S. Klepper, Economics 73-100, Fall 2010

# Solutions to Exam I

Consider first sellers that were taxed \$.20 in round 3.  The lowest price at which they could sell their unit equaled their cost plus \$.20.  The lowest-cost sellers had a cost of \$1.40.  Therefore, they would sell their unit at a price of \$1.60 or greater.  The next lowest-cost sellers had a cost of \$1.50, and they would sell their unit at a price of \$1.70 or greater.  Applying this reasoning through sellers with a cost of \$2.50, it follows that among these sellers the quantity supplied would be four units (there were 80 traders and hence four with each cost) at a price of \$1.60, eight at a price of \$1.70, 12 at a price of \$1.80, 16 at a price of \$1.90, 20 at a price of \$2.10, 24 at a price of \$2.30, 28 at a price of \$2.50, and 32 at a price of \$2.70.  Among the remaining sellers with costs of \$2.70 and \$2.90 that received a payment of \$.40, they would sell their units at a price of \$2.30 and \$2.50 respectively.  Adding in these sellers to the taxed sellers, the quantity supplied would be 28 units at \$2.30, 36 units at \$2.50, and 40 units at \$2.70.

The demand schedule can be derived similarly.  Among the taxed buyers, the highest price at which they could buy a unit equaled their redemption value minus \$.20.  Therefore, the quantity demanded would have been four units at \$3.40, eight at \$3.30, 12 at \$3.20, 16 at \$3.10, 20 at \$2.90, 24 at \$2.70, 28 at \$2.50, and 32 at \$2.30.  Among the buyers with redemption values of \$2.30 and \$2.10 that received a \$.40 payment, they would buy a unit at a price of \$2.70 and \$2.50 respectively.  Adding these buyers to the taxed buyers, the quantity demanded would be 28 at \$2.70, 36 at \$2.50, and 40 at \$2.30.

Summarizing, the supply and demand schedules in the third round would have been:

Demand and Supply Schedules for Round 3

 Price Quantity Demanded Quantity Supplied \$3.40 4 40 3.30 8 40 3.20 12 40 3.10 16 40 2.90 20 40 2.70 28 40 2.50 36 36 2.30 40 28 2.10 40 20 1.90 40 16 1.80 40 12 1.70 40 8 1.60 40 4

In the third round, every seller would have sold a unit at a price of \$2.70 (or higher) and every buyer would have purchased a unit at a price of \$2.30 or lower.  In rounds 1 and 2, the supply and demand schedules were:

Demand and Supply Schedules for Rounds 1 and 2

 Price Quantity Demanded Quantity Supplied 3.60 4 40 3.50 8 40 3.40 12 40 3.30 16 40 3.10 20 40 2.90 24 40 2.70 28 36 2.50 32 32 2.30 36 28 2.10 40 24 1.90 40 20 1.70 40 16 1.60 40 12 1.50 40 8 1.40 40 4

Comparing the supply schedule in round 3 to the supply schedule in rounds 1 and 2, the quantity supplied in round 3 was less than or equal to quantity supplied in rounds 1 and 2 at prices of \$2.30 and below, greater at  prices of \$2.50 and \$2.70, and the same at prices of \$2.90 and higher.  Therefore, the quantity supplied in round 3 was not less than or equal to the quantity supplied in rounds 1 and 2 at every price. Comparing the demand schedules, the quantity demanded in round 3 was less than the quantity demanded in rounds 1 and 2 at prices of \$2.90 and higher, the same as in rounds 1 and 2 at the price of \$2.70, greater than in rounds 1 and 2 at prices of \$2.50 and \$2.30, and the same at prices of \$2.10 and below.  Therefore, the quantity demanded at a price of \$2.70 was the same in round 3 as in rounds 1 and 2.

The equilibrium price in round 3 (where the quantity demanded equaled the quantity supplied) was \$2.50.  At this price, 36 of the buyers and sellers, or 90% of the traders, would have bought or sold their unit.

Among the sellers that paid a tax of \$.20, all sold their unit in rounds 1 and 2 at a price of \$2.50.  All those with costs of \$2.70 or higher would have continued to sell their unit at a price of \$2.50 but would have paid the tax of \$.20 and so would have earned \$.20 less in profit.  The sellers with a cost of \$2.50 also had to pay the tax of \$.20 but would not have been able to sell their unit at a price of \$2.50.  Thus they would have earned zero profits, which is the same as they earned in rounds 1 and 2 excluding the commission (they sold their units in rounds 1 and 2 but only earned the commission).  Therefore, among all the sellers that paid the tax of \$.20, their profits in round 3 were less than or equal to their profits in rounds 1 and 2.  The same applies to demanders that paid the tax of \$.20—those with redemption values of \$2.70 or greater experienced a decrease in their profits of \$.20 while those with a redemption value of \$2.50 earned zero profits, which is the same as they earned in rounds 1 and 2 (excluding the commission).  Consequently, all traders that paid the tax earned profits in round 3 less than or equal to the profits they earned in rounds 1 and 2.

