1. Suppose that utility function and the budget line are given by:
U(X, Y) = X1/2.Y1/2.................... Utility function
PxX = PyY = M .................... Budget line
a. Derive MU functions for both goods.
b. Derive the Marshallian demand functions for X and Y.
c. If Px is $2 and Py is $3, and M (money income) is $120, graph and find the utility maximizing consumption bundle for the above utility function.
d. If consumers' income was increased by $30, find demand for X and Y and graph the new optimal point.
e. After the consumers' money income increased as noted in part d, the government imposed taxes on X by 50%, graph and find new utility maximizing consumption bundle (i.e demand for X and Y).
2. A beauty salon in a country-side university got enjoys a monopoly power since due to its geographical location and isolation from cities and villages. As a monopoly, the the salon provides all industry output to the university community. For simplicity, assume that the Salon operates with Marginal Cost = Average Total Cost = $10 per styling. Assume that demand curve for hair stylings and cutting in the University market is: P = 40 - 5Q
where Q is number of hair stylings per day (in 100) and P is the market price.
A. Graph and calculate the profit-maximizing price/output combination, economic profits, producer surplus, and consumer surplus if the Salon enjoys an effective monopoly power.
B. Graph and calculate the price/output combination, total economic profits, producer surplus, and consumer surplus that would result if competitors enter the market that make the market perfectly competitive.
C. Graph and calculate total deadweight loss if the industry is run by an unregulated monopoly.
D. Use the graph to help you ascertain the amount of consumer surplus transferred to the monopoly producer following a change from a competitive market to a monopoly market. How much is the net gain in producer surplus?
E. Use the graph to help you ascertain the value of transferred inputs to the rest of the economy following a change from a competitive market to a monopoly market. How much is the net gain in producer surplus?