The Paraguayan edible sock market is perfectly competitive and has market demand that
can be represented by the equation P = 200 – 2Q. Furthermore, you are told that all firms
in the market are identical and that the total cost function and the marginal cost function
for a representative firm are given by the following equations: TC = 100 + 20q + 10q2
and MC = 20 + 20q. There are 10 firms initially in this market.
a. Find the market supply curve given the above information. (2 pts)
b. Given the above information and the market supply curve you found in (a),
calculate the equilibrium price and quantity in this market in the short run. (2 pts)
c. If each firm is identical, how many units of output will each firm produce in the
short run? (2 pts)
d. Calculate the representative firm’s short run profits
a. To find the market supply curve, we need to sum up the quantities supplied by each firm at each price level. Since there are 10 identical firms in the market, we can simply multiply the quantity supplied by each firm by 10 to get the total market supply at each price level.
To get the quantity supplied by a single firm, we need to equate the market price (P) to the firm's marginal cost (MC) and solve for quantity (q):
P = MC
200 - 2Q = 20 + 20q
180 = 20q
q = 9
So, each individual firm will supply 9 units of output. Therefore, the market supply at each price level will be 10 * 9 = 90Q.
b. To find the equilibrium price and quantity in the short run, we need to set market demand equal to market supply and solve for price:
200 - 2Q = 90Q
200 = 92Q
Q = 2.1739
Plugging this quantity back into the demand equation to find the equilibrium price:
P = 200 - 2(2.1739)
P = 195.6522
Therefore, the equilibrium price is approximately $195.65 and the equilibrium quantity is approximately 21.74 units.
c. Each firm will produce 9 units of output in the short run as calculated in part a.
d. To calculate the representative firm's short run profits, we need to subtract total costs from total revenue:
TR = P * Q
TR = 195.65 * 9
TR = 1760.85
TC = 100 + 20(9) + 10(9)^2
TC = 100 + 180 + 810
TC = 1090
Profits = TR - TC
Profits = 1760.85 - 1090
Profits = 670.85
Therefore, the representative firm's short run profits are $670.85.