Q.A consumer consumes only two goods. Explain his equilibrium with the help of utility approach.
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Start your 14-day free trial to unlock the full solution →A consumer buying two goods X and Y reaches equilibrium (the utility-maximising combination) where MUx/Px = MUy/Py = MUm, given diminishing marginal utility — this is the Law of Equi-Marginal Utility.
Consumer's equilibrium — utility (cardinal) approach
Assumptions: utility is cardinally measurable (in 'utils'), the marginal utility of money stays constant, utilities of the two goods are independent, and marginal utility diminishes as more units of a good are consumed.
The consumer's income (M) is spent entirely on X and Y: M = Px·Qx + Py·Qy.
Equilibrium condition: the consumer keeps reallocating spending between X and Y until
MUx / Px = MUy / Py = MUm
Reasoning: if MUx/Px > MUy/Py, the consumer gets more utility per rupee from X than from Y, so it pays to buy more of X and less of Y. As more X is bought, MUx falls (diminishing marginal utility); as less Y is bought, MUy rises. This reallocation continues until the marginal utility per rupee is equalised across both goods — this is the Law of Equi-Marginal Utility (Gossen's Second Law). At this point, no further reallocation of the same income can raise total utility, so the consumer is in equilibrium. The second-order condition for a true maximum (not minimum) is that marginal utility must be diminishing for both goods.
OR — Why does the Law of Demand operate?
The Law of Demand states that, other things remaining constant, the quantity demanded of a commodity is inversely related to its price. It operates because of:
- Law of Diminishing Marginal Utility — as a consumer buys more units, the marginal utility from each additional unit falls, so the consumer is willing to buy more only if the price also falls. …
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