Suppose that a consumer's preferences are well behaved in that properties 4-1 to 4-4 are satisfied and the initial budget constraint is given by 300 = 2X + 4Y. At the initial budget constraint, this consumer purchases 100 units of good X and 25 units of good Y. Suppose the price of X increases to $4 per unit, resulting in a new consumption bundle consisting of 60 units of X and 15 units of Y. Then, the slope of the inverse demand for good X over this consumption range is:
A) 0.05.
B) -0.05.
C) -0.267.
D) -0.444.

Question

Quizplus · Accepted Answer

To find the slope of the inverse demand for good X, we need to find the change in the price of X and the change in the quantity demanded of X, and then take the ratio of the two.

The change in the price of X is $4 - $2 = $2. The change in the quantity demanded of X is 60 - 100 = -40. (Note that this is a decrease in quantity demanded because the price of X has increased.)

So, the slope of the inverse demand for good X is:

(change in price of X) / (change in quantity demanded of X) = $2 / -40 = -0.05

Therefore, the answer is B.

Suppose That a Consumer's Preferences Are Well Behaved in That