Question

. Project L and M are two projects such as roads or dams. For L, Stage L1 would be the first stage; L2 the next stage, etc. No stage can begin unless preceding stages have been completed. Thus L2 must be preceded by L1. The projects show the following patterns of costs and benefits.

 

                          PROJECT L                                                       PROJECT M

            Total Cost   Total Benefit                                    Total Cost     Total Benefit

            $5,000               9,000                Stage 1              $5,000               8,000

            10,000              16,000               Stage 2              10,000              14,000

            15,000              21,000               Stage 3              15,000              21,000

            20,000              24,000               Stage 4              20,000              29,000       

 

  

            b.) The money can be split in $5,000 increments in any way between L and M. What should be funded if the agency has total funds of: $15,000; $20,000; $30,000; $40,000?

  

            c.) To what extent does the cost/benefit pattern of project M contradict the principle of decreasing marginal benefits?

Projects A and B have the following patterns of costs and benefits.

 

                                     Project A                                                 Project B

                        Total Costs   Total Benefits                    Total Costs  Total Benefits

                        $4,000                $6,000                           $8,000               13,000

                         8,000                12,000                           16,000               24,000

                        12,000               19,000                           20,000               30,000

                        16,000               25,000                           24,000               36,000

 

            a) Show the marginal cost, marginal benefit, net marginal benefit and net total benefit for each stage (i.e., funding level).

 

            b) As in previous problems, no stage can be chosen without first choosing its predecessors. What should be funded if the agency has total funds of $8,000; $12,000; $16,000; $24,000; $32,000?

Project W returns $5, 000 in benefits for the first $2,000 in costs. The next $2,000 in costs produce $3,000 more in benefits; and the final $2,000 in costs produces an additional $1,200 in benefits.

            a. Sketch a rough graph of total benefit vs. total cost. (In all graphs, the cost should be on the x axis, the horizontal axis.)

            b. Graph marginal benefit vs. total cost.

            c. Graph net marginal benefit vs. total cost.

            d. Which graph provides the most useful information in considering whether to approve                                      Project W at each level of funding?

 

What factors would produce a declining net marginal benefit curve (such as graphed above in 6c) for

             (a) a cancer screening program;

             (b) a remedial reading program for grades 1‑3;

             (c) a garbage collection program;

             (d) a fire protection program?