Problem: Carl only consumes sandwiches, denoted S, and coffee, denoted C. His utility function for coffee and sandwiches is given by:
U (S, C) = 1/4 S^(1/3) C^(2/3)
a. Write down the function for the MRS sc.
b. Would the consumption bundle (S, C) =(4,4) AND (S',C')=(1,8) be on the same indifference curve? Explain.
c. Are Carl's preferences convex? Explain.
d. Suppose Pcoffee= 9 and Psandwiches=3 and Carl has 54 dollars in his wallet is the bundle (S,C)=(6,3) Carl's optimal bundle? Explain. Be sure to support your response with specifics.