4. Fred, Ethel, Lucy and Ricky share a duplex. They are trying to decide whether

Question

4. Fred, Ethel, Lucy and Ricky share a duplex. They are trying to decide whether or not to purchase a weight machine. Ricky and Lucy are weight-lifters and each value the machine at S350. Fred and Ethel rarely exercise. Fred values the machine at S20 and Ethel values is at S90. If bought, the machine would be placed in the common basement, so that it can be considered a public good. The machine costs S800. In terms of economic efficiency should they buy the machine? If yes, explain why. If no, explain why not. Suppose that they agree to use the Clarke Tax to decide whether or not to buy the machine and how to pay for it. Will they buy it? Calculate the Clarke Tax that each of them will have to pay. Now, suppose instead that Fred values the machine at S0. Should the machine be purchased? Will it be purchased? Calculate the Clarke Tax in this case

Explanation / Answer

Value receivable from the machine to all = $350 + $350 + $20 + $90

= $810

Cost of the machine = $800

Excess of benefits over cost of the machine = $810 - $800

= $10.

Therefore, in terms of economic efficiency, the machine should be bought, since the benefit is more than the cost of the machine.

Clarke Tax for all = $10 (Since, there would be net benefit when all are involved).

If Fred values that machine at $0 instead of $20, then the total benefit receivable is $790.

Then, Net benefit = $790 - $800

= ($10) or simply 0

Since, the net benefit is negative, it is not advisable to purchase the machine.

Clarke tax now = $0.

Person Benefit / Cost Fred - Benefit 20 Ethel - Benefit 90 Lucy - Benefit 350 Ricky - Benefit 350 Cost 800 Net Benefit 10

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