Amelia spends her income on Coffee and Sandwiches. She has Cobb-Douglas preferences given by: U(C, S) = 10C 2S

(a) This consumer has an income of M = 45 dollars. and the price of Coffee is PC = 1. Write down her inverse demand function for Sandwiches.

(b) Draw the demand curve from the previous part, at the given budget level and price of Coffee. Label on your diagram the Sandwich prices of $1 and $3, as well as numerical values for the corresponding quantities demanded.

(c) The price of Coffee is PC = 1, and the price of a Sandwich is PS = 3. Write down the graph equation for this consumer's Engel curve (Income vs. Quantity) for Sandwiches.

(d) Draw the Engel curve from the previous part. Label on your curve the income level M = 45 and the corresponding quantity demanded for Sandwiches.