Consider a competitive firm.
a) Sketch the cost function as a function of the price of good 1, assuming that the production function is Leontiff.
b) Sketch the cost function as a function of the price of good 2, assuming the production function is linear in good 2.
a) The following is an example of a Leontief production function:
The firm's cost function is given by:
From the given production function, the firm treats labor and capital as complements and always hires equal amounts of both at equilibrium. Hence, L = K = Q. The cost function now becomes:
In order to maximize profit, a competitive firm sets price equal to its marginal cost.
Hence,
Plotting the firm's cost with price on the vertical axis and quantity on the horizontal axis.
b) An example of a linear production function is:
The firm's cost function is given by:
Since the firm treats the two goods as perfect substitutes, it will only hire the factor which is cheaper. Hence, the firm's cost function is given by:
Following the same process as the previous part, a competitive firm sets price equal to its marginal cost to maximize profit. Cost function is:
Plotting the firm's cost with price on the vertical axis and quantity on the horizontal axis.
Consider a competitive firm. a) Sketch the cost function as a function of the price of...
A firm has the cost function That is, it has a fixed production capacity i, below which marginal cost is constant, at e (a) Sketch the firm's marginal- and average-cost function. (b) Solve for its profit-maximizing output if it sells in a perfectly competitive market. (e) Describe the solution possibilities for output if the firm is a profit- maximizing monopoly with linear demand (d) Identify the "shadow price of capacity in each of cases (b) and (c).
A firm has...
1. Consider the production function y = f(L,K) for a firm in a competitive market setting. The price of the output good is p > 0. The prices of the inputs Labour and Capital are w> 0 and r>0 respectively. The firm chooses L and K in order to maximize profits, (L.K). (a) How does the short-run production function differ from the long-run production function? (b) Write out the profit function for the firm, (L,K). (c) Derive the first order...
Question 4 Consider the Sunshine Company, a perfectly competitive firm with the following cost function TC 12006Q + 202 where Q is the firm's output per day. a) Find the firm's marginal cost function. [2 marks] C b) If the price of Sunshine's product equals $66, how many units per day should the firm produce? [4 marks] c) Find the firm's average variable cost function. [3 marks] d) Is average variable cost at the quantity you calculated in part b)...
1. Suppose a perfectly competitive firm has a cost function described by TC = 200Q + Q 2 + 225 Each firm’s marginal revenue is $240. a. Find the profit maximizing level of output. b. Is this a short-run or long-run situation? How do you know? c. Assuming that this firm’s total cost curve is the same as all other producers, find the long-run price for this good.
Consider a perfectly competitive market comprised of identical firms each facing the following cost function: C(q) = 4 +q? where q is the firm-specific level of production of the representative firm. The market demand function is Q(p) = 400 - 4p where Q(p) is the aggregate demand in the market (expressed as function of price) and p is the price a) Derive the firm-specific supply function of the representative firm as a function of price b) Assume there are N...
Consider the following cost curve for a firm in a competitive industry where the market price equals $200 C = 1/3q3+4q+750 What is the firm's marginal cost (MC)? MC = At what level of output does the firm maximize profits (minimize losses)? Profit is maximized at __units of output. (Round your answer to two decimal places.) What is the firm's profit maximizing price? The profit-maximizing price is $___ In the short-run, this firm should produce ____ .
Suppose that a price taker had a marginal cost function given by: MC = 10 + 2q. In a competitive market, the price is $20. If the firms in this industry form a cartel, this firm will have a production quota of 4 units. The cartel will be able to increase the price to $24. 21 betermine the producer surplus when the firm produces the production quota. 22)Suppose that if this firm cheats on the cartel, the price remains at...
3. [30%] Consider a competitive industry. Each firm has the following production func- tion: f (K, L) = K}L. WON (a) Set up the cost-minimization problem of the firm, given output y, output price p and input prices are WK = WL = 1. (b) Derive the firm's cost function. (c) Derive the equilibrium price p, given no entry cost to this industry.
(d) A perfectly competitive firm has the following production function: Q=L The price of labor is equal to w. If the firm maximizes profit and the price, p, is equal to 4w, then the firm will supply 2 units of output and profit is equal to 4w.
10)Consider two firms producing the same good for a common market. Firm 1 has the cost function ofc(q1)=2q1 and firm 2 has the cost function of c(q2)=q2. Assuming they compete as Bertrandduopolists, what price would you expect to prevail? a)1 b)2.5 c)2 d)3 need explain!