a. A monopolist producing and selling cooking gas faces a demand curve,

Q = 100 - 0.2P. If Total Cost is TC=4000+ 50Q.

i. Determine the quantity of cooking gas she will produce and the price she will charge to maximize profits and determine her profit.

ii. Explain how her profits she will affected if regulators forced her to operate like a perfectly competitive firm.

iii. Illustrate and compute dead-weight loss and lost consumer surplus associated with her Monopoly operations.

a. Suppose the joint cost function of a firm producing two products X and Y IS given by C = 250X² + 120Y². Assuming that output of the two products is restricted at 1369.

i. Using Lagrangian multiplier technique find the amounts of X and Y that will minimize cost and compute this cost.

ii. Examine the cost implications of changing this optimal combination so as to produce 236 additional units of X and 236 fewer units of Y.