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%.

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%

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.