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%.
Hint: Calculate your price elasticity of demand based on the Columbian Delegates belief.
Given this price elasticity-what is the anticipated change in price as the result of an 10% decrease in output (remember monopolists and oligopolists control output not price; price is the result of output and demand)
Now-did the change in price resemble 20%
Question 1: 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?
Question 2: 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.