Solving the consumer's optimization problem ( Ex 1) with u(X)=x1cx2d yields: x1=c+dcp1mandx2=c+ddp2m The optimal point X=(x1,x2) is shown in Panel A of figure 5.1. Rearranging this solution yields the shares of both expenditures in her income: s1=mp1x1=c+dcands2=mp2x2=c+dd Thus the C-D consumer always spends a fixed fraction of her income on each good. The fraction is determined by the exponents of the UF. If choosing u(X)=x1ax21a as the C-D preference, then we know that s1=a&s2=Ia, and that the exponents in the UF are just the expenditure shares. So, if observing sl=1/4&s2=3/4 from data (on the average level), you may obtain the UF of u(X)=x141x243. We can use this UF to forecast future demand and evaluate policy proposals. Q5: Suppose that the UF is u(X)=x0.2x20.8, which represents a consumer's preferences. The data on demand show that x1=30,x2=I5. Derive the MRS at optimum. Give the prices if income is pegged to unity. Solving the consumer's optimization problem ( Ex 1) with u(X)=x1cx2d yields: x1=c+dcp1mandx2=c+ddp2m The optimal point X=(x1,x2) is shown in Panel A of figure 5.1. Rearranging this solution yields the shares of both expenditures in her income: s1=mp1x1=c+dcands2=mp2x2=c+dd Thus the C-D consumer always spends a fixed fraction of her income on each good. The fraction is determined by the exponents of the UF. If choosing u(X)=x1ax21a as the C-D preference, then we know that s1=a&s2=Ia, and that the exponents in the UF are just the expenditure shares. So, if observing sl=1/4&s2=3/4 from data (on the average level), you may obtain the UF of u(X)=x141x243. We can use this UF to forecast future demand and evaluate policy proposals. Q5: Suppose that the UF is u(X)=x0.2x20.8, which represents a consumer's preferences. The data on demand show that x1=30,x2=I5. Derive the MRS at optimum. Give the prices if income is pegged to unity