Post by: Sadjam2 on Nov 23, 2022
The graph shows the marginal social cost (MSC) and marginal social benefit of national security, a public good.
Assume that P1= 124, P2=$210, P3=$255, P4=$365, P5=$527, Q1=1,255, Q2=1,830, and Q3=2,760. After performing cost-benefit analysis, what is the net benefit of providing the optimal level of national security?
Please round your final answer to two decimal places.
◦ $715,530.00
◦ $1,062,315
◦ $368,745
◦ $346,785.00
Post by: viper01 on Nov 23, 2022
The net benefit of national security, a public good, is the difference between total benefits and total costs.
Net benefit = Total benefit - Total cost
The optimal level of national security is where marginal social cost (MSC) equals marginal social benefit (MSB).
In this example, at a price of P3 = $255 and a quantity of Q2 = $1,830.
At this point, total benefit is the area below the MSB curve to Q2.
Total benefit = area of rectangle + area of triangle = A + B
A = base * height = (Q2 - 0)*(P3 - 0) = 1,830*255 = $466,650
B = 0.5 * base * height = 0.5*(Q2 - 0)*(P5 - P3) = 0.5*1,830*(527-255) = $248,880.00
Total benefit = A + B = 466,650 + 248,880.00 = $715,530.00
At this point, total cost is the area below the MC curve to Q2.
Total cost = area of rectangle + area of triangle = C + D
C = base * height = (Q2 - 0)*(P1 - 0) = 1,830*124 = $226,920.00
D = 0.5 * base * height = 0.5*(Q2 - 0)*(P3 - P1) = 0.5*1,830*(255-124) = $119,865.00
Total cost = C = D = 226,920.00 + 119,865.00 = $346,785.00
Therefore, net benefit = total benefit - total cost = 715,530.00 - 346,785.00 = $368,745