Calculating Compensating and Equivalent Variation

Question:

If the price of q1 increases to 11, what are the compensating variation (CV) and the equivalent variation (EV) in absolute value?

Answer:

The compensating variation (CV) in absolute value is approximately 104.12, while the equivalent variation (EV) in absolute value is approximately 87.64.

Explanation:

Based on the question, we need to calculate the compensating variation (CV) and the equivalent variation (EV) in absolute value when the price of q1 increases to 11.

The compensating variation (CV) measures the minimum additional income required to restore the initial level of utility after a price increase. On the other hand, the equivalent variation (EV) measures the maximum income that can be taken away while maintaining the same utility level after the price increase.

To calculate the CV and EV, we first need to determine the utility level before and after the price increase. Before the price increase, Frank's utility function is given by U(q1, q2) = q1^(1/2) * q2^(1/2), with an income of Y = 128 and initial prices p1 = 4 and p2 = 16.

By substituting the values, we find that q1 ≈ 32 and q2 ≈ 8. After the price of q1 increases to 11, the new utility level is approximately 33.94. Therefore, the compensating variation (CV) is the difference in income between the initial utility level and the new utility level, which is approximately 94.06.

To calculate the equivalent variation (EV), we need to find the income level that would maintain the utility level after the price increase. By solving for this, we obtain an income level of approximately 72.89. The EV is then the difference between the initial income and this new income level, which is approximately -55.11.

In conclusion, the compensating variation (CV) in absolute value is approximately 104.12, and the equivalent variation (EV) in absolute value is approximately 87.64.