Suppose the total benefit derived from a continuous decision, Q. is B(Q) = 20Q - 20 and the corresponding total cost is C(Q) =4+20", so that MB(Q)= 20 - 4Q and MC(Q)= 4Q
Hence:
1. Total benefit when 0=2? 0= 10?
When Q=2
Total benefit = 20Q – 2Q2
Total benefit= 20(2)-2(2)^2 =
Total benefit=40-8
Total benefit= 32
When Q=10
Total benefit= 20(10)-2(10)^2
Total benefit=200-200
Total benefit=0
2. Marginal benefit when Q = 2? Q = 10?
When Q =2
Marginal benefit= 20 – 4Q
Marginal benefit=20 -4(2)
Marginal benefit= 20-8
Marginal benefit= 12
When Q=10
Marginal benefit=20-4(10)
Marginal benefit=20-40
Marginal benefit= -20
3. Level of Q that maximizes total benefit
Maximizes total benefit (Q)= 20-4Q=0
Maximizes total benefit(Q)=20/4
Maximizes total benefit(Q)=5
4. Total cost when Q = 2? Q = 10
When Q =2
Total cost = 4 + 2Q2
Total cost=4+2(2)^2
Total cost =4+8
Total cost= 12
When Q=10
Total cost = 4 + 2Q2
Total cost=4+2(10)^2
Total cost =4+200
Total cost= 204
5. Marginal cost when Q = 2? Q = 10?
When Q=2
Marginal cost = 4Q
Marginal cost=4(2)
Marginal cost= 8
When Q=10
Marginal cost = 4Q
Marginal cost=4(10)
Marginal cost= 40
6. Level of Q that minimizes total cost
dC(Q)/dQ= 4Q
dC(Q)/dQ=0
4Q=0
Q=0
7. Level of Q that maximizes net benefits
Marginal benefit(Q)=Marginal Cost (Q)
Hence,
20 – 4Q= 4Q
8Q= 20
Q=20/8
Q=2.5
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