a)
Q1=500-10P1
Q2=200-5P2
TC = 2000+10Q
Step 1. Find marginal revenues
curve
P1 = (500-Q1)/10 = 50-0.1*Q1
P2 = 100-0.2Q2
TR1(Q1) = p1Q1 = (50-0.1Q1)*Q1 = 50Q1-0.1Q1^2
TR2(Q2) = p2Q2 = (100-0.2Q2)*Q2 = 100Q2-0.2Q2^2
MR1(Q1) = 50-0.2Q1
MR2(Q2) = 100-0.4Q2
Step 2 Find optimal sales for Q1 and
Q2 group
MC (Q1+Q2) = 10
MR1Q1= MC
50-0.2Q1 = 10
200 = Q1
MR2(Q2) = MC
100-0.4Q2=10
Q2=225
Step 3 Find prices by replacing
quantities
P1 = 50-0.1*200= 50-20=30
P2 = 100-0.2*225 = 55
b) He needs to charge P1= 30 as it would still be under profit
Q P TR TC Profit
425 30 12750 6250 6500
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