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Economics

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1. Suppose the utility function of the consumer is U(x,y)=x+Iny. a. What is the marginal rate of substitution between x and y? Is the marginal rate of substitution decreasing? b. Is the consumer's preference in order? Please specify c. Derive the general demand function of x and y, and prove that the two demands are homogeneous. d. Derive x the substitution effect, the resultant effect and the total effect of price changes to prove that the Slutsky equation is established. 2. Assuming that consumers prefer a sandwich made from toast (t) and egg (g), the utility function is u(t,g)= min{t, g}. Knowing the consumer's income (w), the price of toast and eggs (represented by pt and pg respectively). a. Please derive the consumer demand function for toast and eggs. [Reminder: Lagrange method is not suitable for this preference form Method to solve; pay attention to the characteristics of preference] b. Are the toast and eggs normal or inferior wealth? Please specify c. Derive the impact of egg price changes on the demand for toast (cross effect), which shows that eggs and toast are complementary Taste.