(a) What is the equilibrium of a consumer? [5 marks] (b) Explain how a consumer attains equilibrium in spending his income. [15 marks]

Answer Details

(a) Equilibrium of a consumer. A consumer is in equilibrium when, given his fixed income and the ruling prices of goods, he has spent his income in the way that yields him the maximum total satisfaction (utility), so that he has no incentive to change his pattern of spending.

(b) How a consumer attains equilibrium. There are two standard explanations.

Using marginal utility (the equi-marginal principle). A consumer buying several goods maximises satisfaction by arranging his spending so that the marginal utility of the last unit of money spent on each good is equal. That is, he equalises the marginal utility per naira across all goods:

\[ \frac{MU_x}{P_x} = \frac{MU_y}{P_y} = \cdots = MU_m \]

where \( MU_x, MU_y \) are the marginal utilities of goods \( x \) and \( y \), \( P_x, P_y \) their prices, and \( MU_m \) the marginal utility of money. If a naira spent on one good gave more satisfaction than a naira spent on another, he would transfer spending to the first good; because marginal utility diminishes, this transfer continues until the ratios are equal, at which point total satisfaction is greatest and he is in equilibrium.

Using indifference curves. The consumer is in equilibrium at the point where his budget line is tangent to the highest attainable indifference curve. At that point the slope of the indifference curve (the marginal rate of substitution) equals the slope of the budget line (the price ratio):

\[ MRS_{xy} = \frac{P_x}{P_y} \]

Here he is on the highest indifference curve his income allows, so satisfaction is maximised.

Examination takeaway: state the condition as a formula and explain the adjustment process, the consumer keeps shifting spending until the marginal utility per naira is equal everywhere; that equalising is what "attaining equilibrium" means.