Problem 2 (40 pts) Explain your answers! Andy consumes only coffee and sandwiches and has a utility function n(a:1, 2:2) = 31n($1)+ 61n($2) where 2:1 is the quantity of coffee and 2:2 is the number of sandwiches consumed. ln(:r) denotes the natural logarithm of 3:. Suppose a coffee costs $2 and a sandwich costs $10. Andy's income is $m. (a) Write down Andy's consumer's problem of choosing his optimal consumption bundle. (b) Find Andy's demand function for sandwiches. How does it depend on p and m (increas- ing, decreasing, constant)? Are sandwiches an ordinary good for Andy? Explain why or why not. (c) Find the equation of Andy's Engel curve for sandwiches (i.e., express an in terms of 2:3}. Are sandwiches a normal good for Andy? (d) How many coffees and sandwiches would Andy consume if his income is m = $120 and a sandwich costs p = $5? Starting from that, how would Andy's optimal consumption bundle change if a $1 quantity tax is imposed on coffee and Andy is given $15 lump-sum subsidy to his income? Is he better off or worse off after the tax and subsidy compared to before? (e) Jenny also consumes only coffee (at price $2) and sandwiches (at price $39) but has the utility function 23:1 + 251n(:r2). If her income is $55 and p = $5 nd her optimal consumption bundle. What quantities of coifee and sandwiches would Jenny consume if her income was $10 instead