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third_ans

# third_ans - Problems on Third degree price discrimination 1...

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Problems on Third degree price discrimination 1. An event in a stadium was sold out. While 60% of the participants paid full price, the other 40% paid only half price. Some people that were willing to pay more than half price were left out. Conclusion : the organizers could have made more money. True or False. Explain. False. If the consumers that were left out generated lower marginal revenue than the ones that were included, this is con- sistent with pro°t maximization. For example, if there are two groups of consumers with aggregate demands p = 100 ° q h and p = 60 ° q l , pro°t maximization with third degree price dis- crimination requires equating marginal revenues between the two groups: 100 ° 2 q h = 60 ° 2 q l which implies that q l = q h ° 20 : So for example if the capacity of the stadium is 60, then pro°ts are maximized setting q h = 40 and q l = 20 : This implies p h = 60 and p l = 40 ; so there are some consumers from the h group (those with reservations values between 40 and 60 that are excluded even though their willingess to pay is higher than the lower end of the included consumers of the l group. 2. A °rm sells in two separate markets. There is an additional marginal cost of selling in the second market. Therefore, the price in the second market must be higher. True or False. Explain. False. The price in each market also depends on demand elasticity. In other words, if the two costs are c 1 < c 2 and market elasticities are ° 1 and ° 2 ; p 1 ° 1 ° 1 ° 1 ± = c 1 p 2 ° 1 ° 1 ° 2 ± = c 2 so it follows that p 1 p 2 = c 1 (1 ° 1 1 ) c 2 (1 ° 1 2 ) : So even if c 1 < c 2 it could still be true that p 1 > p 2 : 1

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3. A monopolist sells to several markets and is able to do third degree price discrimination. It will choose quantities so that elasticities are equated across these markets. True or False? Explain. False. This is not necessarily true even if marginal cost is the same in both markets. In that case it will choose quantities until marginal revenues are equal across the °rms: p 1 ° 1 ° 1 ° 1 ± = p 2 ° 1 ° 1 ° 2 ± = c elasticities can be di/erent and prices also di/erent so that it is still true that marginal revenues are equal. 4. Demand elasticity in market A is half the demand elasticity in market B and the price a monopolist is charging twice as high. Show that the price in market B is 50% higher than marginal cost. p A ° c p A = 1 ° A p B ° c p B = 1 ° B Dividing the °rst equation by the second one: ° p A ° c p B ° c ± ° p B p A ± = ° B ° A and using p A = 2 p B and ° A = ° B = 2 4( p B ° c ) = p A ° c = 2 p B ° c so it follows that: 2 p B = 3 c and hence p B = 1 : 5 c: 5. There are two groups of consumers. A monopolist is using third degree price discrimination (group pricing). Marginal cost c = 1 is the same in both markets. One of the markets have twice the demand elasticity of the other market. The price in the market with low elasticity p = 2 : What can you infer about the ratio of the prices? Explain your answer.
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