Luke has $16 to spend on his lunch at his school cafeteria every week. A slice of pizza (P) costs $2 and a submarine sandwich (S) costs $4. Luke likes an average more than extremes.

Likewise, his marginal rate of substitution of a slice of pizza in terms of submarine sandwiches can be described by the following equation: MRS = S/3P, where S is the number of submarine sandwiches and P is the number of pizza slices.

a) Draw an indifference curve diagram (place pizza on the horizontal axis) that illustrates Luke’s situation and then show his optimal bundle. How many slices of pizza and how many sandwiches does he buy on average (i.e., the answer can be fraction) every week?

b) The cafeteria has announced to cut the price of a slice of pizza by half in the following week. Draw a new indifference curve diagram and analyze the effect of this price change on Luke’s consumption decision for the following two cases:

Case 1: Pizza is a normal good for Luke

Case 2: Pizza is an inferior good for Luke

For each case, show clearly their optimal bundle before and after the price change, the substitution effect and income effect on your diagram. (No calculation is required).