1. Suppose jack's preferences can be represented by the utility function, U(x1, x2) = max(3x1, x2)

A. Draw an indifference map for jack's utility function. Label your axis, clearly mark any points of importance, and indicate which curves are associated with higher utility.

B. Suppose jack's income is $100, p1=$10 and p2=$5. What commodity bundle will maximize jack's utility subject to her budget constraint?

2.Consider the consumer's problem to maximize her utility subject to a budget constraint: Max U(x1,x2) = x1^ax2^2 for a>0, subject to p1x1 +p2x2=I

A. illustrate the consumer's problem. Be sure to indicate on your graph what you know and what you are solving for.

B. Set up the Lagrangian and solve the first order conditions to derive the Marshallian demand functions, x1^*(p1,p2,I) and x2^*(p1,p2,I)

3.. John loves to cook and is following a recipe to make fruitcake. Each fruitcake he cooks requires two apples and one wildberry. Each fruitcake John cooks gives him more utility, but he does not like eating either apples or wildberries on their own.

A. What type of preferences does John have over apples and wildberries (I am looking for a name here)? Provide a utility function that capture's John's preferences.

B. Suppose each apple costs $1 and each wildberry costs $2. If John's income is $30, how many of each fruit will he buy to maximize his utility? How many fruitcakes can John make with his budget?