1. Industry demand function: Q = 14 - ½P + 0.001(Income). Marginal Cost is fixed and equal to $16. Fixed costs = $0. You are uncertain about the level of income. Your statistics department believes that there are 4 reasonable probable income levels with the following probabilities. 10% chance income is 80,000; 50% chance income is 60,000; 30% chance income is 50,000; and 10% chance income is 30,000.
a. Calculate the appropriate value to use for income in your analysis. Explain why you choose to use that level of income.
b. Assume this industry is a monopoly; determine the optimal price, corresponding level of sales and total profit earned by the monopolist. Show your work.
c. In the unlikely event that the highest possible income ($80,000) is realized how much profit has the monopoly missed out on by underproducing?
d. If this industry was perfectly competitive, what would be the industry wide price and output level? How do you know? At this price how much profit would there be in the industry? (For this part use the income you calculated in part a)
e. What is the dead weight loss associated with monopoly. If you can't calculate the exact value, show the area on a graph.
Bonus: Repeat parts b and e assuming the industry is a Cournot oligopoly.