Question

ou are given the following total cost and total benefit curves regarding a lumber development project. TB = 400Q − 2Q2 TC = 20Q (c) Compute the total costs, total benefits, and net benefits in optimum. (d) Compute and interpret the benefit/cost ratio. What policy recommendation would you make regarding the initiation of the project? (e) Present your solution graphically. (f) Now assume that both benefits and costs occur once a year for three years (and are identical in each year), i.e. they are a stream of benefits and costs. What is the present value of net benefits of this project, when discounting begins in year 2 (i.e. year 1: i = 0, year 2: i = 1, year 3: i = 2) and r = 0.05?

Answer 1

We are given with the Total Cost Function and Total Benefit Function:

To find the optimum value of Output, we need to maximize Net Benefits:

On simplifying we get:

We can solve this simply finding the first order derivative and equating it to zero to get the maximum benefits at optimum level of output:

On solving we get:   

c) Total Benefit at Optimum level of Output:

Total Cost at Optimum level of Output:

Net Benefits at Optimum level of Output:

d) Benefit/Cost Ratio:

Interpretation: We can infer that we gain 10.5 units of benefits from spending 1-unit cost

e)