2011HWS3

2011HWS3 - Economics 104B Solution for Problem Set #3...

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Unformatted text preview: Economics 104B Solution for Problem Set #3 Spring 2011 1. You have been just hired as manager of a health spa. The owner has commis- sioned a market study that estimates the average consumers monthly demand for visiting the health spa to be Q = 10- 1 2 P. The cost of operating is C ( Q ) = 2 Q , where Q is the number of visits. The owner has been charging a $64 per month membership fee and a $4 per-visit fee. Part of your salary is 10% of the monthly profits. Suggest a pricing strategy that will increase your salary. Answer: Notice first that the more monthly profits the owner makes the more you will be paid. Thus, the pricing strategy you are going to suggest should increase the monthly profits, in order to increase your salary. Notice also that the cost function implies that the marginal cost is $3 for any number of visits. This together with the given average consumers monthly demand implies that a two-part tariff is possible. The per-unit fee the owner has been charging is $5 which is different from the owners constant marginal cost. Observe next that the average consumers monthly demand implies that the consumer surplus of an average consumer at price p=$3 is 197 2 / 8. Consequently, the best two-part tariff contains $197 2 / 8 for the monthly membership fee and $3 for the per-visit fee. To verify, with this new two-part tariff, the owner makes as monthly profits per consumer $4851.125, whereas with the old two-part tariff the monthly profits per consumer is only $117.5. 2. Suppose a mail-order business has a monopoly on video games in the places A and B. These two places are quite a distance away from each other. The demand for video games in place A is Q A = 55- p A and the demand in place B is Q B = 70- 2 p B . The monopolist can produce video games at the constant marginal cost of $5 per unit. 1 a. If the firm can ensure that video games sold in place A are not resold place B, and vice versa, how many video games will the firm sell in these two places?...
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2011HWS3 - Economics 104B Solution for Problem Set #3...

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