17.25. A small town in Florida is considering hiring an orchestra to play in the park during the year. The music from the orchestra is nonrival and nonexclusive. A careful study of the town’s music tastes reveals two types of individuals: music lovers and intense music lovers. If forced to pay for an outdoor concert, the demand curve for music lovers would be Q1 = 100 - (1/20)P1, where Q1 is the number of concerts that would be attended and P1 is the price per (hypothetical) ticket (in dollars) to the concert. The demand curve for intense music lovers would be Q2 = 200 - (1/10)P2. Assuming the marginal cost of a concert is $2800, what is the efficient number of concerts to offer each year?
Concerts are public demand so we find their market demand by vertical summation of individual demand curve.
Q1 = 100 - (1/20)P1
So, (1/20)P1 = 100 - Q1
So, P1 = 20*(100 - Q1)
So, P1 = 2000 - 20Q1
Q2 = 200 - (1/10)P2
So, (1/10)P2 = 200 - Q2
So, P2 = 10*(200 - Q2)
So, P2 = 2000 - 10Q2
Market demand, P = P1 + P2 = 2000 - 20Q + 2000 - 10Q = 4000 -
30Q
(Because Q1 = Q2 = Q)
Efficient number of concerts are determined where P = Marginal
cost. So, we get,
4000 - 30Q = 2800
So, 30Q = 4000 - 2800 = 1200
So, Q = 1200/30
So, Q = 40
The efficient number of concerts to offer each year is 40.
17.25. A small town in Florida is considering hiring an orchestra to play in the park...