Answer:
Pam would need $5.8 to compensate for the price increase and allow her to reach the same level of utility as before
Step-by-step explanation:
Assuming the price of good Y is equal to 1, find Pam's compensating variation if the price of good X rises from 2 to 3.4 dollars.
The compensating variation is the amount of money that would compensate Pam for the price increase and allow her to reach the same level of utility as before.
To calculate the compensating variation, we first need to find Pam's initial demand for good X. We can do this by substituting px=2 and py=1 into the demand function:
X* = 37.2 - 3 * 2 / 1 = 33.2
This means that Pam was initially demanding 33.2 units of good X.
After the price increase, Pam's demand for good X will decrease. We can find the new demand by substituting px=3.4 and py=1 into the demand function:
X* = 37.2 - 3 * 3.4 / 1 = 27.4
This means that Pam will now demand 27.4 units of good X.
The compensating variation is the difference between the amount of good X that Pam was initially demanding and the amount of good X that she will demand after the price increase. In this case, the compensating variation is:
CV = 33.2 - 27.4 = 5.8
Therefore, Pam would need $5.8 to compensate for the price increase and allow her to reach the same level of utility as before.