Question

Explain the equilibrium of a consumer in case of two commodities with the help of utility approach.

Answer 1

The customer who wants to maximize his utility must divide his income among different goods so that the final rupees he spends on each good provides him with the same (equal) marginal utility.

Let's take a closer look at this utility-maximization rule of consumer equilibrium. A rupee's marginal utility is calculated by dividing the good's marginal utility by the price we pay. The marginal utility per rupee spent on commodity X will be `(MU_x)/P_x` if we represent the price of the last unit of X by Px and its marginal utility by MUx. For instance, the marginal utility per rupee is `35/5` = 7 utils if a customer purchases 4 units of product X, the price of which is ₹5, and the marginal utility from the fourth unit is 35 utils (i.e., magnitude of utility). Likewise, `(MU_y)/P_y` will show the marginal utility per rupee spent on Y, where MUy is the marginal utility from the last unit of commodity Y and Py is the price of Y.

Assume that a consumer exclusively buys two items, X and Y, with his income. Consider a consumer who receives more marginal value from a rupee spent on X than from a rupee spent on Y to see why a consumer maximizes their total utility when the marginal utility of the last rupee spent on each commodity is equal. Consider the following scenario: X receives 5 utils of utility from the last rupee spent on him, but Y receives 3 utils. By moving one rupee from commodity Y to commodity X and earning the difference between the utility of the last rupee spent on each, or by two units (5 - 3 = 2), the overall utility in this scenario can be raised. As a result, overall utility will rise. As long as one rupee spent on X provides him with greater value than a rupee spent on Y, the utility-maximizing consumer will keep shifting his spending from Y to X. However, because of the rule of diminishing marginal utility, this shift of expenditure from Y increases the marginal utility of Y while decreasing the amount of Y consumed. As the amount of X consumed rises, the marginal utility of X decreases in accordance with the law of diminishing marginal utility.

The law of equimarginal utility can also be expressed as follows in light of the reasoning above: A customer who maximizes his utility will spend his income on a variety of commodities so that the marginal utility of each good is proportionate to its price. When the ratio of marginal utilities obtained from various commodities and their prices is equal, the customer will maximize utility. The proportionality rule is the name given to this. Stated differently, the buyer will be in balance when they buy X and Y, when

However, the budget constraint that states that the money spent on two commodities must equal income (i.e., (Px × Qx) + (Py × Qy) = Y) applies to this.

The marginal utility of a unit of money (let's say a rupee) spent on commodity X is displayed above as `(MU_x)/(P_x)`. Likewise, the marginal utility of a unit of money spent on commodity Y is shown as `(MU_y)/P_y`.