a.
The firm is in the competitive market and in the long-run; therefore, equilibrium output be at the minimum of average total cost (min ATC).
Given, total cost (TC) as below:
TC = 2,000 + 20q + 5q^2
ATC = TC/q = 2,000/q + 20q/q + 5q^2/q
= 2,000/q + 20 + 5q
ATC would be the minimum if derivative of ATC with respect to q is 0.
ATC = 2,000/q + 20 + 5q
Derivative of ATC = - 2,000/q^2 + 0 + 5
0 = - 2,000/q^2 + 5
Now, by solving,
2,000/q^2 = 5
2,000 = 5q^2
2,000/5 = q^2
400 = q^2
Square root of 400 = q
q = 20
Answer: required equilibrium output is 20 units.
b.
Equilibrium price (P) in the long-run for a competitive firm is the min ATC. ATC would be the minimum if (q = 20).
P = min ATC
= 2,000/q + 20 + 5q
= 2,000/20 + 20 + 5 × 20
= 100 + 20 + 100
= 220
Answer: required equilibrium price is 220.
c.
The long-run price (220) should be placed in the demand equation in order to get equilibrium industry output (Qd).
Qd = 10,000 – 40P
= 10,000 – 40 × 220
= 10,000 – 8,000
= 2,000 (Answer)
A representative firm with long-run total cost given by TC = 2,000 + 20q + 5q2...
1. For a perfectly competitive firm, long-run average cost is: LAC = 300 - 20Q + 1.8Q2, where Q denotes the firm’s output. The firm’s long-run profit-maximizing price is _____. 2. Demand for a good is given by: QD = 50 – 2P and supply by QS = 1P – 10, where P is the market price of the good. In equilibrium, price would be ___. 3. Demand for a good is given by: QD = 50 – 2P and...
Numerical Example A representative firm is operating in a perfectly competitive industry. The firm’s total cost, TC, is given by the equation TC = 50 + 5q2 , where q is output. Based on this equation, the marginal cost, MC, is 10q. 1. If the output price is $100, what is the short-run profit-maximizing output? 2. How much profit does this firm make at that level of output? 3. What do you expect to happen in the market in the...
Suppose that the long-run total cost function for the typical mushroom producer is given by: TC=wq2 -10q+100 Where q represents the output of the typical firm and w represents the hourly wage rate mushroom pickers. The market for mushrooms is perfectly competitive. Suppose also that the demand for mushrooms is given by Q= -1000p+35,000 Where Q is the total quantity demand and P is the market price of mushrooms. 1. If the wage rate for mushroom pickers is $4.00, what...
Suppose that the market for laptops is perfectly competitive. These companies are identical with their long-run cost functions for a full day of keyboarding given by: TC(Q) = 6Q3-30Q2+200Q Market Demand is: Qd = 8,000 - 20P a. Find the long-run equilibirum price in this industry b. Use market demand to find the equilibrium total industry output. c. Find the equilibrium number of firms.
13. If Firm A operates in a perfectly competitive industry, with market price = $1,200/unit. If Firm A’s total cost function is given by TC(q)= 20q^2+ 80q + 200, find Firm A’s profit maximizing level of output. 14. Using the information from the above question: is the market in which Firm A is selling its output currently in long run equilibrium?
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...
Consider a representative firm with total cost of TC=16+Q^2 (and a marginal cost of of 2Q, MC=2Q). The market demand curve is given by P=18-(1/2)Q and the starting market price is $12. 1) Graph the starting condition of a comparative static scenario. 2) Annotate what happens in order to transition to the long run. 3) Graph the long run equilibrium using comparative statics. 4) How many firms are in the market in the long run?
All firms in a competitive industry have the following (firm-level) long-run total cost curve: C(q) = q3–10q2 + 36q where q is the output of the firm. a. Compute the long run equilibrium price. What does the long-run supply curve look like if this is a constant cost industry? Explain. b. Suppose the market demand is given by Q = 111–p. Determine the long-run equilibrium number of firms in the industry.
Consider a perfectly competitive industry in which each firm i has a total cost function given by the equation: TC= 128 + 4q+2q^2. Further assume that the industry demand function is given by the following: P = 84 – 2Q. a) Describe the long run market equilibrium. That is, identify the equilibrium price and quantity, output for each firm, the number of firms in the industry and the level of producer and consumer surplus. What is the value of own...
1. Each firm in a perfectly competitive industry has the long-run total cost function c(y) = 3y - (y^2/3) + (y^3/27) Demand is given by the inverse demand curve p = 15 - (Qd/600). Calculate, for the long-run equilibrium, a. The price b.The market quantity c. The number of firms d. The profit for each firm