Problem 1 (25 pts) John always spends 1/3 of his income m on food, with quantity 11 and price pi per unit. He spends the remaining part of his income on all other goods, with quantity 22 and price p2. (a) Explain that John's demand function for food equals x1(P1, P2, m) = 3p Find John's demand function for all other goods, x(P1, P2, m). Is food an inferior good for John? Are "all other goods ordinary or Giffen for John? Explain. From now on use that John's income is m= $120 and p2 = $1. (b) Suppose pi = $2. Put food on the horizontal axis and plot John's budget set and find his optimal consumption bundle. (c) Let p = $2 still but the store offers John a one-time $12 coupon redeemable for any good he wants, after purchasing his first $20 worth of food (no coupon if he purchases less than $30 of food; no additional coupons if he purchases more). Plot John's budget set after the coupon offer and find his new optimal consumption choice. (d) Suppose instead the government subsidizes food which reduces p1 to $1 per unit (there is no coupon). If John's income remains m = $120, find the income and substitution effects (IE and SE) of the food price change on John's quantity demanded of food. Explain the direction of the JE and SE. Is John better off or worse off after the subsidy? Explain why or why not