There are currently 40 firms in the perfectly competitive tobacco farming indust
ID: 1105640 • Letter: T
Question
There are currently 40 firms in the perfectly competitive tobacco farming industry. All firms have identical production technology, and hence identical cost functions C(q) = 1 + 5q2. Marginal cost is MC(q) = 10q. Market demand is known to be QD(p) = 100 6p. a) (2 Points) Determine each firm’s supply function qS(p). b) (2 Points) Determine the short run market supply function QS(p). c) (2 Points) What will be the market equilibrium price of tobacco in the short run? d) (2 Points) Determine whether the firm would want to shutdown or operate according to its supply function. e) (2 Points) What type of profits are tobacco firms earning in the short run? Do you expect firms to enter or exit or neither? f) (2 Points) Determine the long run price and number of tobacco farmers. g) (2 Points) Illustrate the transition to the long run equilibrium in graph. In your graph should be the long run market price, short run market price, MC, and AC. Clearly indicate how the price changes from the short run to long run. h)(2 Points) Suppose there was a demand shock for the good. Specifically, people learn of the health dangers of tobacco and demand decreases to QD(p) = 50 6p. Determine the new short run equilibrium price and profits. i) (2 Points) How will this demand shock affect firms’ behavior? Would you expect firms to enter or exit? j) (2 Points) Determine the new long run equilibrium price and number of firms. k) (2 Points) Illustrate the transition to the new long run in a graph. This graph should be at the market level. Illustrate the initial long run, the new short run, and the new long run. Your graph should also illustrate the relevant shifts in supply and demand.
Explanation / Answer
(a) For each firm, its supply function is its Marginal cost (MC) function.Therefore, supply function is:
p = 10q, or
q = p / 10 = 0.1p
(b) Since there are 40 firms, market supply (QS) = 40 x q
q = QS / 40
QS / 40 = 0.1p
QS = 4p [Market supply]
(c) In equilibrium, QD = QS
100 - 6p = 4p
10p = 100
p = 10
Q = 4 x 10 = 40
q = Q / 40 = 40/40 = 1
(d) When q = 1,
Average variable cost (AVC) = Total variable cost / q = 5q2 / q = 5q = 5 x 1 = 5
Since price is higher than AVC (10 > 5), firm will continue production in short run.
(e) When q = 1,
C(q) = 1 + (5 x 1 x 1) = 1 + 5 = 6
Total revenue (TR) = p x q = 10 x 1 = 10
Profit = TR - C(q) = 10 - 6 = 4
There is positive economic profit in short run, therefore new firms will enter the market.
NOTE: First 4 parts are answered.
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