(a) Martha has $200 to spend on sneakers and sweaters. Sneakers cost $50 per pair and sweaters cost $20 each. She is thinking about buying 2 pairs of sneakers and 5 pairs of sweaters. She tells you that the additional utility that she would get from the second pair of sneakers is the same as the additional utility that she would get from the fifth sweater, i. e., the marginal utility of the second sneaker is equal to the marginal utility of the fifth sweater. Show that this bundle (2 sneakers and 5 sweaters) is not optimal. Tell her how she can increase her utility by reallocating her expenditures (while still spending the same amount in total, $200). Note that I am not looking for a specific numerical answer in terms of numbers of sneakers and sweaters. I want to know what she should buy more of and what less. Explain your answer. (b) The demand equation for a Good A has been estimated to be the following:
Q_A=1,000 50 P_A - 100 P_B+ 0.1 Y,
Where Q_A is the quantity of Good A, P_A is the price of good A, P_B is the price of good B, and Y is the income. Find the income elasticity of demand when Y = $1,000 and Q_A = 200. Is Good A inferior or normal? Explain your answer.
(c) The price of a good falls, and the consumer buys more of the good. Is the good normal, inferior, or can you not tell?