Calculate a consumer's demand for goods 1 and 2 as a function of p1 and p2-the prices of goods 1 and 2, respectively, when the consumer's utility function and initial endowment are as below. Draw the offer curve in each case.
(a) u(X, Y) = X^5Y^2, e = (10, 0)
(b) u(X, Y) = min(5X, 2Y), e = (10, 0)
(c) u(X,Y)=5X+2Y, e=(10,0)
(d) u(X, Y) = ln(X) + ln(Y), e = (1, 1)