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 p2]. His demand function for sandwiches is 1'; 2 3?": where m is his income. [a] Use the budget constraint to find Peter's demand for juice. {b} Suppose m : $27f}. pl 2 $5 and p2 ; $2. Find Peter's optimal consumption bundle and call it .4. Suppose now the sandwich price increases to p; : $5. {c} 'What are the new optimal amounts of sandwiches and juice that Peter would choose? Call them bundle C. {d} IGit-fen your answers to {h} 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 explain their direction. {e} Suppose Peter's friend Sam faces the same prices as Peter but has preferences n{r1_. 1'2} : 3:1 + 3:2 and income or 2 Slel. Find the income and substitution effects of the price increase on Sam's sandwich consumption