Question

Suppose the demand for tickets to a Titans' football game is given by the equation P = 200 - .002Q^d. Total player costs are $40m, and the remaining costs of operating the franchise are $10m. All of the costs are fixed (let MC=0), and stadium capacity is 55,000.

1. What is the profit maximizing price and quantity for Titans tickets?
2. Depict your solution in a diagram. Be thorough and precise.
3. Suppose the Titans signed better players. What would happen to ticket prices? What would happen to the number of tickets sold?
4. Draw a new diagram which depicts these changes. Does this effect depend on player salaries, per se?
5. Suppose that demand increased to P = 300 -.002Q^d. Recall the constraints listed at the outset in the problem and calculate the profit maximizing ticket price. Be sure to discuss how many tickets the Titans "wish" they could sell vs. the number that they can sell.

Answer 1

P=200-0.002Qd

MC=0

a) For profit maximizng quantity, condition is:

MR=MC

MR=Differentiation of TR with respect to Qd

TR=PxQd= 200Qd-0.002Qd2

MR=200-0.004Qd

Profit maximizing quantity:

MR=MC

200-0.004Qd=0

200=0.004Qd

Qd=200/0.004= 50000 Equilibrium quantity for titan tickets.

P=200-0.002Qd=200-100=100 equilibrium ticket price.

b) Demand curve is downward sloping as AR curve. Revenue and cost on Y axis and quantity on x axis. MR is also starts at point on Y axis from where demand curve starts and MR is more steep than AR.

As MC is zero so equilibrium arises where MR cuts X axis at quantity of 50000 tickets and through point A on AR price is 100.

c) Suppose the Titans signed better players, this will cause rise demand for titan's ticket. So now it can sell more ticket at a higher quantity.

d) Due to rise in demand, AR curve shift to right as AR1 and MR also shift to right as MR1. MR1 cuts the X axis at q2 quantity which is an equilibrium quantity and thorigh point B on AR1 the new equilibrium price is P1.

We can observe that both Price and quantity rises

When deciding about the equilibrium, the fixed cost does not play any vital role so here player salary does not affect the solution.