The price of good x, px , is £1 and the price of y, py , is £1 and the budget is £100. The utility function for the two goods has strictly decreasing marginal rate of substitution.

(a) Explain the meaning of strictly decreasing marginal rate of substitution in economic terms. Explain the opportunity cost of good x in economic terms. Calculate the opportunity cost of good x.

(b) Use a graph where good x is on the horizontal axis and good y is on the vertical axis and draw the optimal solution to the utility maximisation problem subject to the budget constraint. Show the indifference curve that provides the optimal solution. What condition must be satisfied in this optimum? Interpret this condition economically in two different ways. Explain and sketch what could happen if the marginal rates of substitution are not strictly decreasing. Interpret.