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Suppose x represents weekly meat consumption and y represents weekly vegetables consumption. Their prices are px and py. Paul's utility function is U1(x,y) = x2y2 and Peter's utility function is U2(x,y) = ln x + ln y. Please

a. Derive the MRS for both at the bundle (1,1) respectively.

b. Are their MRS the same at (1,1)? Explain the economic interpretation of this MRS value at (1,1).

c. Do Paul and Peter have the same preference? Explain why.

d. What are Paul's optimal consumption of meat and vegetables respectivey (as functions of his budet m, meat price p_x, and vegetables price p_y)? Is Paul's demand for meat and vegetables complying with the Law of Demand? Why or why not?

e. Are meat and vegetables substitutes or complements for Paul? Hint: how does the optimal consumption of meat change when the price of vegetables increases or decreases? How about the optimal consumption of vegetables in response to meat price changes?