

(i) y = f(x1, x2) = 2x1 + x2

(ii) y = min(x1, 3x2)

b) For each of the production functions above, determine the short-run input demands and short run total cost function when input 2 is limited to x2 = 100 units

Suppose that a fully automated production process can produce output according to the production function Q = 10K – 0.5K2 where Q = output and K = capital input. Assume further that the expression for the marginal product of capital, MPK, is given as MPK = 10 – K. In this production process capital costs $90 to rent (MFC = $90) and the output sells for $30 per unit (and therefore P = MR = $30).

a. Based on this information, what is the expression for the marginal revenue product of capital, MRPK in this production process? 

b. Given that the production function has a single variable input, what is the optimal quantity of capital the firm should rent (K*) given the existing rental cost of capital and price per unit of output?

c. Based on the optimal rental of capital, how much output (Q) would this company produce per production period? Total Output (Q) = ____________________.

Weekly leaderboard

Home
Homework Help 3,900,000
Economics 400,000
Start filling in the gaps now
Log in