Suppose that an individual gains utility from two goods: (i) Cheese (C) and (ii) Milk (M). This utility is given by the following utility function. For the purposes of figures, assume that Cheese (C) is on the x-axis and Milk (M) is on the y-axis. U(C,M)=10C 1/4 M 3/4
Note that I have not given you values for p c,p M,or m in this question yet. For now, leave them in their general forms.
m=p C C+p M M We are going to solve this using the Unconstrained Optimization method (\#2).
1. Use the general form of the Budget Constraint to convert the Utility Function into a function of only Cheese (C). [2 points]
2. What is Demand for Cheese as a function of p c,p M and m ? Show your work. [3 points]
3. What is Demand for Milk as a function of p c,p M, and m ? Show your work. [1 point]
Suppose that m=$100,p C=$5, and pM=$4.
4. What is the Demand for Milk and Cheese using the above specific prices and income numbers? Show your work. [1 point]
5. Are Milk and Cheese gross substitutes, gross compliments, or neither according to these preferences? How do you know? [3 points] [Hint: To solve this fully, you would want to take the derivative of the Demand for one good with respect to the price or quantity of the other good, to see how they change together.]