Amovie theater has been charging $10 per person and selling about 500 tickets on a typical weeknight. after surveying their customers, the theater estimates that for every 50 cents that they lower the price, the number of moviegoers will increase by 50 per night. find the demand function and calculate the comsumer surplus when the tickets are $8.

We let x be the number of 50 cents that the price of the ticket had been lowered. This variable is also equal to the number of 50 persons that the total number of moviegoers will increase. The demand function is therefore,
                            Q = a - bP
If the ticket is $10 each,
                           500 = a - b(10)
If the ticket is $9 each,
                          600 = a - b(9)
The values of a and b in the equations are 1500 and 100. 
The demand function is therefore,
                          Q = 1500 - 100P
When the price is only $8
                          Q = 1500 - 100(8) = 700
The consumer surplus is equal to 200.