Suppose the utility function of a consumer of goods x and y has the simple form u(X, Y) = √X. Y a) Graph (sketch) the u= 10 indifference curve associated with this utility function.

b) If X= 5, what must Y be equal to on the u= 10 indifference curve. What is the marginal rate of substitution (MRS) at this point?

c) In general, develop an expression for MRS for this utility function showing how this can be interpreted as the ratio of marginal utilities for X and Y

Suppose that two firms produce differentiated products and compete in prices. as in class, the two firms are located at two ends of a line one mile apart. consumers are evenly distributed along the line. the firms have identical marginal cost, $60. firm b produces a product with value $110 to consumers. firm a (located at 0 on the unit line) produces a higher quality product with value $120 to consumers. the cost of travel are directly related to the distance a consumer travels to purchase a good. if a consumerhas to travel a mile to purchase a good, the incur a cost of $20. if they have to travel x fraction of a mile, they incur a cost of $20x. (a) write down the expressions for how much a consumer at location d would value the products sold by firms a and b, if they set prices p_{a} and p_{b} ? (b) based on your expressions in (a), how much will be demanded from each firm if prices p_{a} and p_{b} are set? (c) what are the nash equilibrium prices?