1. Suppose a consumer buys clothing for the heat it provides and that each unit of clothing provides 2 units of heat. Assume that the consumer also buys housing for the shelter it provides, and that one unit of housing provides one unit of shelter. IfHis the number of housing units andCis the number of clothing units consumed, then his utility isu(H, C) = min{H,2C}. The per-unit prices of housing and clothing arepHandpC, respectively, and his income ism.

(a) Set up the maximization problem and derive the demand functions forHandC.

(b) Re-dopart (a) assuming that u(H,C)=H+2C, pH=2, pC=3, and m=300.