1. 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

a.) For each stage of L and M, show: marginal cost, marginal benefit; net marginal benefit; net total benefit.

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?

2.

Projects R and S show the following patterns of costs and benefits.

PROJECT R                                         PROJECT S

Total Costs   Total Benefit              Total Cost Total Benefit

$ 5,000             7,000                         $5,000           9,000

10,000             18,000                        10,000           21,000

15,000             41,000                          15,000           40,000

20,000             58,000                            20,000           60,000

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

b.) As in problem #1, available money can be split in $5,000 increments in any way between R and S. What should be funded if the agency has total funds of $10,000; $15,000; $20,000? Why?

3.

Projects C and D have the following patterns of costs and benefits.

Project C                                                         Project D

Marginal Costs($) Marg. Benefits            ($) Marg. Costs Marg. Benefits

6,000                   8,000                                           6,000               7,000

6,000                   8,000                                           6,000                 8,500

6,000                   9,000                                            6,000                   10,000

6,000                   8,000                                             6,000                    11,000

a.) Show the total cost, total 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 $6,000; $12,000; $18,000; $30,000?