<p>Consider a movie theater as a monopolist. There are two groups of moviegoers,

Question

<p>Consider a movie theater as a monopolist. There are two groups of moviegoers, students<br />and non-students. The students' demand function for movie tickets is Qs = 200-20ps,&#160;and the non-students' demand function is Qn = 100- 5pn. The movie theater incurs&#160;zero marginal cost for serving additional customer, but there is a fixed cost of showing&#160;a movie at $100.</p>
<p>(a) Suppose the movie theater charges a uniform ticket price to both students and<br />non-students.<br />i. How many tickets will be sold to students and non-students? And at what<br />price?<br />ii. What will be the movie theater's profit?</p>
<p><br />(b) Suppose now the movie theater charges dierent prices to students and non-students,<br />using student IDs as a means to separate the two groups.<br />i. How many tickets will be sold to students and non-students? And at what<br />prices?<br />ii. What will be the movie theater's prfit?<br /><br /></p>

Explanation / Answer

For optimum strategy...Marginal cost = Marginal return here marginal cost = 0 (given) So optimality exists for Marginal Return = 0 When both the prices are same... Total Quantity = 300 - 25P Return = Quantity*Price = Q*P P = (300 - Q)/25 for previous equation i.e. return = (300Q - Q^2)/25 Marginal return = (300 - 2Q)/25 differentiating the return function hence, (300 - 2Q)/25 = 0 i.e. Q = 150 P = $6 Number of tickets sold to students = 200 - 20*6 = 80 Number of tickets sold to non students = 100 - 5*6 = 70 Price for both = $6 Movie theatre's profit = 150*$6 - $100 = $800 When both prices are different.... For students, Marginal Return = 0 Return = Quantity*Price = Q*( 200 - Q)/20 Return = (200Q-Q^2)/20 Marginal return = (200 - 2Q)/20 = 0 differentiating hence, Q = 100 P = $5 Tickets sold to students = 100 Price for students = $5 For non students, Marginal Return = 0 Return = Quantity*Price = Q*( 100 - Q)/5 Return = (100Q-Q^2)/5 Marginal return = (100 - 2Q)/5 = 0 differentiating hence, Q = 50 P = $10 Tickets sold to non students = 50 Price for non students = $10 Movie Theatre's Profit = 50*$10+100*$5 -$100 = $900

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