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You are the manager of a monopoly that sells a product to two groups of consumers in different parts of the country. Analysts at your firm have determined that group 1’s elasticity of demand is −2, while group 2’s is −4. Your marginal cost of producing the product is $40.

a. Determine your optimal markups and prices under third-degree price discrimination.

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Final answer:

The optimal markups for third-degree price discrimination are calculated using the price elasticity of demand for each group. The optimal price for Group 1 with an elasticity of -2 is $53.33, while for Group 2 with an elasticity of -4 it is $48. The prices were derived by adding the respective markups to the $40 marginal cost.

Step-by-step explanation:

The student has asked about third-degree price discrimination in the context of a monopolistic market. You are given the elasticity of demand for two different consumer groups and the marginal cost of production. Elasticity of demand is a measure of how consumers will respond to a change in price. A higher absolute value of elasticity indicates that consumers are more responsive to price changes.

To determine the optimal markups and prices under third-degree price discrimination, we first consider the price elasticity of demand. The formula used to calculate the optimal markup over marginal cost is given as Markup = (1 / (1 + Elasticity)). Group 1’s elasticity of demand is −2 and for Group 2, it is −4.

  • For Group 1: Markup 1 = 1 / (1 + 2) = 1/3
  • For Group 2: Markup 2 = 1 / (1 + 4) = 1/5

The optimal markups are 1/3 for Group 1 and 1/5 for Group 2. To find the optimal prices, we add these markups to the marginal cost:

  • Optimal Price for Group 1 = Marginal Cost + (Markup × Marginal Cost) = $40 + (1/3 × $40) = $40 + $13.33 = $53.33
  • Optimal Price for Group 2 = Marginal Cost + (Markup × Marginal Cost) = $40 + (1/5 × $40) = $40 + $8 = $48

The optimal price for Group 1 is $53.33, while for Group 2 it is $48. This strategy allows the monopolist to maximize profits by charging different prices to different groups based on their elasticity of demand.

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