Question

The demand function for a truckload of firewood in a small town with a college is Q = 200 - 1.5p for non-students and Q = 200 - p for students, where p is the price of firewood, in $/truckload. For the town as a whole, including the students, the slope of the inverse demand curve to the right of the kink is ? A. -1 B. -2 C. -.5 D. -.4

Answer 1

The correct answer is (D) -0.4

Let's first find the equation of the demand curve.

Aggregate demand is the horizontal sum of individual demand curves.

The demand function for a truckload of firewood in a small town with a college is Q = 200 - 1.5p for non students.

Hence maximum price non students are willing to pay is the price when Q = 0.

So, Q = 0 implies 0 = 200 - 1.5p => p = 133.33

The demand function for a truckload of firewood in a small town with a college is Q = 200 - p for students.

Hence maximum price students are willing to pay is the price when Q = 0.

So, Q = 0 implies 0 = 200 - p => p = 200.

Hence Price for which both will demand is price 0 < p < 133.33

Price for which only Students will demand is 133.33 < p < 200.

As p is on vertical axis and Q is on horizontal axis, thus Demand to the right side of the kink is the demand when both of them will demand i.e. for the price 0 < p < 133.33

Hence demand to the right of kink is Demand of students + demand of non students.

=> Q = 200 - p + 200 - 1.5p

=> Q = 400 - 2.5p => p = (1/2.5)(400 - Q)

As p is on vertical axis and Q is on horizontal axis, Slope of demand dp/dQ = -1/2.5 = -0.4

Thus,  the slope of the inverse demand curve to the right of the kink is -0.4.

Hence, the correct answer is (D) -0.4