How do you go about this ? - checking answers

3. Let there be two goods 1 and 2. et x1 and x2 denote their respective quantities. (X1, X2) represents a bundle and U(X1, X2) the consumer's utility function. The consumer's problem is max U(X1, X2) S. t. (x1, X2) EB(P1, P2, M) where B(P1, P2, M) = {(x1, X2) ER4 | PIX1 + P2X2 0. a. Solve the consumer's problem when (P1, P2, M) = (p1, 1, 25). Note: the solution will be a function of p1 . (7) b. Suppose the price of good 1 falls from p1 = 2 to p1 = 1. What is the change in consumer surplus to this consumer from the price change? (2) c. Find the income and substitution effect from the price change using the Slutsky method. (6) d. Is U(x1, X2) = 100In(x1) + N NN a quasiconcave function over R ? Again, assume X, > 0. (5.5)