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.

At a price of $150 per truckload, will college students buy any firewood?

At a price of $150 per truckload, will non-students buy any firewood?

The (inverse) demand curve for the town as a whole has a kink at Q =

For the town as a whole, including the students, the slope of the inverse demand curve to the left of the kink is For the town as a whole, including the students, the slope of the inverse demand curve to the right of the kink is

For the town as a whole, including the students, the slope of the inverse demand curve to the right of the kink is

Answer 1

At p=150,

Students demand; Q=200-150=50

Yes , students will buy at p=150 and the QUANTITY demanded would be 50

Non student demand; Q=200-1.5*150=200-225=-25

0=200-1.5p

P=200/1.5=133.33

No, students won't buy at p=150, because the maximum amount they are willing to pay is 133.33

The whole town demand curve will be kinked at that p=133.33(non student MAXIMUM willingness yo pay)

The QUANTITY will be ;Q=200-133.33=66.67

To the left of the kink, the slope of the whole town demand slope will be Equal as slope of demand curve of students,

Because price is on y axis and quantity on x axis ,we need to change direct demand into inverse demand.

Q=200-p

P=200-Q

The slope of students demand curve is - 1{ coefficient with Q is the slope of the demand}

Right of the kink ,whole town demand :Q=student demand+ non student demand ; Q=400-2.5p

Inverse demand; p=160-0.4Q

Slope of whole town,right of the kink =0.4

the third one is whole town demand including students demand