HomeworkLib
Question

For this problem, please use a continuous cost function and allow the firm to produce non-integer...

For this problem, please use a continuous cost function and allow the firm to produce non-integer units of output. Consider a firm with production function:

Q=8K^(.2) L^(.6)

And which faces a wage of $10/unit and a rental rate on capital of $30/unit.

a) Please write the long-run cost function of this firm.

b) Please write the equation for the long-run marginal cost function and the long run average cost function of this firm.

c) In the long-run, how much will this firm offer to the market and what are the profits of the firm when the price of output is $10?

d) Please write the short-run cost function, the short-run marginal cost function, and the short-run average cost function of the firm when capital is fixed at .03125. Draw the supply curve of the firm.

e) How much will this firm offer to the market and what are the profits of the firm when the price of output is $10?

f) Please give an intuitive explanation for the differences in your answers for parts c) and e).

g) For what value of Q are the short-run cost function and the long-run cost function equal?

business   economics   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

0 0
Add a comment
Know the answer?
Add Answer to:
For this problem, please use a continuous cost function and allow the firm to produce non-integer...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • For a constant cost industry in which all firms the same cost functions, their long-run average...

    For a constant cost industry in which all firms the same cost functions, their long-run average cost is minimized at $10 per unit output and 20 units (i.e. q = 20). Market demand is given by QD=DP=1,500-50P. Find the long-run market supply function Find the long-run equilibrium price (P*), market quantity (Q*), firm output (q*), number of firms (n), and each firm’s profit. The short-run total cost function associated with each firm’s long-run costs is SCq=0.5q2-10q+200. Calculate the short-run average...

  • Suppose a firm has a total cost function, T C = 3/8(Q^2) − 50, and therefore...

    Suppose a firm has a total cost function, T C = 3/8(Q^2) − 50, and therefore marginal costs of MC = 3/4Q. Assume the market for this firm’s goods is perfectly competitive with a market price, P = 24. (a) Given the information above, is the firm in the short-run or long-run? (1 point) (b) Write down the firm’s marginal revenue equation. (1 points) (c) How many units should the firm produce if it wants to maximize profit? (3 points)...

  • Suppose that a particular firm is in a perfectly competitive constant-cost industry. When it is using...

    Suppose that a particular firm is in a perfectly competitive constant-cost industry. When it is using the optimal amount of capital for the long-run, total cost is C(q)=1000+(q2/10), ATC(q)=(1000/q)+q/10, and marginal cost is MC(q)=2q/10. This implies that ATC=MC at a quantity of 100 and a per unit cost of $20. 1. At what quantity is average total cost minimized? 2. What is the long-run competitive equilibrium price? 3. If market demand is QD=12,000-200P and short-run market supply is QS=300P, what...

  • NEED ALL ANSWERS PLEASE Problem 3 [24 marks] A competitive firm uses two inputs, capital (k) and labour (), to produce...

    NEED ALL ANSWERS PLEASE Problem 3 [24 marks] A competitive firm uses two inputs, capital (k) and labour (), to produce one output, (y). The price of capital, W, is S1 per unit and the price of labor, wi, is SI per unit. The firm operates in competitive markets for outputs and inputs, so takes the prices as given. The production function is f(k,l) 3k025/025. The maximum amount of output produced for a givern amount of inputs is y(k, l)...

  • 2. Assume that a monopolists sells a product in the short- run with a total cost function STC(Q)-...

    Please write essential steps and clear writing 2. Assume that a monopolists sells a product in the short- run with a total cost function STC(Q)- 108 125 + 440 Q2 Q >0 The market demand curve is given by the equation P(Q)80- 2Q (a) Find the marginal cost for the firm. (b) Find the profit-maximizing output and price (P", (c) What are the monopolists profits? (d) Does the monopolist want to stay in business? 2. Assume that a monopolists sells...

  • Problem 3: A firm has a production function ?(?,?) = ?? with associated marginal products ???...

    Problem 3: A firm has a production function ?(?,?) = ?? with associated marginal products ??? = ?, ??? = ?. The price of labor is ? = 18 and the price of capital is ? = 2. In the short run, capital is fixed at ?̅ = 3. a) Find the long run total cost function. b) Find the short run total cost function. c) Find the short run average cost function. d) What is the firm’s short run...

  • 2. An industry consists of many identical firms, each with the cost function C(q) = 100...

    2. An industry consists of many identical firms, each with the cost function C(q) = 100 + 30q – 8q2 + q3 a. Derive the average cost, average variable cost, and marginal cost curves of a firm. b. Compute the outputs at which the AC and AVC curves reach their minimums. C. If the market price is $40, and each firm is a price-taker, how much output will each firm supply? d. How much profit or loss is each firm...

  • 3. Suppose the firm in monopolistic market faces the following demand function: Q = 5,000 -...

    3. Suppose the firm in monopolistic market faces the following demand function: Q = 5,000 - 125P ; and total cost function TC - 50 +0.00802 a. Write the equation for the inverse demand function. (1 pt) b. Find the marginal revenue function. (1 pt) c. How much output should the manager produce to maximize profit? What price should be charged for the output? (2 pt) d. Calculate the marginal cost function. (2 pt) e. At the output level, how...

  • Suppose a firm's production function is Q = (KL)0.5. In the short run, this firm's capital stock ...

    Suppose a firm's production function is Q = (KL)0.5. In the short run, this firm's capital stock is fixed at 100. Calculate the firm's short run total cost curve if w = 5 and v = 5. It can be shown (using calculus) that this firm's short run marginal costs are .1Q. In order to maximize its profits, how much would the firm choose to produce if the market price of its output was $5, $10, or $20. For each...

  • Consider a firm with the following production function y = 20K21 For the whole exercise let...

    Consider a firm with the following production function y = 20K21 For the whole exercise let the price of a unit of capital be $200, the price of a unit of labor be $150 and consider the case where capital is fixed at K = 1. a) Calculate the short run profit of the firm when the price of output is $300. (5 points) b) Calculate the short run cost function. (5 points) c) On the same graph, plot the...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT