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AK9.8

AK9.8 - ECON 211 Fall 2009 Problem Set 9(100 points Due on...

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ECON 211, Fall 2009 Problem Set 9 (100 points) Due on Friday, Nov. 13 Part I. Graded Questions Problem 1: (40 points) A multimarket (third-degree) price discriminating monopolist offers tickets for children and adults. The demand for adult tickets is given by p a =10 - q a and the demand for children tickets is given by p c = 5 - (1/2)q c . Marginal cost equals to 2. a. (5 points) What price does it charge for adult tickets? p a =10-q a => MR=10-2q a Setting MR=MC gives 10-2q a =2 => q a =4 => p a =6 b. (5 points) What price does it charge for child tickets? p c =5-(1/2)q c => MR=5-q c Setting MR=MC gives 5-q c =2 => q c =3 => p c =3.5 c. (5 points) How many tickets does it sell of each type? From A and B we know that q a =4 and q c =3. d. (5 points) What is the profit of the monopolist? Profit = q a *(p a -2) + q c *(p c -2) = 4*(6-2)+3*(3.5-2) = 20.5 Suppose the monopolist is not allowed to discriminate between children and adults, so it has to charge a single price to everybody. e. (10 points) Calculate the demand function of the combined demand for tickets. Hint: Calculate one equation for prices between 0 and 5 and another for prices between 5 and 10. p a =10-q a => q a =10-p a p c =5-(1/2)q c => q c = 10 – 2 p c If p<5 then both Children and Adults buy tickets: q a+c = q a + q c = 10-p a + 10 – 2 p c p a = p c = p => q a+c = 20 - 3p => p = 20/3 – q a+c /3 for p < 5

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If 5<p<10 then only Adults buy tickets: q a+c = q a = 10-p a p a = p c = p => p=10-q a+c for 5<p<10 f. (5 points) Compute the equilibrium price and quantity without discrimination. Hint: Check both of the two equations of the demand curve. If we assume p<5 p = 20/3 – q a+c /3 => MR = 20/3 – 2*q a+c /3 Setting MR = MC => 2 = 20/3 – 2*q a+c /3 => q a+c = 7 => p = 4.333… The demand function we used assumed p<5. So we must check our final answer for p<5. 4.33… < 5 so the answer does not violate our assumptions Profit = 7* (4.333… – 2) = 16.333… If we assume 5<p<10 p=10-q a+c => MR = 10- q a+c Setting MR=MC gives 10-2q a+C =2 => q a+c =4 => p=6 The demand function we used assumed 5<p<10. So we must check our final answer for 5<p<10. 5<6<10 so the answer does not violate our assumptions Profit = 4*(6-2)=16 Profit is larger selling to both than just adults, so that price and quantity will be chosen: q a+c = 7 , p = 4.333… g. (5 points) Compute the profit without discrimination and compare it to the profit with discrimination.
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AK9.8 - ECON 211 Fall 2009 Problem Set 9(100 points Due on...

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