Question

Perfect Competition Question

The market for study desks is characterized by perfect competition. All firms are identical; in particular, they have the same technology (and thus
the same cost function). The total cost function of the representative firm is given by the following equation:
TC = 4(q_S)²+8(q_S)+64

Suppose that the market demand is given by:
P_D = 840 − 2Q_D
Note: Q represents market values and q represents individual firm values.
a) Determine the equation for average total cost for the firm.
b) What is the long-run equilibrium price in this market?
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?
Now suppose that the number of students increases such that the market demand curve for study
desks shifts out and is given by P_D = 1240 − 2Q_D
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? (0.5 points)
i) At the new long-run equilibrium, how many firms will be in the industry?
Now suppose that the number of students had indeed increased compared to the the original
situation but by less than before and the new demand is P_D = 844 − 2Q_D
j) Calculate the long run equilibrium price, the long run ouput of each firm and the number of
firms in the long run. Compare you answer with subquestions a) to d). (hint: you will have to deal
with the integer problem).

Answer 1