Question 6 A monopolist sells the same product at the same price into two differ
ID: 1132361 • Letter: Q
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Question 6 A monopolist sells the same product at the same price into two different markets. The demand for the product in market #1 is denoted D1 (p-30-2p where p is the unit price. The demand for the product in market #2 is given by D2(p) 80-3p. 1. If the monopolist sets a price of $5 per unit, what is the demand in market 1? 2. If the monopolist sets a price of $5 per unit, what is the demand in market 2? 3. If the monopolist sets a price of $5 per unit, what is the total demand? 4. If the monopolist sets a price of $20 per unit, what is the demand in market 1? 5. If the monopolist sets a price of $20 per unit, what is the demand in market 2? 6. If the monopolist sets a price of $20 per unit, what will total demand be? . What is the elasticity of total demand at a price of S5 per unit? 8. What is the elasticity of total demand at a price of $20 per unit? 9. Explain why elasticity of total demand is not defined at a unit price of $15. 10. Assume the monopolist's cost function is C(q) = cy. If c 2, what is the optimal price for the monopolist to charge?Explanation / Answer
1. Demand in market 1 = 30 - 2p = 30 - 2(5) = 20
2. Demand in market 2 = 80 - 3p = 80 - 3(5) = 65
3. Total demand = Demand in market 1 + Demand in market 2 = 20 + 65 = 85
4. Demand in market 1 = 30 - 2p = 30 - 2(20) = -10
5. Demand in market 2 = 80 - 3p = 80 - 3(20) = 20
6. Total demand = Demand in market 1 + Demand in market 2 = -10 + 20 = 10
7. The Total demand function = (30 - 2p) + (80 - 3p) = 110 - 5p
Elasticity of demand = (Q/P) * (P/Q)
[Where, Q/P is the price coefficient in the demand function]
= -5 * (5 / 85)
= -0.29 (The absolute value of elasticity is 0.29)
8. The Total demand function = (30 - 2p) + (80 - 3p) = 110 - 5p
Elasticity of demand = (Q/P) * (P/Q)
[Where, Q/P is the price coefficient in the demand function]
= -5 * (20 / 10)
= -10 (The absolute value of elasticity is 10)
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