Complete This In About One Hour: Jevons Demonstrated That Co
Complete This In About One Hourjevons Demonstrated That Consumers De
Complete this in about one hour! Jevons demonstrated that consumers’ demand behavior could be derived from consumer’s utility maximization. In a context of two commodities (X and Y), give a simple and brief proof that a utility-maximizing consumer would exchange the two commodities up to the point where the relative ratio of marginal utility between the two commodities exactly equals their relative price ratio (no numerical calculation is required, just explain the logic and reasoning).
Paper For Above instruction
The fundamental principle underlying consumer behavior in microeconomics is the concept of utility maximization. According to Jevons's theory, consumers aim to allocate their limited income in a manner that maximizes their total utility derived from consumption of goods. When considering two commodities, X and Y, this principle implies that at the point of optimal consumption, the consumer has no incentive to reallocate their expenditure because they have achieved the highest possible satisfaction given their budget constraint.
The core reasoning involves marginal utility, which measures the additional satisfaction gained from consuming an additional unit of a good. To understand why at the equilibrium point the ratio of marginal utilities must equal the ratio of prices, consider the following logical steps.
Suppose a consumer is initially consuming quantities of X and Y that maximize their utility. If the consumer were to reallocate some expenditure—say, by transferring a small amount of money from good Y to good X—they would adjust their consumption bundle slightly. The change in total utility resulting from this reallocation depends on the marginal utility of each good and their respective prices.
Mathematically, the consumer's goal is to maximize total utility U(X, Y), subject to their budget constraint P_X X + P_Y Y = I, where P_X and P_Y are the prices of commodities X and Y, and I is the consumer’s income. At the optimum, the consumer will adjust quantities until the marginal utility per dollar spent on each good is equal, i.e.,
MU_X / P_X = MU_Y / P_Y.
This condition ensures that the consumer cannot improve their overall utility by reallocating their expenditure between the two goods. If MU_X / P_X > MU_Y / P_Y, the consumer could increase utility by reducing consumption of Y and increasing X, since the additional utility gained per dollar spent on X exceeds that of Y. Conversely, if MU_X / P_X
This equality of the ratio of marginal utilities to the ratio of prices is a direct outcome of the consumer reaching a point where the marginal utility per dollar spent is equal across all goods—an optimal point. Rearranged, this condition is expressed as:
MU_X / MU_Y = P_X / P_Y.
Hence, under utility maximization, the consumer will exchange X and Y until the marginal utility ratio equals the price ratio. This equilibrium condition ensures no further reallocation can increase overall utility, which exemplifies Jevons's assertion that demand behavior is driven by utility maximization principles, producing the demand curve where the relative marginal utility of goods equals their relative prices.
References
- Jeveons, W. Stanley. (1871). The Theory of Political Economy. Macmillan.