Determine the social optimal price and quantity. Find consumer and producer surpluses under the social optimal condition. Determine the monopolistic price and quantity. Find consumer and producer surpluses under the monopoly condition. What is the deadweight loss caused by monopoly?

1. Firm’s cost function shows the relationship between total cost (C) and output (Q).
2. Derive the cost function by minimizing C = 2K + 10L subject to a production function of Q = K⁵L^0.3.
3. Does the average cost (AC) increase with output level? Show your work.
4. Is the marginal cost (MC) greater than the average cost? Show your work.

2. Suppose that a consumer has a Cobb-Douglas utility function U(X,Y)=100X^0.4Y^0.8 , where X and Y are quantities of goods X and Y consumed, with a budget constraint of P_xX + P_yY = M, where P_x, P_y, and M are the price of X, price of Y, and income (money), respectively.
3. Determine the demand functions of goods X and Y,
4. Write out the indirect utility function, V,
5. Prove that λ = ∂V/∂M.

3. Given an (inverse) demand function P = 485 – 5Q and the marginal cost curve

MC = 5  – Q + Q².  (Keep at least two decimal points in your calculations.)

1. Determine the social optimal price and quantity.
2. Find consumer and producer surpluses under the social optimal condition.
3. Determine the monopolistic price and quantity.
4. Find consumer and producer surpluses under the monopoly condition.
5. What is the deadweight loss caused by monopoly?