Consider a consumer whose utility function over food and clothing is u(xf,xc). The consumer has income w and faces prices p=(pf,pc). Suppose further that she lives in a country where clothing is taxed but food is not. Tax on clothing is ad valorem so that the effective price consumer pays on clothing is (1+t)pc, where t is the tax rate. (a) Formulate the consumer's utility maximization problem. (b) Suppose the consumer's indirect utility function is given by v(p,t,w)=16(1+t)pfpc3w2. Derive the Marshallian demands for clothing and food, xc(p,t,w) and xf(p,t,w) How do they change as t changes? (c) Derive the expenditure function, e(p,t,u) and the Hicksian demands. How do they change as t changes? Interpret these results. Consider a consumer whose utility function over food and clothing is u(xf,xc). The consumer has income w and faces prices p=(pf,pc). Suppose further that she lives in a country where clothing is taxed but food is not. Tax on clothing is ad valorem so that the effective price consumer pays on clothing is (1+t)pc, where t is the tax rate. (a) Formulate the consumer's utility maximization problem. (b) Suppose the consumer's indirect utility function is given by v(p,t,w)=16(1+t)pfpc3w2. Derive the Marshallian demands for clothing and food, xc(p,t,w) and xf(p,t,w) How do they change as t changes? (c) Derive the expenditure function, e(p,t,u) and the Hicksian demands. How do they change as t changes? Interpret these results