As revealed in class, Qi's world is comprised of two goods, Chinese food (X) and sports cars (Y). Qi's utility function in term of X and Y can be characterized as U = 2XY . Suppose (hypothetically) that PX = $2, PY = $1, and income I = $20. a) Suppose at the moment Qi is consuming 4 units of X and 12 units of Y . Is this an optimal bundle? If not, how should Qi improve this bundle toward an optimal consumption bundle? b) Disregard your answer in Part a). Solve for Qi's Marshallian demand, i.e., the optimal level of X and Y . 2 c) If X is an inferior good and Y is a normal good, when price of Y increases, what will happen to the optimal consumption bundle between X and Y ? Perform a general prediction by analyzing the income and substitution effects. d) Draw a graph of income and substitution effects that is consistent with your prediction in Part c). e) Based on your drawing, which effect seems to dominate? Explain your reasoning. f) Derive the demand curve for Y based on your answers in Part c)

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To determine if the current bundle is optimal we need to compare the marginal utilities per dollar spent on each good The marginal utility of X is given by UX 2Y and the marginal utility of Y is UY 2X ... View the full answer