Question

A local sports bar routinely promotes sporting events, such as the Super Bowl, the NCAA Sweet Sixteen tournament, the BCS games, the Masters, NBA and NFL playoffs, NHL, baseball, NASCAR, and key curling bonspiels.

By keeping records, the owner has determined that when the cover price is $17 the average number of patrons is 210. For every $1 change in cover charge, the number of patrons changes by 11. Assuming a linear demand curve, calculate the maximum willingness to buy for sporting events at this sports bar.

Answer is 397. Please develop a formula that I could use to answer similar questions and show the work.

Answer 1

We have the three pieces of information

Price P = 17 and at this price Quantity Q = 210. Also the slope of the demand function = derivative of demand function with respect to the price = change in quantity / a $ change in price = 11

The demand function is Q = A - BP where B is the slope and A is the quantity at which P is 0.

Here we use the given values as

210 = A - 11*17

A = 397

Hence the demand function is Q = 397 - 11P. This shows that the maximum willingness to buy for sporting events is 397.