2. Suppose that a perfectly competitive firm’s total cost of producing output q is T C(q) = 5 + 5q 6q2 + 4q3. (a) Find the short-run supply curve of a firm in this industry. Be sure to identify the point at which the firm shuts down. (b) How much will the firm produce at p⇤ = 5?
We have the following information
Total Cost (TC) = 5 + 5q + 6q2 + 4q3
Price = 5
In a perfectly competitive market structure the short-run supply curve of a firm is equal to the marginal cost (MC) curve.
MC = ΔTC/Δq = 5 + 12q + 12q2
In the short the shut-down point for a firm is that point where the price is equal to the minimum point of average variable cost (AVC)
From the TC function we can get the Variable Cost (VC) function as 5q + 6q2 + 4q3
AVC = VC/q = (5q + 6q2 + 4q3)/q
AVC = 5 + 6q + 4q2
Taking first derivative
ΔAVC/Δq = 6 + 8q
Equating it equal to zero we get
6 + 8q = 0
q = 8/6
q = 4/3
Taking the second derivative we get
Δ2AVC/Δq2 = 8
Since, the second derivative is positive so, at q = 4/3 the AVC is minimum.
For price equal to 5 the equilibrium quantity can be determined by equating it to the MC
Price = MC
5 = 5 + 12q + 12q2
12q + 12q2 = 0
12q(1 + q) = 0
So, either the q = 0 or the q = – 1. Since, quantity cannot be negative so at price 5 the equilibrium quantity is zero which means producers need higher price to start the production.
2. Suppose that a perfectly competitive firm’s total cost of producing output q is T C(q)...
In a perfectly competitive market, a firm has the following short-run total cost function: C(q)=16+4q+q2 The market demand is Q(p)=220-p a. Show that marginal cost curve passes through the minimum point of average cost curve. Draw a figure to show it. b. Find the firm’s individual short-run supply function. Draw it on the above figure. For the following questions, suppose that there are currently 10 identical firms in this market. c. What is the market supply curve? What are the...
20. Which of the following statements is not a characteristic of a perfectly competitive firm? a. Perfectly competitive firms view each other as fierce rivals. b. Firms are price-takers. c. All firms produce a homogeneous product. d. Perfectly competitive markets allow freedom of entry and exit. 21. Since the firm’s demand curve is perfectly elastic for a price-taking firm, a. P = MR. b. P = MRP. c. P = TR. d. both a and b. e. both a and...
Please solve the above sum (B) Q = 50k E (d) A firm in a perfectly competitive industry has the following long run cost function C(q) q-60q+1500q O) If the firm can sell its output at p Rs. 975, how much will it produce to maximise profit? (i) Is the output of the firm in (i)compatible with industry equilibrium? (Gii) If the industry is that of constant average cost, derive the equation for the long run supply curve of the...
Question: These diagrams, pertain to a perfectly competitive firm producing output q and the industry in which it operates. What should we expect in the long run on the number of firms, market supply and equilibrium price? MC ATC AVC MR P
The loss of a perfectly competitive firm which shuts down in the short run: Multiple Choice O is equal to its total variable costs. O O ь is zero. гето. O is equal to its total fixed costs. cannot be determined. Refer to the diagrams, which show the demand and cost curves for a perfectly competitive firm producing output and the demand and supply curve for the industry in which it operates. Which of the following is correct? ATC AVC...
The market for candy is perfectly competitive, and the current market price of candy is $10. A particular firm has a short-run marginal cost of production of MC = 0.2q, where q is the number of bicycles produced by the firm. a. If it is optimal for the firm to produce a positive amount of output in the short run, how much should it produce? b. Suppose that the firm has fixed costs of $30, and its average variable cost...
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)...
Question 27 A perfectly competitive industry is composed of 100 firms. Each firm has an identical short-run marginal cost function SMC = 5+10q (where q is the firm's level of output). If Q denotes industry output, what is the short-run market supply curve for output? a) Q = -50 + 10p if p > 5 and 0 if p 5 5 α Q = -5 + TOP p if p > 5 and 0 if p < 5 + α...
Suppose that a competitive firm's marginal cost of producing output q (MC) is given by MC(q) = 3 + 2q. Assume that the market price (P) of the firm's product is $15. What level of output (q) will the firm produce? The firm will produce units of output. (Enter your response rounded to two decimal places.) What is the firm's producer surplus? Producer surplus (PS) is $ . (Enter your response rounded to two decimal places.) Suppose that the average...
Suppose that a competitive firm's marginal cost of producing output q (MC) is given by MC(q) = 6 +29. Assume that the market price (P) of the firm's product is $18. What level of output (q) will the firm produce? The firm will produce 6.00 units of output. (Enter your response rounded to two decimal places.) What is the firm's producer surplus? Producer surplus (PS) is $ 36.00. (Enter your response rounded to two decimal places.) Suppose that the average...