Question

Jill and Jack both have two pails that can be used to carry water down from a hill. Each makes only one trip down the hill, and each pail of water can be sold for $6. Carrying the pails of water down requires considerable effort. Both Jill and Jack would be willing to pay $5 each to avoid carrying one pail down the hill, and an additional $5 to avoid carrying a second pail down the hill.

a. If Jack and Jill each must decide whether to carry one or two pails of water down from the top of the hill, how many pails will each child choose to carry? pails.

b. Jill and Jack’s parents are worried that the two children don’t cooperate enough with one another. Suppose they make Jill and Jack share equally their revenues from selling the water. Given that both are self-interested, construct the payoff matrix for the decisions Jill and Jack face regarding the number of pails of water each should carry.

Answer 1

Solution:

Given

Jill and Jack both have two pails

cost of each pail of water = $6

and Jack would be willing to pay $5 each to avoid carrying one pail down the hill, and an additional $5 to avoid carrying a second pail down the hill.

(a) pails will each child choose to carry:

Marginal Cost for each child to fetch a pail of water down the hill = $5.

And Revenue that each child get from sell of a pail of waiter = $6.

We know that each child can make only one trip and both of them have two pails only.

Thus, to maximize profit, they will try to get maximum pail to get sold.

At first jack will get two pails by occurring costs $10

and then Jill will get two pails again occurring costs $10.

Total cost will be $12

and Total revenue will be $24.

Thus profit will be $4 ie (24 - 20)

hence each child will get 2 pails of water.

(b) If Jill and Jack share equally their revenues from selling the water. Given that both are self-interested, the payoff matrix for the decisions Jill and Jack face regarding the number of pails of water each should carry is:

The matrix is given below:

		Jack
		Carry 1 pail	carry 2 pail
Jill	Carry 1 pail	($6,$6)	($6,$12)
	Carry 2 pail	($12,$6)	($12,$12)

From the above matrix it is clear that both the child get maximum payoff with ($12,$12).

Hence the equilibrium outcome is that each child will carry two pails of water.