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.