Question

Suppose that there two goods X and Y, available in arbitrary non- negative quantities (so the the consumption set is R2). The consumer has preferences over consumption bundles that are strongly monotone, strictly convex, and represented by the following (differentiable) utility function: u(x, y)-y+2aVT, where z is the quantity of good X, and y is the quantity of good Y, and a 20 is a utility parameter The consumer has strictly positive wealth w > 0. The price of good Y is py 1. However, the price of good X depends on the quantity of good X that the consumer purchases. In particular, px(x) , where z is the quantity of good X the consumer purchases. (Note that px(r) is the price per unit when the consumer purchases x units) (1) In an appropriate diagram, illustrate (i) the indifference map for the consumer, and (ii) the consumer's budget set. Make sure you label diagrams clearly, and include as part of your answer any cal- culations about the slopes and intercepts of the indifference curves and the budget line. (2) Formulate and solve the consumer's utility maximization problem, and find the demand and value functions. Your demand and value functions should be functions of the paraeters w and a (3) Suppose w-10. In an appropriate diagram, illustrate the demand function for good X, x(a 10), and for good Y, y(al 10)

Answer 1

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