Question is in the attached image. Thank you! ### Monopolist Pricing and Profit Analysis#### Problem Description1. **Consumer Demand Functions**: - Consumer 1 has the demand function \( y(p_1) = 20 - \frac{p_1}{2} \) - Consumer 2 has the demand function \( y(p_2) = 15 - \frac{p_2}{2} \) **Inverse Demand Functions**: - For Consumer 1: \( p_1 = 40 - 2y_1 \) - For Consumer 2: \( p_2 = 30 - 2y_2 \) The monopolist wants to implement price discrimination by charging different prices to each consumer.2. **Marginal Cost**: - The marginal cost (MC) of the monopolist is 10.3. **Marginal Revenue Functions**: - From Consumer 1: \( MR_1 = 40 - 4y_1 \) - From Consumer 2: \( MR_2 = 30 - 4y_2 \)#### Tasksa) **Calculate the monopolist's price for each consumer**.b) **Common Pricing**: - If the monopolist cannot differentiate between consumers and must charge a common price \( p \), what would \( p \) and \( y \) be? - The inverse demand function for the common price is given by \( p = 70 - 2y \) and the marginal revenue is \( MR = 70 - 4y \).c) **Calculate the difference in profits between the two cases**.#### Detailed Steps1. **Individual Pricing**: - **For Consumer 1**: - Marginal Revenue (MR) function: \( MR_1 = 40 - 4y_1 \) - Set \( MR_1 = MC \): \( 40 - 4y_1 = 10 \) ⟹ \( 4y_1 = 30 \) ⟹ \( y_1 = 7.5 \) - Inverse demand, \( p_1 = 40 - 2y_1 = 40 - 2(7.5) = 25 \) - **For Consumer 2**: - Marginal Revenue (MR) function: \( MR_2 = 30 - 4

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1) Suppose there are two consumers. Consumer 1 has the demand func- tion y(pı) 20 – P1/2, the second consumer has the demand function y(P2) = 15 – = 40 – 2yı – p2/2. Inverse demands are then given by p1 and p2 = 30 – 2y2 The monopolist wants to charge different prices for each consumer. Suppose that marginal cost of the monopolist is 10. Marginal revenue from consumer 1 is then MR 40 – 4y1 and from consumer 2, MR2 3 30 — 4у2 %3D a) Calculate the monopolists price for each consumer. b) Suppose the monopolist cannot differentiate between each consumer and much charge the common price p. What would p and y be? In this case the inverse demand is given by p = 70–2y and marginal revenue is MR=70–4y c). Calculate the difference in profits between the two cases.