All the traders that received a \$.40 payment in round 3 would have made a transaction in round 3.  The sellers with a cost of \$2.70 and the buyers with a redemption value of \$2.30 would have earned a profit (excluding the commission) of \$.20, which is \$.20 more than they earned in rounds 1 and 2 when they did not sell or buy a unit.  The sellers with a cost of \$2.90 and the buyers with a redemption value of \$2.10 would also have traded their unit in round 3 but earned no profit (excluding the commission), which is the same as the profit they earned in rounds 1 and 2 when they did not sell or buy a unit.  Therefore, all the traders that received a payment of \$.40 in round 3 would not have earned a greater profit than in rounds 1 and 2.

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

 1. True

 2. True

 3. False

 4. False

 5. True

 6. False—not the traders with costs and redemption values of \$2.50.

 7. True

 8. True

 9. True

 10. False

2.  If in 1990 each unit of food required the same amount of labor but the amount of labor needed to produce each unit of oil increased as more oil was produced, then the production possibilities curve of the country was concave shaped in 1990.  If in 2010 the same amount of labor is still needed to produce each unit of food but twice as much labor is needed to produce each unit of oil then it still must be the case that as more oil is produced, the amount of labor needed to produce each additional unit of oil increases.  Therefore, the country’s production possibilities curve must still be concave shaped in 2010.

If the same amount of labor is still required to produce each unit of food then the maximum number of units of food the country can produce in 2010 must be the same as in 1990.   Consider the maximum number of units of oil it can produce in 2010 versus 1990.  In 1990, the same amount of oil could be produced with half as much labor.  Therefore, if in 1990 the country produced the maximum amount of oil that could be produced in 2010, it would still have had half the labor force to produce additional units of oil. But the second half of the labor force could not have produced as much oil as the first half of the labor force because the amount of labor needed to produce additional units of oil increased as more oil was produced. Therefore, the maximum amount of oil that could have been produced in 1990 was less than twice as much as the maximum amount of oil that could be produced in 2010.  Expressed alternatively, the maximum amount of oil that could be produced in 2010 is more than half as much as the maximum amount of oil that could have been produced in 1990.

Consider the opportunity cost of food and oil in 2010 versus 1990. The opportunity cost of each unit of food is not the same in 2010 as in 1990.  To see this, consider the opportunity cost in 2010 of the last unit of food that can be produced.  This unit of food requires the same amount of labor to produce as in 1990.  But the amount of oil that could be produced with this labor is half as much as could be produced in 1990.  Therefore, the opportunity cost of the last unit of food in 2010 is less than in 1990.  The opportunity cost of each unit of oil that can be produced in 2010 is twice as much as in 1990 because each unit of oil requires twice as much labor to produce in 2010 versus 1990 and each unit of food requires the same amount of labor to produce in 2010 as 1990.

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

 11. False

 12. False

 13. False

 14. True

 15. True

3. The original budget line of the consumer and a possible budget line after the tax are drawn in the figure below.  The original budget line is a straight line.  The consumer originally consumed G0 units of gasoline and F0 units of food.  The new budget line for quantities of gasoline consumed less than 300 gallons is the same as the original budget line because the price of gasoline on the first 300 units consumed is the same.  But after 300 gallons of gasoline are consumed the price of gasoline rises by the extent of the tax, so the budget line becomes steeper at 300 gallons of gasoline.  It has a kink at this point because the effective price of gasoline is greater on all gallons of gasoline consumed above 300.  The figure reflects that after the tax the consumer can still purchase the original amount of gasoline consumed.  However, the original amount of gasoline consumed could also have been greater than the gasoline intercept of the new budget line, in which case the consumer could no longer purchase the original amount of gasoline consumed. The consumer has sustained a decrease in real income due to the tax because the new budget line is such that some combinations of food and gasoline can no longer be purchased and no additional combinations of food and gasoline can be purchased.  The consumer must be worse off as the original combination of food and gasoline can no longer be purchased and whatever combination is purchased after the tax was available before the tax but the consumer chose to purchase a different (preferred) combination of food and gasoline.

It is not possible to tell how much food or gasoline the consumer will consume after the tax.  Depending on the consumer’s preferences, it is certainly possible that the consumer would consume more than 300 gallons of gasoline after the tax.  Regarding food, the price of gasoline for units above 300 has increased, which would lead the consumer to substitute food for gasoline.  However, the consumer has also lost purchasing power as a result of the increase in the price of gasoline, which will generally lead to a decrease in the quantity of food consumed.  The consumer’s choice of gasoline and food could be such that the consumer consumes less of both goods than originally.  For example, the consumer might choose the point (G1, F1), which involves less of both goods and also more than 300 gallons of gasoline.

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

 16. True

 17. False—not necessarily.

 18. False—not necessarily.

 19. True

 20. False