1. Consider a personal computer market with two firms, X and Y. Suppose that Firm X and Y have the following total cost function: TCX=10QXTCY=10QY . The market is given by P=100-QX-QY.
(a) Calculate the Cournot equilibrium outputs of firm X and Y in this market. (b) Calculate their market price in the Cournot equilibrium. (c) Calculate their profits in the Cournot equilibrium.
(d) Suppose that firm X is considering implementing a proprietary technology they have developed. The onetime sunk cost of implementing this process is $300. Once the investment is made, marginal cost will be reduced to $4. Firm Y has no access to this, or any other cost-saving technology, and its marginal cost will remain at $10. Is it worthwhile for firm X to implement this technology or not? Prove your answer.
2. A monopolist sells in two markets. The demand curve for the monopolist’s product is x1=a1-b1P1 in market 1 and x2=a2-b2P2 in market 2, where x1 and x2 are the quantities sold in each market, and P1 and P2 are the prices charged in each market. The monopolist has zero marginal costs. Note that although the monopolist can charge different prices in the two markets, it must sell all units within a market at the same price. (a) Under what conditions on the parameters (a1,b1,a2,b2) will the monopolist optimally choose not to price discriminate? (Assume interior solutions) (b) Now suppose that the demand function take the from xi=AiPi-bi, for i=1,2 and the monopolist has some constant marginal cost of c>0. Under what conditions will the monopolist choose not to price discriminate?
3. A consumer has preferences which are described by the function: Ux1,x2=3x1+2x2, so that MU1=32x1 and MU2=1x2.
(a) Derive a formula for the person’s Engel curve for good x1, at general prices P1 and P2. (b) Derive the demand curve for good x1
(c) Derive the person’s indirect utility and expenditure function (d) Sketch the Engel and demand curves; mark the curves precisely (e) Do the...
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