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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%

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.

Solution Preview

1. Let me first introduce you the formula for calculating price elasticity of demand

elasticity = (P/Q) X (dQ/dP)

we know that output is 11 mil, so price = 17 - 11 = 6 $mil/mil pound.

p = 17 - Q gives us Q = 17 - P
hence dQ/dP = -1

now we plug everything back into the elasticity ...