SHORT PROBLEMS
1. Consider the market for a Procter and
Gamble biodegradable detergent. Suppose that market demand is QD
= 120 â 3P, and market supply is QS
= â50 + 2P, where P is the price per case and Q is the quantity in thousands per week.
a. Find equilibrium quantity and price.
b. What is the value of consumer surplus (CS) and producer surplus (PS) at equilibrium?
c. If each case of detergent were sold at
$30, determine the amount of the shortage or surplus that would result.
2.
In the competitive market for
organic corn, market demand is QD = 340 â 2P and market supply is QS
= 100 + 4P, where P is the price per bushel, and Q is market output in thousands of
bushels. Each individual farmer faces a marginal cost function of MC
= 10 + 3q, where q is the single farmerâs output level in
thousands.
a. What is the equation for the demand (which is also MR) faced by the individual farmer?
b. Based on your answer to part (a), find the profit-maximizing
output level for each farmer.
c. At an output level of 8 thousand
bushels, explain in terms of both marginal profit and total profit why the
individual farmer should expand production.
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