Suppose that the inverse demand function for movies is P = 120 – Q1 for college students and P = 120 – 2Q2 for other town residents. What is the town’s total demand function ( Q = Q1 + Q2 as a functiof P )?

The demand curve for the town is the horizontal summation of the demand curves for the two groups. Suppose P =100,then Q1= 20 and Q2 =10. hence Q=30. For P = 60, Q1 =60 and Q2=30. Hence Q=90. We have two points on the demand curve (30,100) and (90,60). Using the point slope formula…

for a line we have, (P-100) = [(60-100)/(90-30)](Q-30), i.e. (P-100) = [-40/60](Q-30), i.e. 3P-300 = 60-2Q, i.e. P = (360-2Q)/3 = 120 -0.67Q. Hence the market demand curve is P= 120 -0.67Q.