Let the utility function be given by u(x1, x2) = √x1 + x2. Let m be...

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 1 and 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 of feasible bundles using a figure.

(b) Suppose that m = £100 and that P2 = £10. Find the optimal bundle for the consumer. In other words, find the combination of x1 and 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 has increased to p2 = £30. Find the optimal bundle for the consumer. In other words, find the combination of x1 and x2 that maximizes the consumer’s utility when the prices are p2 = £30, p1 = £1 and her income is m = £100.

(d) How can we explain the drastic change in demand for the goods when the price of good 2 increased from £10 to £30?

Solutions

Expert Solution

D) there is a drastic change in consumption when price of x2 rises from 10 to 30 £ because of substitution and income effects. The budget curve is now more steeper and consuming x2 is more costly so the consumer will substitute it with x1.

Hope this helps, let me know if you have any doubts. Also , graph in part c is rough ,just for explanation, it's not accurate.

Rahul Sunny answered 1 week ago

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