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Question
A consumer consumes only two goods X and Y and is in equilibrium. Show that when the price of good X rises, the consumer buys less of good X. Use utility analysis.
Solution
When a consumer buys both Goods X and Y, the consumer’s equilibrium condition is expressed through the equation:
`"MU"_x/P_x = "MU"_y/P_y = "MU"_m/P_n = MU_m`
Consider the following numerical example to understand the consumer’s equilibrium using marginal utility. A consumer’s Marginal Utility of Money (MUm) is 16 utils and two commodities x and y whose prices are Rs 1 (Px) and Rs 1 (Py) per unit, respectively. Consider the following schedule to analyse the marginal utility of commodity x (MUx) and commodity y (MUy).
| Units of x |
MU x (Utils) |
MU y3 (Utils) |
| 1 | 28 | 32 |
| 2 | 24 | 29 |
| 3 | 21 | 27 |
| 4 | 20 | 23 |
| 5 | 16 | 20 |
| 6 | 13 | 18 |
| 7 | 9 | 17 |
| 8 | 5 | 16 |
| 9 | 3 | 12 |
| 10 | 1 | 9 |
Based on the given schedule, the consumer is in equilibrium at the consumption of 5 units of commodity x and 8 units of commodity y. At such a consumption combination, the marginal utility of a rupee spent on commodity `x((MU_x)/P_x)` is equal to the marginal utility of a rupee spent on commodity y`((MU_y)/P_y)` and also equal to the marginal utility of money (`MU_m`).
If the price of commodity x rises, the ratio of marginal utility to the price of `X((MU_x)/P_x)` will be lesser than that of y
`"MU"_x/P_x < "MU"_y/P_y`
Here, the consumer reorganises his consumption combination to attain equilibrium.
Therefore, the consumption of commodity x decreases till it reaches equality.
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RELATED QUESTIONS
A consumer consumes only two goods X and Y and is in equilibrium. Show that when the price of good X falls, demand for good X rises. Use Utility Analysis.
______ states that as the consumer will distribute his money income between the goods in such a way that the utility derived from the last rupee spent on each good is equal.
Read the following passage and answer the question that follows:
| The ordinal list revolution originates in the criticism of the psychological foundations of the theory of demand, namely, the principle of decreasing marginal utility as Alfred Marshall ([1890] 1898) used it. The rejection of hedonist hypotheses led Irving Fisher (1892) and Pareto (1896-97, 1900, 1909) to favour an objective or "positive" approach to economic concepts. The "ordinal list revolution" (Omarzabal 1995, 116) is grounded in a methodological transformation of economics that put the facts of objective experience as a foundation of economics and provided a research program for the ensuing years (Green and Moss 1993; Lewin 1996). Mathematically, ordinalism is entirely based upon the idea that one can dispense with the use of a specific utility function and that no meaning shall be attached to utility measurement, except as an ordinal principle. Clearly, the development of ordinalism must be separated from the introduction of the concept of the indifference curve. Ordinalism was first advocated in Fisher's "Mathematics Investigations" (1892) and Pareto's Sunto (1900) and Manual ([1909] 1971), while the indifference curve had appeared in F. Y. Edge Worth's Mathematical Psychics (1881). It was thus only through Fisher's and Pareto's recasting that the concept of the indifference curve became irreversibly associated with the promotion of ordinalism. Along the way, the recasting of the theory of choice along ordinal list lines raised a number of issues (about integrability, measurability, and complementarity) that would be progressively settled. The reasonable closing date for the ordinalist revolution is 1950, after Houthakker's (1950) and Samuelson's (1950) contributions. From the late 1920s, the Paretian school was progressively gaining a larger audience while the use of the concept of marginal utility and other derivative concepts was challenged. Consequently, demand theory was recast along with the principles of individual preferences and ordinal utility functions. Nevertheless, English authors proved very silent about the meaning of indifference curves. Most if not all of the reflections after 1920 about the nature of indifference curves took place in America, mainly under the impulse of Henry Schultz at Chicago. This is an American story. |
Which of the following is not the way of studying Utility?
Statement 1: A rational firm aims to operate in the second phase of the law of variable proportion.
Statement 2: In diminishing returns to a factor, i.e., the second phase of the law of variable proportion, MP falls.
______ states that as more and more units of a commodity are consumed, the marginal utility derived from the additional units must decline.
Total utility is ______ at the point of satiety.
Assertion (A): TU curve starts from the origin, increases at a decreasing rate, reaches a maximum, and then starts falling.
Reason (R): The rising MU curve shows the law of diminishing marginal utility.
Which of the following statement is false?
"The law states that a consumer will so allocate his expenditure so that the utility gained from the last rupee spent on each commodity is equal." Identify the law defined above.
When the marginal product becomes negative, then the total product starts ______
When is the consumer in equilibrium?
Identify the correctly matched pair of column A to that of Column B:
| Column A | Column B |
| (1) Marginal Utility | (a) The power or capacity of a commodity to satisfy human wants. |
| (2) Cardinal measure of utility | (b) The addition to total utility on consuming an additional unit of a commodity. |
| (3) Total Utility | (c) It is the sum total of utility derived from the consumption of all units of a commodity. |
| (4) Utility | (d) It is that measurement of utility, which is measured in terms of units. |
Which of the following are the correct assumptions for the utility approach?
The utility is a ______ concept.
