Utility Maximization with Substitutes Carol needs to decide how to spend her wealth on fish and chicken. For Carol, 1 lb of fish is equivalent to 2 lb of chicken. Her preferences can be represented by the utility function u(x, y) = 2x +y

where x is the quantity of fish (in lbs) and y is the quantity of chicken (in lbs). The consumption set is R 2 +. (a) Draw two typical indifference curves for Carol, one corresponding to a utility level of u1 and one corresponding to a utility level u2, where 0 < u1 < u2. Make sure you label the slope of the indifference curves and the intercepts with the horizontal and vertical axes. (b) Suppose the price of fish is $1.5 per lb and the price of chicken is $1 per lb. Carol has $20 to spend on fish and chicken. (i) Draw Carol’s budget set, labeling the slope and the intercept points clearly. (ii) How much fish and chicken will Carol choose to purchase? (c) Suppose now that the price of fish increases to $2 per pound. (i) Draw Carol’s budget set, labeling the slope and the intercept points clearly. (ii) How much fish and chicken will Carol choose to purchase? (d) Suppose that Carol goes to a different supermarket where the price of fish is pX > 0 (in dollars per pound of fish) and the price of chicken is pY > 0 (in dollars per pound of chicken). (i) Find Carol’s demand for fish as a function of the prices pX and pY . You can assume that she still has $20 to spend. (ii) Assume that the price of chicken is pY = 1. Draw Carol’s demand function for fish as a function of the price of fish (pX) in a diagram with the quantity of fish on the vertical axis and the price of fish on the horizontal ax