11 Find the marginal utility of good X and the marginal util

11. Find the marginal utility of good X and the marginal utility of good Y ifor the consumer, whose preferences are described by utility function U(x;y) = 2x + y. 12. Find the marginal utility of good X and the marginal utility of good Y for the consumer, whose preferences are described by utility function U(x;y) = xy2. 13. Explain, what should be taken into account in order to find the consumer’s optimal choice of goods. 14. Outline and explain those two conditions, which must hold at the optimal choice of non-perfect substitutes. 15. Outline and explain those two conditions, which must hold at the optimal choice of perfect complements. Use a simple numerical example to illustrate these conditions. 16. Explain, how is the consumer’s optimal choice determined in case of perfect substitutes. Use a simple numerical example to illustrate the criteria for decision-making in case of goods, which are perfect substitutes.

Solution

Question 11

Utility function is as follows -

U(x,y) = 2x+y

Calculate the marginal utility of good X -

MU_x = dU/dx = d(2x+y)/dx = 2

The marginal utility of good X is 2.

Calculate the marginal utility of good Y -

MUy = dU/dy = d(2x+y)/dy = 1

The marginal utility of good Y is 1.

Question 12

Utility function is as follows -

U(x,y) = xy²

Calculate the marginal utility of good X -

MU_x = dU/dx = d(xy²)/dx = y²

The marginal utility of good X is y².

Calculate the marginal utility of good Y -

MUy = dU/dy = d(xy²)/dy = 2xy

The marginal utility of good Y is 2xy.