S. Klepper, Economics 73-100, Fall 2010

 

Solutions to Exam III

 

1. The total willingness to pay for cleaning up the lake is 250 x $25 + 250 x $35 = $15,000.This exceeds the cost of $10,000 of cleaning up the lake.Therefore, it is economically efficient for the lake to be cleaned up.

 

If residents of the community could use the lake whether they contributed to cleaning it up or not, then no one will voluntarily contribute toward the clean up.They would know that the total willingness to pay of the community for the lake exceeded the cost of cleaning up the lake and their contribution was not needed to clean up the lake.Furthermore, they could not be prevented from using the lake even if they did not contribute to cleaning it up.Therefore, the dominant strategy of each resident is not to contribute voluntarily to cleaning up the lake.This is true under any circumstances, including when the state government agreed to pay half the cost of cleaning up the lake.

 

If a fence could be built around the lake at a cost of $2,000 and individuals charged for using the lake, then an entrepreneur could make positive profits from cleaning up the lake and building the fence.He or she could charge say $24.50 per person and know that everyone would pay the fee to use the lake because the willingness to pay of everyone was (known to be) greater than $24.50.Therefore, the total revenue he would collect, 500 x $24.50 = $12,250 would exceed his total costs and hence the entrepreneur would undertake the effort.

 

If the community conducted a referendum in which everyone would be taxed $20 to pay for the clean up, it would raise $10,000, which would be enough to cover the clean up of the lake.Every member of the community would vote for the referendum because each would pay less than his willingness to pay and enough money would be raised to clean up the lake, so everyone would be better off.

 

Based on this discussion, the answers to the individual questions, with points allotted to the questions, are:

 

[3] 1. False

 

[6] 2. True

 

[4] 3. False

 

[5] 4. False

 

[6] 5. True

 

 

 

2. With the new redemption schedule, the market demand curve is now:

 

Price

Quantity Demanded

$1.10

24

1.05

48

0.96

72

0.94

96

0.90

120

0.69

144

0.60

168

 

Nothing is changed for the sellers who continue to be offered a payment of $.99 if they sell no output in round 2.They would still be willing to supply up to four units of output at a price of $0.69, but would not sell any output at a price less than $0.69. ††The price would have to be at least $0.90 to get them to supply a fifth unit of output as their marginal cost for the fifth unit is $0.90.

 

For the sellers offered a payment of $1.83 if they sold no output in round 2, their cost of the first unit would be $1.83 + $.23 = $2.06, their total cost of the second unit would be $1.83 + $0.23 + $0.34= $2.40, and so forth.This yields the following total, average, and marginal cost schedules:

 

Quantity

Total Cost

ATC

MC

 

 

 

 

1

$2.06

$2.06

$2.06

2

2.40

1.20

0.34

3

2.91

0.97

0.51

4

3.60

0.90

0.69

5

4.50

0.90

0.90

6

5.70

0.95

1.20

7

7.35

1.05

1.65

 

Their minimum average total cost is $0.90, which is realized at five units of output.Therefore, if the price was less than $0.90, they would sell no output as if they sold output their profits would be less $1.83.Hence no seller offered a payment of $1.83 would sell a unit of output at a price less than $0.90 in round 2.If the price were $0.90 in round 2 then these sellers would have to sell five units of output to earn $1.83 in profit.They would want to sell five units of output rather than none as they would also earn a commission of $.05 on the fifth unit sold and hence earn $0.05 more, including the commission, than if they sold no output.

 

The lowest price at which any sellers would sell output in round 2 is $0.69, and at this output the 16 sellers offered a payment of $0.99 would collectively supply 64 units of output.Buyers would each demand six units of output and the total quantity demanded would be 144.†† This is clearly not an equilibrium as the total quantity demanded exceeds the total quantity supplied.The price will have to rise to lower the quantity demanded and/or raise the quantity supplied.Neither changes until the price rises to $0.90.At this price, each buyer demands five units and the total quantity demanded is 120 units.On the supply side, every seller would want to sell five units of output, hence the total quantity supplied would be 200.Since the quantity supplied exceeds the quantity demanded, price will not go higher than this, and it cannot be lower than this as otherwise buyers would bid up the price.So the price in round 2 will be $0.90 and some suppliers will exit the market.††

 

If every supplier that sold output sold five units of output in round 2 at $0.90, then the total number of units demanded by buyers would be 5 x 24 = 120.This would enable 24 of the 40 suppliers to sell five units each, necessitating the exit of 16 of the 40 suppliers, or 40% of the suppliers.

