Determine the equation for average total cost for the firm.
Question 1- Suppose there is a perfectly competitive industry where all the firms are identical with identical cost curves. Furthermore, suppose that a representative firm’s total cost is given by the equation TC = 100 + q2 + q where q is the quantity of output produced by the firm. You also know that the market demand for this product is given by the equation P = 1000 – 2Q where Q is the market quantity. In addition you are told that the market supply curve is given by the equation P = 100 + Q.
a. What is the equilibrium quantity and price in this market given this information?
b. The firm’s MC equation based upon its TC equation is MC = 2q + 1. Given this information and your answer in part (a), what is the firm’s profit maximizing level of production, total revenue, total cost and profit at this market equilibrium? Is this a short-run or long-run equilibrium? Explain your answer.
c. Given your answer in part (b), what do you anticipate will happen in this market in the long-run?
d. In this market, what is the long-run equilibrium price and what is the long-run equilibrium quantity for a representative firm to produce? Explain your answer.
e. Given the long-run equilibrium price you calculated in part (d), how many units of this good are produced in this market?
Question 2 – The market for study desks is characterized by perfect competition. Firms and consumers are price takers and in the long run there is free entry and exit of firms in this industry. All firms are identical in terms of their technological capabilities. Thus the cost function as given below for a representative firm can be assumed to be the cost function faced by each firm in the industry. The total cost and marginal cost functions for the representative firm are given by the following equations:
TC = 2qs2 + 5qs + 50
MC = 4qs + 5
Suppose that the market demand is given by:
PD = 1025 – 2QD
Note: Q represents market values and q represents firm values. The two are different.
a) Determine the equation for average total cost for the firm.
b) What is the long-run equilibrium price in this market? (Hint: since the market supply is unknown at this point, it’s better not to think of trying to solve this problem using demand and supply equations. Instead you should think about this problem from the perspective for a firm. Specifically, a long run equilibrium occurs where ATC = MC = Price)
c) What is the long-run output of each representative firm in this industry?
d) When this industry is in long-run equilibrium, how many firms are in the industry? (Hint: firms are identically sized).
Now suppose that the number of students increases such that the market demand curve for study desks shifts out and is given by,
PD = 1525 – 2QD
e) In the short-run will a representative firm in this industry earn negative economic profits, positive economic profits, or zero economic profits? (Hint: You can solve this without calculation.)
f) In the long-run will a representative firm in this industry earn negative economic profits, positive economic profits, or zero economic profits? (Hint: again, no calculation required).
g) What will be the new long-run equilibrium price in this industry?
h) At the new long-run equilibrium, what will be the output of each representative firm in the industry?
i) At the new long-run equilibrium, how many firms will be in the industry?
Now, consider another scenario where technology advancement changes the cost functions of each representative firm. The market demand is still the original one (before the increase in the number of students). The new cost functions are:
TC = qs2 + 5qs + 36
MC = 2qs + 5
j) What will be the new equilibrium price? Is it higher or lower than the original equilibrium price?
k) In the long-run given this technological advance, how many firms will there be in the industry?
Question 3 –
a) Describe the factors that drive profits to zero in perfectly competitive markets in the long run. Explain carefully the incentives that drive the market to a long run equilibrium.
b) Why would a firm choose to operate at a loss in the short run? Explain carefully.
c) When do firms decide to shut down production in the short run? Explain carefully.
d) Draw a graph for a perfectly competitive market, specifically showing the short run supply curve. What is the relationship between the short run supply curve and what we talked about in parts (b) and (c)? Explain carefully.
Question 4 – Consider a perfectly competitive market in the short run. Assume that market demand is P = 100 – 4QD and market supply is P=QS. Denoting firm level quantity by q, assume TC=50+4q+2q2 so that MC=4+4q.
a) What is the market equilibrium price and quantity?
b) How many firms are in the industry in the short run?
c) Do firms make a profit or loss in the short run, and how much are these profits/losses?
d) What is the equilibrium price in the long run? What will be equilibrium profit in the long run? How many firms will there be in the long run? Hint, for the last part of the question, assume that there can be fractional firms, if necessary – if the numbers of firms are in units of 10,000, for example, the answer will be fine. Moreover, assume the entry or exit in the industry will cause the supply curve to shift, while the demand curve does not shift. Therefore, industry output can be found by taking the long-run price and plugging it into the demand curve.
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