Q. 1. Use production function q(L, K) = L'"ª KV and derive the followings: Short-run and long-run profit functions Short-run and long-run cost functions Short-run and long-run supply function using Hotelling's lemma. Short-run and long-run supply function using Shephard's lemma. (a) (b) (d)

Q. 1. Use production function q(L, K) = L'"ª KV and derive the followings: Short-run and long-run profit functions Short-run and long-run cost functions Short-run and long-run supply function using Hotelling's lemma. Short-run and long-run supply function using Shephard's lemma. (a) (b) (d)

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter7: Proudction Costs

Section: Chapter Questions

Problem 11SQP

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Are there fixed costs in the lung-run? Explain briefly.
Exercise 3 A firm has a long-run cost function Cl(y) = y 3 − 10y 2 + 30y. (1) Derive the firm’s long-run average cost function. (2) Derive the firm’s long-run marginal cost function. (3) Find the level of production with the lowest average cost. (4) What is the long-run supply function for this firm? (5) If the market price is p = $18, how much would the firm decide to produce?
Q. 1. Use production function q(L, K) = L'"ª KV* and derive the followings: (a) (b) (c) (d) Short-run and long-run profit functions Short-run and long-run cost functions Short-run and long-run supply function using Hotelling's lemma. Short-run and long-run supply function using Shephard's lemma.
COURSE: ECONOMY A company has a total cost function TC = 80+3q+2q2 and a marginal cost function MC = 3+4q. If market price is P = $30 and it is producing 10 units:(a) Is firm maximizing its profits?b) What quantity should it produce in long run? Hint: MC= ATCc) Construct a table with all costs.d) Plot profit maximization points in short and long run.
2. Suppose the hourly wage is $10 and the price of each unit of capital is $25. The price of output is constant at $50 per unit. The production function is f(E, K) = E'/²K'/2. (a) Write a firm's short-run profit maximization problem. (b) Find a firm's marginal product of labor MP(E). (c) Find the second order condition and derive the labor demand function (i.e. An increase in wage decreases the number of workers hired). (d) If the current capital is fixed at 1,600 units, how much labor should the firm employ in the short run? (e) How much profit will the firm earn?
2. A competitive firm uses two variable factors to produce its output, with a production function q min{x₁, x₂}. The price of factor 1 is $8 and the price of factor 2 is $5. Due to a lack of warehouse space, the company cannot use more than 10 units of x₁. The firm must pay a fixed cost of $80 if it produces any positive amount but doesn't have to pay this cost if it produces no butput. What is the smallest integer price that would make a firm willing to produce a positive amount? b. d. $44 $41 $29 $13 $21
The table below shows the short-run cost data of a perfectly competitive firm that produces plastic camera cases. Assume that output can only be increased in batches of 100 units. Quantity 0 It must fall. 100 200 300 400 500 600 It must rise to offset the increased cost. Total Cost Variable Cost (dollars) (dollars) $1,000 $0 1,360 360 1,560 560 1,960 2,760 4,000 5,800 Suppose the fixed cost of production rises by $500 and the price per unit is still $8. What happens to the firm's profit-maximizing output level? The firm will shut down. O It will remain the same. 960 1,760 3,000 4,800
3.
A perfectly competitive industry currently has 100 identical firms in the short run, each of which has fixed costs of S8 and average variable costs as follows: Quantity Total cost Average variable cost Marginal cost Average total cost N/A N/A N/A 1 4 7 6 11 a) Complete the above table by computing the total cost, marginal cost, and average total cost for each quantity from 1 to 6. Submit the completed table in your answer. b) Suppose the market equilibrium price is currently $15. How much will each firm produce in the short run? What is the aggregate supply in this market in the short run? c) The initial market equilibrium price is still $15, but we now consider what will happen in the long run, when firms can freely enter and exit the market. Suppose that all entrants have the same costs, and that these costs are as in the previous table. As this industry makes the transition from short run equilibrium to its long-run equilibrium, how will the new equilibrium price change? Will it…
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