Suppose you have two types of customers. Type 1 customers typically purchases your firm's product in bundles of 100 units, while type 2 customers typically purchase less than 50 units. The cost of producing one unit is $1 plus packaging costs. Packaging costs $1 per unit for small orders, but only $10 for a bundle of 100 units. Finally, suppose type 1 buyers have a price elasticity of demand equal to -2, while type 2 buyers have an elasticity equal to -1.25. What price will you charge each type of buyer?

Suppose that your firm produces two products in fixed proportions, so that if you decide to produce one more unit of X, your firm must also produce one more unit of Y. If TC = 100 +3Q +1/2Q^{2} and the demand curves for X and Y are Qx=100-2Px and Qy=101-Py find the profit maximizing outputs.

a. Find the expressions for MR for good X and Y. (Hing solve each demand curve for P, multiply by Q, take the first derivative with respect to Q to get MR.)

b. Find the expression for MC.

c. Find the profit maximizing output.

d. Find the price of each good.

Suppose your firm produces electricity by burning coal. Currently it buys central Appalachia 12,500 BTU per ton coal at the market price of $52 per ton. The Board of Directors has informed you that currently the average cost of producing that coal is only $35 per ton. They therefore are considering buying the mine because this would save the $17 per ton of coal burned. (Each 500-megawatt power plant your firm owns burns about 1.4 million tons of coal per year.) They have asked you whether this is a good idea. What do you say?

In reference to limit pricing (a) suppose your firm produces a product at a constant marginal cost equal to $1. Suppose the elasticity of demand is -3. What is the profit-maximizing price if one ignores that possibility of entry? (b) Suppose at the above price economic profits are quite large, so your firm can expect entry. Assume that if one firm enters it would increase the elasticity of demand from -3 to -4, while if two firms enter it would increase the elasticity of demand to -6. What do you recommend that the firm do to deter entry? Discuss briefly.

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