1. Sally's utility function is U = 4q0.5 + 92. (a) Derive Sally's Engel curves to show how Sally's consumption depends on income. (b) Suppose p = 2, p2 = 4, and q2 * 0. Draw Sally's Engel curve for q2 as her income grows from $10 to $70. (c) Classify each good. Are they normal or inferior? How do you know? (d) Calculate Sally's income elasticity of demand for q2 when her income is $50. Interpret. 1 2. Jackie's utility function for music tracks (9) and live music (92) is given by U = q4q26. In Homework 1, you calculated Jackie's uncompensated demand functions given prices,p and p2, and income, Y. In class, we calculated Jackie's compensated demand function for q. Use those results to show that the Slutsky equation (as elasticities) holds for Jackie's consumption of 91. Hint 1: Calculate each component of the Slutsky equation. You should get numbers for each component. Hint 2: How will you get numbers if there are a lot of variables? First, note that each of the elasticities depends on Jackie's optimal choice of good 1 (music tracks). Use her uncompensated demand function in your simplification process. Second, note that compensated demand holds Jackie's original utility level constant. Use indirect utility in your simplification process. 3. Vinny's utility function for gym time (g) and beach time (b) in a given quarter is U = g0.5 0.5. (a) Derive Vinny's uncompensated (Marshallian) demand functions. Let the price of gym time be pg and the price of beach time be pb. Let income be Y. (b) Derive Vinny's compensated (Hicksian) demand function for beach time. Let the price of gym time be pg and the price of beach time be pb. Let income be Y. (c) Suppose Vinny has $500 to spend. One hour of gym time costs $5 and one hour of beach time costs $2. How many hours will Vinny spend at the gym in a given quarter? What about the beach? (d) Suppose the beach closest to Vinny's house closes down, forcing him to go to a beach further away. This increases the cost of beach time to $4. Now how many hours will Vinny spend at the gym versus the beach in a given quarter? (e) Calculate the substitution effect from the price change for beach time. (f) Calculate the income effect from the price change for beach time. 1. Sally's utility function is U = 4q0.5 + 92. (a) Derive Sally's Engel curves to show how Sally's consumption depends on income. (b) Suppose p = 2, p2 = 4, and q2 * 0. Draw Sally's Engel curve for q2 as her income grows from $10 to $70. (c) Classify each good. Are they normal or inferior? How do you know? (d) Calculate Sally's income elasticity of demand for q2 when her income is $50. Interpret. 1 2. Jackie's utility function for music tracks (9) and live music (92) is given by U = q4q26. In Homework 1, you calculated Jackie's uncompensated demand functions given prices,p and p2, and income, Y. In class, we calculated Jackie's compensated demand function for q. Use those results to show that the Slutsky equation (as elasticities) holds for Jackie's consumption of 91. Hint 1: Calculate each component of the Slutsky equation. You should get numbers for each component. Hint 2: How will you get numbers if there are a lot of variables? First, note that each of the elasticities depends on Jackie's optimal choice of good 1 (music tracks). Use her uncompensated demand function in your simplification process. Second, note that compensated demand holds Jackie's original utility level constant. Use indirect utility in your simplification process. 3. Vinny's utility function for gym time (g) and beach time (b) in a given quarter is U = g0.5 p0.5 (a) Derive Vinny's uncompensated (Marshallian) demand functions. Let the price of gym time be pg and the price of beach time be pb. Let income be Y. (b) Derive Vinny's compensated (Hicksian) demand function for beach time. Let the price of gym time be pg and the price of beach time be pb. Let income be Y. (c) Suppose Vinny has $500 to spend. One hour of gym time costs $5 and one hour of beach time costs $2. How many hours will Vinny spend at the gym in a given quarter? What about the beach? (d) Suppose the beach closest to Vinny's house closes down, forcing him to go to a beach further away. This increases the cost of beach time to $4. Now how many hours will Vinny spend at the gym versus the beach in a given quarter? (e) Calculate the substitution effect from the price change for beach time. (f) Calculate the income effect from the price change for beach time.