Let the utility function be given by
u(x1, x2) = √x1 + x2.
Let m be the income of the consumer, P1 and P2 the prices of good 1and good 2, respectively.
To simplify, normalize the price of good 1, that is P1 = £1.
(a) Write down the budget constraint and illustrate the set offeasible bundles using a figure.
(b) Suppose that m = £100 and that P2 = £10. Find the optimalbundle for the consumer. In other words, find the combination of x1and x2 that maximizes the consumer’s utility when the prices are p2= £10, p1 = £1 and her income is m = £100.
(c) Suppose still that m = £100 but now the price of good 2 hasincreased to p2 = £30. Find the optimal bundle for the consumer. Inother words, find the combination of x1 and x2 that maximizes theconsumer’s utility when the prices are p2 = £30, p1 = £1 and herincome is m = £100.
(d) How can we explain the drastic change in demand for the goodswhen the price of good 2 increased from £10 to £30?
