Suppose that there are two goods (X and Y). The price of X is £2 per unit, and the price of Y is £1 per unit. There are two consumers, A and B. Their utility functions are UA(X,Y) = 0.5logX + 0.5logY and UB(X,Y) = 0.8logX + 0.2logY. Consumer A has an income of £100, and Consumer B has an income of £300.
A. Use Lagrangeans to solve the constrained utility-maximization problems for Consumer A and Consumer B. (70%)
B. Calculate the marginal rate of substitution for each consumer at his or her optimal consumption bundles. (30%)