IL PROBLEMS Problem 1 [25 pts] Explain your answers. Make sure you label the axes on any graphs you draw and explain what you are plotting. The answers may not be integer numbers. Peter consumes sandwiches [good 1_. with price p1] and juice {good 2. with price :32). His demand function for sandwiches is :sf = if where m is his income. {a} Use the budget constraint to nd Peter's demand for juice. {in} Suppose m = 52H]. p1 = $5 and p2 = 52. Find Peter's optimal consumption bundle and call it A. Suppose now the sandwich price increases to pi = $8. [c] 'What are the new optimal amounts of sandwiches and juice that Peter would choose? Call them bundle C. {d} Given your answers to (b) and {c}: calculate the income and substitution effects on Peter's sandwich and juice consumption caused by the price increase. Plot a graph: like in class. to illustrate the two effects and eiqilain their direction. (e) Suppose Peter's friend Earn faces the same prices as Peter but has preferences \"tr-{331. a2) = :51 + 55;; and income m = $120. Find the income and substitution effects of the price increase on Sam's sandwich consumption