The Consumer’s Problem

Utility Maximisation

$$ \max_x \text{ U}(x_1,x_2) \hspace{0.5cm} \text{ such that } P_1x_1 + P_2x_2 = I $$

Arbitrage Argument /Marginal Utility of Income

$$ \frac{MU_1}{P_1}= \frac{MU_2}{P_2} $$

MRS: $\frac{MU_1}{MU_2}$

Slope of Budget Line = $\frac{P_1}{P_2}$

• perfect substitutes Two goods for which the marginal rate of substitution of one for the other is a constant.

$U = ax + by$ • perfect complements Two goods for which the MRS is zero or infinite; the indifference curves are shaped as right angles.

$U = \min{(ax, by)}$

A budget line describes the combinations of goods that can be purchased given the consumer’s income and the prices of the goods.

• corner solution in which the marginal rate of substitution of one good for another in a chosen market basket is not equal to the slope of the budget line.