The Concept of Compensating Variation in Economics

Understanding Kayla's Compensating Variation

Let the price of good Q 1 initially be $20 and the price of good Q 2 be $10. Kayla has income of $1,800. If the price of good Q 1 increases from $20 to $60, what is Kayla's compensating variation?

Kayla's compensating variation (CV) is, Kayla's compensating variation is 10 - (-900) = $910. This is the amount of additional income she would need in order to remain as satisfied with her current consumption as before the price of good Q 1 increased from $20 to $60.

Kayla's compensating variation is the amount of additional income she would need to remain as satisfied with her current consumption as before the price of good Q 1 increased from $20 to $60. This increase in price causes a decrease in Kayla's real income, and the compensating variation measures the amount of additional income that would be needed to compensate for the decrease in real income.

To calculate the compensating variation, the first step is to calculate the budget line. The budget line is the line that represents all combinations of good Q 1 and good Q 2 that Kayla can purchase with her income of $1,800. Assuming that the price of good Q 1 has increased from $20 to $60, and the price of good Q 2 is still $10, Kayla can purchase a maximum of 30 units of good Q 1 and 180 units of good Q 2. The budget line equation can be calculated using the two price and income values: 30Q1 + 180Q2 = 1,800

The second step is to calculate the maximum utility Kayla can obtain from the budget line. This can be calculated by considering Kayla's utility function. If Kayla has an additive utility function of U = Q1 + Q2, then the maximum utility she can obtain from the budget line is 30 + 180 = 210.

The third step is to calculate the equivalent variation. This is the amount of income that would need to be taken away from Kayla to leave her with the same level of utility she had before the price of good Q 1 increased from $20 to $60. In this case, the equivalent variation is the difference between the maximum utility that Kayla can obtain before and after the price change. Since the maximum utility before the price change was 200, and the maximum utility after the price change was 210, the equivalent variation is 10.

Finally, Kayla's compensating variation is the difference between the equivalent variation and the change in real income caused by the price change. In this case, the change in real income is -$900, since the price of good Q 1 has doubled.

What is the definition of compensating variation in economics?

Compensating variation in economics refers to the amount of additional income an individual would need to maintain the same level of utility or satisfaction after a change in prices. It measures the income adjustment required to offset the impact of price changes on an individual's purchasing power and welfare.