Priyesh’s preferences for goods x and y is given by the utility function U = x2/3y1/3. His income is $192 and the price of good y is always $1. Suppose the price of x starts at $8 and then decreases to $4. (For parts a-c, fill in the blanks with the numerical change in each good. For example, if the SE results in Priyesh buying 30 fewer units of good x, write -30.)
(a) The substitution effect results in Priyesh buying ________ x and _______ y.
(b) The income effect results in Priyesh buying _______ x and _______ y.
(c) The total effect results in Priyesh buying _______ x and _______ y.
(d) What can you say, if anything, about the relative magnitudes of the income and substitution effects of this price decrease? Explain.
(e) Graphically decompose the total effect of this price decrease into the substitution and income effects on a well annotated graph. Make sure you clearly label each of the 3 effects.