There two goods, X and Y , available in arbitrary non-negative quantities (so the consumption set is R2+). A consumer has preferences over consumption bundles that are strongly monotone, strictly convex, and represented by the following (di erentiable) utility function: u(x; y) = x + xy + y; where x is the quantity of good X and y is the quantity of good Y . The consumer has wealth w > 0. The price for good X is p > 0, and the price for good Y is q > 0. (a) In an appropriate diagram, illustrate the consumers map of indi erence curves. Make sure you label the diagram clearly, and include as part of your answer any calculations about the slopes of the indi erence curves and where the indi erence curves intersect either of the axes. (b) Formulate and solve the consumer's utility maximization problem. Your nal answer should describe the consumer's demand for goods X and Y as a function of w, p, and q, as well as the consumer's indi- rect utility function.
There two goods, X and Y , available in arbitrary non-negative quantities
(so the consumption set is R2+). A consumer has preferences over consumption bundles that are strongly monotone, strictly convex, and represented by the following (di erentiable) utility function:
u(x; y) = x + xy + y;
where x is the quantity of good X and y is the quantity of good Y .
The consumer has wealth w > 0. The price for good X is p > 0, and the price for good Y is q > 0.
(a) In an appropriate diagram, illustrate the consumers map of indi erence
of your answer any calculations about the slopes of the indi erence
curves and where the indi erence curves intersect either of the axes.
(b) Formulate and solve the consumer's utility maximization problem.
Your nal answer should describe the consumer's demand for goods
X and Y as a function of w, p, and q, as well as the consumer's indi-
rect utility function.
(c) Now assume that w = 100 and p = 10.
(i) Illustrate the consumer's demand function for good Y in an appro-
priate diagram.
(ii) Illustrate the consumer's cross-price demand function for good X
in an appropriate diagram.
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