The cost function of a competitive firm is C = 16Q1/2 + Q2 in the long...

The cost function of a competitive firm is C = 16Q^1/2 + Q² in the long run after the fix costs are paid. The marker demand curve is estimated as D(P) = 200 – 15P. In the long run. What is the competitive equilibrium output level, competitive equilibrium price, and the number of firms in the market?

Expert Solution

Rahul Sunny answered 2 years ago

14. Each firm belonging to a competitive industry has the following long-run cost function C(q) =...

14. Each firm belonging to a competitive industry has the following long-run cost function C(q) = 10q − 2q^2 + q^3 where q denotes the output of a representative firm. Firms can enter and exit the industry freely. The industry has constant costs: input prices do not change as industry output changes. The market demand facing the industry is given by Q = 20 − P (a) Derive the long-run industry supply curve. [5 marks] (b) How many firms operate...

Suppose a competitive firm has a short-run cost function: C(q) = 100 + 10q − q^2...

Suppose a competitive firm has a short-run cost function: C(q) = 100 + 10q − q^2 + q^3 , where q is the quantity of output. 1. Is this a short-run or a long-run cost function? Explain. 2. Find the firm’s marginal cost function: MC(q). 3. Find the firm’s average variable cost function: AVC(q). 4. Find the output quantity that the firm AVC at the minimum. Does the MC increasing or decreasing before the quantity. And does the MC increasing...

A competitive firm has a single factory with the cost function c(y) = 4y2+ 89 and...

A competitive firm has a single factory with the cost function c(y) = 4y2+ 89 and produces 28 units in order to maximize profits. Although the price of output does not change, the firm decides to build a second factory with the cost function c(y) = 8y2+ 39. To maximize its profits, how many units should it produce in the second factory?

Consider a competitive firm. a) Sketch the cost function as a function of the price of...

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.

1. Consider the cost function, C = 2q^2(wr)^1/2. Suppose the firm with this cost function is...

1. Consider the cost function, C = 2q^2(wr)^1/2. Suppose the firm with this cost function is perfectly competitive in its output market and faces an output price, p. A. Find the marginal cost function for output. B. Find the average cost function. Show your work. C. Is this a long-run or short-run cost function? Explain. D. Derive the cost elasticity with respect to output. Show your formula and all calculations. What does this value of cost elasticity tell you about...

1- Given a Perfect competition firm cost function C(Q) = 5 + Q2 & Market Price...

1- Given a Perfect competition firm cost function C(Q) = 5 + Q2 & Market Price (P = $10 ) - Find MR - Maximum Profits p? - What is the Effect of Entry on Firms Output & Profit ? 2- If You are a monopolist with an inverse demand P = 100 – Q and Cost Function C(Q) = 125+4Q2 - Find Q* and P* - Max Tp

3. A firm in a perfectly competitive market has the following cost function: c(y) = 4y2...

3. A firm in a perfectly competitive market has the following cost function: c(y) = 4y2 + 450. a. If the market price of their product is $200, how many units should they produce, and what will their profits be? Should they shut down or exit the market? (2 points) b. If the market price falls to $50, how many units should they produce, and what will their profits be? Should they shut down or exit the market? (3 points)...

A competitive firm has the following short run cost function T C = Q 3 −...

A competitive firm has the following short run cost function T C = Q 3 − 8Q 2 + 30Q + 5 . (a) Find marginal cost, average cost, and average variable cost and sketch them on a graph. (b) At what range of prices will the firm supply zero output, i.e. shutdown? (c) Identify the firms supply curve (d) At what price would the firm supply exactly 6 units of output? (e) Compute the price elasticity of supply at...

Consider a competitive firm with the short-run cost function C(q) = 20 + 6q + 5q2...

Consider a competitive firm with the short-run cost function C(q) = 20 + 6q + 5q2 The firm faces a market price of p for its output. a. Derive the firm's profit maximizing condition. Is the sufficient second order condition satisfied? b. Suppose a specific tax of t (t < p) is levied on only this firm in the industry. What is the profit maximizing level of output as a function of p and t? (Assume the price is high...

A perfectly competitive firm has a total cost function equal to: C(Q) = 20,000 + 450Q...

A perfectly competitive firm has a total cost function equal to: C(Q) = 20,000 + 450Q - 4Q2 + 0.01Q3 If the market price for the firm is $142 and the firm is producing 220 units, what are their profits/losses? Refer to the firm above. What is the minimum market price the firm needs in order to produce in the short-run? Suppose you are a manager of perfectly competitive firm and at your optimal / profit-maximizing Q, ATC = $20...

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