A consumer’s preferences over pizza (x) and steak (y) are given by u(x,y) = x^2y (HINT: MUx = 2xy and MUy = x2) and his income is I = $120 and py = $1. (a) Calculate his optimal bundle when pX = $8 (call this bundle A) and separately when pX = $1 (call this point C). (b) Finding the decomposition bundle B, calculate the income and substitution effects on the amount of pizza of a decrease in the price of pizza from pX = $8 down to pX = $1. (c) Forget about the decomposition bundle and the two effects. In (a), the price of pizza decreases, hence the agent ends up better off. Let’s quantify how much “better off” the agent becomes after this price drop, in dollars. For this, instead of the price drop, suppose the agent is given some money $m and he optimize utility with this additional gift included to his budget. What should m be, so that his optimal utility with his expanded budget is exactly equal to his utility at the bundle C (the bundle he chooses optimally when pizza price drops to pX = $1). (d) Now forget about the decomposition bundle and the two effects. Assume again as in (a) that pX decreases from $8 to $1. How much should the price of steak py be increased, so that the agent is indifferent (neither better off nor worse off) after these two price changes compared to the initial situation (i.e., before the two price changes)?
A consumer’s preferences over pizza (x) and steak (y) are given by u(x,y) = x^2y (HINT: MUx = 2xy and MUy = x2) and his income is I = $120 and py = $1.
(a) Calculate his optimal bundle when pX = $8 (call this bundle A) and separately when pX = $1 (call this point C).
(b) Finding the decomposition bundle B, calculate the income and substitution effects on the amount of pizza of a decrease in the
(c) Forget about the decomposition bundle and the two effects. In (a), the price of pizza decreases, hence the agent ends up better off. Let’s quantify how much “better off” the agent becomes after this price drop, in dollars. For this, instead of the price drop, suppose the agent is given some money $m and he optimize utility with this additional gift included to his budget. What should m be, so that his optimal utility with his expanded budget is exactly equal to his utility at the bundle C (the bundle he chooses optimally when pizza price drops to pX = $1).
(d) Now forget about the decomposition bundle and the two effects. Assume again as in (a) that pX decreases from $8 to $1. How much should the price of steak py be increased, so that the agent is indifferent (neither better off nor worse off) after these two price changes compared to the initial situation (i.e., before the two price changes)?
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