Compensating Variation and Equivalent Variation

Compensating variation and equivalent variation are monetary measures of the gain or loss in a consumer's welfare following an economic change. Compensating Variation (CV) is the compensating payment that leaves the consumer as well off as before the economic change. The compensating payment is positive for a welfare loss and negative for a welfare gain.

Think about the payment as being to the consumer in the case of a welfare loss and from the consumer in the case of a welfare gain.

Let the economic change be an increase in the price of good x for the consumer choice problem discussed in class. In the figure shown below, a price increase moves the consumer from consumption bundle A to consumption bundle B. To be as well off as before the price increase, the consumer must receive a compensating payment that allows the consumer to move to the initial utility level at the new price of x. The budget constraint associated with the compensating payment is shown in red below.

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Think about the CV as the minimum amount that the consumer will accept as compensation for the welfare loss associated with the price increase. The CV for the price increase is easily calculated using Goal Seek. Let's go back and look at a portion of your results for the previous lab. You used Goal Seek to find the income level consistent with consumer equilibrium at the initial level of utility (U=8,000,000) and the new price of x ($4). In other words, Goal Seek gives the income associated with the red budget constraint shown above.

This is the income level needed to calculate the CV for the price increase. The CV for the data shown on the spreadsheet is found by subtracting cell B6 from cell F6. We label the calculation in cell H6 and do the calculation in cell I6. The CV is $352. Equivalent variation (EV) is the compensating payment that in the absence of the economic change moves the consumer to the welfare level associated with the change. Continuing with our price increase example, the EV is the maximum amount the consumer would be willing to pay to avoid the price increase.

In the figure shown below, the consumer is willing to pay an amount up to that implied by the green budget line, which yields the same utility level associated with the price increase. The maximum amount the consumer is willing to pay to avoid the price increase is used to determine the compensating payment for the price increase. Let's use Goal Seek to find the EV for the price increase data in the spreadsheet. Highlight cells A1 to F9. Select Copy from the Edit menu. Move the cursor to cell A12. Select Paste from the Edit menu.

You should see the cell contents of cells A1 to F9 reproduced in cells A12 to F20. Use the cells in A12 to F20 to find the EV for the price increase. Specifically, use Goal Seek to find the income level associated with the new level of utility (U=2,000,000) at the old price of x ($2). Use this level of income to calculate the EV. Your results should look like those shown below. It is important to understand that the CV measures the welfare change with respect to the initial utility level, and the EV measures the welfare change with respect to the new utility level.

Complete the lab by measuring the welfare change associate with a decrease in the price of x from $4 to $2. Continue to assume that a=2, b=1, and the consumer's money income is $600. Calculate both the CV and the EV for the increase in welfare. Use the same format for your spreadsheet as the example shown above. Convert the spreadsheet to an htm file, FTP the file to your web account, and put a like to the file on your Economics 508 homepage. Call the link Compensating Variation and Equivalent Variation.