Price Elasticity of Demand and Profit Maximizing Level of
Output
Question: In 1991, Brazil and Columbia united to form a
coffee cartel and reduce coffee output. Suppose total costs for the cartel are:
TC = 12 + 5Q + Q2
Here Q is millions of pounds of coffee.
The market demand curve for coffee is: P = 17 – Q
Here P is millions of dollars per million pounds. Suppose
before the cartel was formed, output was 11 million pounds.
In the Wall Street Journal a Columbian delegate to the
cartel said that he believed that if the cartel reduced coffee output by 10%,
the price would rise by 20%.
Questions:
a. Before the cartel was formed, What did the Columbian
delegate believe was the price elasticity? What was the actual price elasticity
before the cartel was formed?
b. Compute the profit maximizing level of coffee output, the
price the cartel should charge, the maximum cartel profits, and the price
elasticity at the optimal output.
