Consumer optimizationL
A consumer has preferences for water W and food F with the following form: U (W, F) 8/W + F with marginal utilities Um = Viw and Up = 1. The price of W and F are identical at £1 per unit. The consumer has a budget of £4.
(a) Draw the budget constraint with F on the horizontal axis and W on the vertical axis.
(b) Define the marginal rate of subsitution of food for water. Calculate the marginal rate of substitution when W = 1 and F = 3.
(c) What is the utility level when W = 1 and F = 3? Work out an indifference curve going through this point. Draw this on the graph, showing where it intersects the budget constraint and what it looks like close to the axes.
(d) What is the consumer optimum at the given budget constraint? Illustrate the consumer optimum on the graph. Is the marginal rate of substitution the same as the ratio of prices at this point? Please explain why or why not.