(Rockeconomics). Consider the economic problem of singer Shakira when trying to maximize her individual income. For simplicity assume that she has just two different sources of income, one is the income from performing live music in concerts while the other one is the income coming from royalties on CD sales. Assume also that she can only perform one concert a year and she can only produce one CD title a year.

If she performs a concert she has to pay a fixed cost Fc that includes all costs associated marketing, promotion and security, musician's time.... She receives all the revenue coming from concert ticket sales where we assume that the stadium in which the concert takes place charges Shakira $17 for each person that attends the concert. Shakira has total freedom to decide the concert ticket price with the only constraint that the demand for ticket for a Shakira concert follows the usual negative slope property.

Additionally, Shakira receives 10% of the price of each CD of her album that is sold. She does not control the price of CDs that is fixed by her Music Company at $20 for each unit. Shakira has no control on final CD prices. This means that Shakira receives $2 for each album sold. Since the Music company manufactures directly the CDs the marginal cost of producing and promoting a CDs for Shakira is zero and she just needs to pay a total of fixed costs of Fcd that accounts for the recording equipment and the cost of her crew.

Assume that of Fcd Fc and are low enough such that is profitable both to perform live concerts and sell CD units.

1. Write the profit function of Shakira as a function of concert and CD revenues assuming that demand of CDs and concerts is independent.

2. From the past data inserted in the Table below find the demand price elasticity of concert attendance assuming that demand elasticity is constant across time.

Year Average ticket price Average concert attendance

2001 12.3 314

2005 18.2 191

Source SGAE

3. Find the FOC that defines the concert ticket prices that maximizes Shakira's profit according to the assumptions done in 1. Take the demand elasticity you have found in 2. and using the FOC find the ticket prices that maximize profits. (Note that what you are finding is the monopoly solution for ticket pricing)

4. Now assume that the demand of CDs depends on the number of people that goes to the concert. Write the profit function of Shakira and the FOC that maximizes Shakira's revenue as a function of concert ticket prices. According to the work of Mortimer &Sorensen (2006) we can infer that the cross demand price elasticity between concerts and CD sales is -1.4. Assume also that Shakira sells around $880 million Cds and that total revenue from concerts is around $126 million. With this information find now the concert ticket prices that maximizes Shakira's profit. Why is it lower than the ticket price that you found in 3.?

5. Now assume that because of piracy total CDs sold by Shakira have decreased by 40%. What is now the profit maximizing price for ticket concerts? What is the intuition? What will happen to ticket prices if CD sales keep decreasing?