 

Note, though, that since only 24 of the 40 sellers could sell five units of output, it is possible that some suppliers offered a payment of $0.99 would sell no output and receive a profit of $0.99.If they had offered to sell four units of output at a price of $0.89 (they could not sell a fifth unit because its cost of $0.90 would exceed the price of $0.89), they would have been able to do so because none of the sellers offered a payment of $1.83 would sell any output at a price below $0.90.This would have yielded them profits in round 2 of $1.79, which is obviously better than accepting the $0.99 payment for selling no output in round 2.So it would be expected that some or even all of the 16 sellers offered a payment of $0.99 would first sell four units of output at a price of $0.89 before any other sellers sold their output.

 

This would not alter, though, any of the answers.If the 16 sellers offered a payment of $0.99 each sold four units of output at $0.89, demanders would still want to buy 56 additional units (120-64) at a price of $0.89 or at the higher price of $0.90.In order to get more units supplied by any seller, the price would have to rise to $0.90.At this price each of the 16 sellers offered a payment of $0.99 would want to sell one more unit and the other 24 sellers offered a payment of $1.83 would want to sell five units.Hence the additional quantity supplied at a price of $0.90 would exceed the additional quantity demanded and some sellers would have to exit the market.If only one of the sellers offered a payment of $0.99 sold an additional unit of output, then 11 of the 24 sellers offered a payment of $1.83 would be able to sell in round 2 (collectively these 11 sellers would supply 55 units and the one other seller one unit, for a total of 56 units, and the total quantity demanded would be 56), and hence 13 of these sellers would have to exit.If all the sellers offered a payment of $0.99 were able to sell five units of output in round 2 then collectively they would sell 80 units of output, and the remaining demand of 40 units (120-80) would be supplied by just eight sellers that were offered a payment of $1.83 (each supplying five units), forcing 16 of the sellers offered a payment of $1.83 to exit in round 2.Either way, the number of sellers that would exit in round 2 is less than or equal to 16, which is less than half of all sellers.

 

Based on this discussion, the answers to the individual questions, with the points allotted to them in brackets, are:

 

[4] 6. True

 

[5] 7. True

 

[3] 8. False

 

[6] 9. True

 

[4] 10. True

 

[6] 11. False

 

[6] 12. True

 

[6] 13. False

 

[4] 14. Falseónot true for the sellers offered a payment of $0.99 if they sold no output in round 2.

 

[5] 15. True

 

3. If buyers must make a payment to the government of 10% of the price of a new home in addition to the purchase price of the new home, then at any price charged by sellers, buyers would purchase the same quantity of new homes that they previously would have purchased at a 10% higher price.This is pictured in the figure below by the shift in the demand curve for new homes, where D0 is the original demand curve for new homes and D1 is the demand curve for new homes under the new plan where buyers have to make an extra payment of 10% of the price of a new home to the government. Price in the figure is the price charged by sellers.

 

Originally, at a price of P0, which was the equilibrium price, buyers demanded Q0 homes.But under the new government program, when sellers charge a price of P0, buyers pay a total price of 1.1P0.Consequently, the quantity of new homes they now demand when sellers charge a price of P0 is equal to the quantity Q2 they would have originally purchased at a price of 1.1P0 before the government plan was instituted.Therefore, the demand curve for new homes shifts down at every output, causing the quantity demanded at every price to decline.

 

In the short run, the shift in demand causes the price of new homes charged by sellers to decline.Consequently, the full price paid by buyers does not rise by as much as 10%. The quantity of new homes produced declines to Q1; the extent of the decline depends on the slope of the supply curve and generally will not be 10%.

 

If the industry was in long-run equilibrium before the government plan, the decrease in price will cause sellers to earn negative economic profits.Exit will occur, causing the supply curve to shift from S0 to S1 and the price charged by sellers to be driven back up to P0.Then the full price paid by buyers will be 10% greater than prior to the government plan and the quantity demanded and hence produced will fall to Q2.

 

Based on this discussion, the answers to the individual questions, with points allotted in brackets, are:

 

[6] 16. False

 

[5] 17. False

 

[4] 18. True

 

[7] 19. True

 

[5] 20. True