High Demand: P=20-2Q Low Demand: P=10-2Q MC=$2/unit What are the marginal revenu

Question

High Demand: P=20-2Q
Low Demand: P=10-2Q
MC=$2/unit

What are the marginal revenue curves for each group?
What are the monopoly prices and quantities for each group?
What is the aggregate demand curve for the monopoly?
Find the prices for each group when the firm conducts third degree price discrimination

These are the answers I've worked out myself, though I'm not terribly confident in them:

a) P=20-4Q, P=10-4Q
b) High Demand: (Q:9, P:$2) Low Demand: (Q:4, P:$2)
c) Q=15-P
d) High Demand: (Q:4.5, P:$11) Low Demand: (Q:2, P:$6)

Explanation / Answer

What are the marginal revenue curves for each group? This is P*Q Q*(20-2Q)=20Q-2Q^2 Q(10-2Q)=10Q-2Q^2 What are the monopoly prices and quantities for each group? 2=20-2Q Q=9 then 20-2(9)=2 and 2=10-2Q Q=4 and P=2 What is the aggregate demand curve for the monopoly? solve for Q and sum equations to get Q=15-P Find the prices for each group when the firm conducts third degree price discrimination You are correct here as well with Q=4,P=11 and Q=2,P=6 The only one that looked a little off was the first one. Great job

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