S. Klepper, Economics 73-100, Fall 2008

Solutions to Exam II

1. The reduction in the price of good Y means that more units of good Y must be given up in each round to get one additional unit of good X. For example, if the price of good Y declines by 75% to $.25 per unit, then consumers will have to give up four times as many units of good Y to get another unit of good X in each round than in the version of the experiment conducted in class.

It is optimal for the consumer to consume units of good X as long as the willingness to pay for an additional unit of good X (measured in terms of the number of units of good Y the consumer is willing to give up for an additional unit of good X) is greater than or equal to the price of good X (measured in terms of the number of units of good Y the consumer must give up to get another unit of good X). The consumer’s willingness to pay schedule (in terms of units of good Y the consumer would give up to get another unit of good X) at each possible point defining level 1 is not changed by the decrease in the price of good Y. However, in each round the price of good X, in terms of the number of units of good Y the consumer has to give up to get another unit of good X, goes up. Before the fall in the price of good Y, the optimal choice in each round was such that the consumer’s willingness to pay for the marginal unit of good X (in terms of units of good Y) was just equal to the price of good X (in terms of units of good Y). With the price of good X higher, it will no longer be optimal to consume the last unit of good X (and possibly other units of good X as well), hence the point chosen on level 1 will involve less units of good X and more units of good Y than prior to the decline in the price of good Y.

The consumer must be at least as well off in every round as before the decrease in the price of good Y. The consumer could still consume the same combination of good X and good Y in every round and attain at least as high a level because the cost of this combination would now be less due to the fall in the price of good Y. Indeed, the reason the consumer would choose a point with less of good X and more of good Y is precisely because this combination would cost less than the original combination, enabling the consumer to get to at least as high a level as originally. Since the consumer gets to at least as high a level as in the version of the experiment conducted in class, the total amount of Y consumed in every round must be at least as great, if not greater, than in the version of the experiment conducted in class.

If the price of good Y declined by exactly 75%, to $.25, consumers will choose a point on level 1 involving less of good X and possibly less of good X in total. For example, consider round 1 in which the price of good X was $3 and the consumer’s income was $90. At a price of good Y equal to $.25, the consumer would have to give up 12 units of good Y to get another unit of good X. Therefore, the consumer would choose the point (6,18) rather than the point (9,3), as the consumer’s willingness to pay for the sixth unit of good X is 12 units of good Y. The cost of (6,18) is $22.50, so the consumer would be able to get to level 4 (90/22.50). Hence the total amount consumed of good X would be 4 times 6 or 24 units, which is less than the 27 units consumed in round 1 in the version of the experiment conducted in class. Therefore, the demand curve for good X at an income of $90 would not shift to the right at every price as a result of the decrease in the price of good Y.

Whatever the price of good Y, suppose that in any round the consumer’s income doubled and the price of good X was unchanged. The same point on level 1 would still be optimal but the consumer would get to twice as high a level and hence would increase his or her consumption of good X by 100%. Hence it would still be the case that the income elasticity of demand would be 1 at every point on any demand curve.

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

[3] 1. True

[5] 2. False

[5] 3. False

[5] 4. True

[7] 5. True

[6] 6. True

[6] 7. False

[6] 8. True

2. Suppose firms are taxed based on their 2008 payroll. The amount they pay in tax in 2009 will equal 10% of the firm’s 2008 payroll and hence will not depend on how much output they produce in 2009. Consequently, the tax will only increase the fixed cost of production. It will not affect the firm’s marginal cost curve, hence its supply curve in 2009 would be the same as in 2008. Furthermore, its minimum average variable cost of production would be the same in 2009 as 2008, hence if the price in 2009 was greater than or equal to the price in 2008 then the firm would produce in 2009. Furthermore, if the price of the firm’s output in 2009 was the same as in 2008 then it would produce the same level of output in 2009 as in 2008 and thus hire the same amount of labor in 2009 as 2008. Alternatively, if the price of the firm’s output in 2009 was greater than in 2008 then it would produce a greater level of output in 2009 than 2008 and hence hire more labor in 2009 than 2008.

Suppose alternatively that the tax was imposed on the firm’s 2009 payroll. Then the firm’s marginal and average variable cost curve would rise by 10% at every level of output, causing its supply curve in 2009 to lie to the left of its supply curve in 2008. This is pictured in figures 1 and 2 below, where the subscript 0 denotes 2008 and the subscript 1 denotes 2009. If the price of the firm’s output was the same in 2009 as 2008, then the minimum level of the average variable cost could exceed the price in 2009, in which case the firm would shut down. Alternatively, suppose the price of the firm’s output was the same in 2009 as 2008 but the minimum level of average variable cost was still below the price in 2009, as pictured in figure 1, where P₀ denotes the price in 2008 and 2009. The firm would produce in 2009 but at a lower level of output than in 2008 and hence would hire a lower amount of labor in 2009 than 2008. Therefore, its payroll would be less in 2009 than 2008 and the total tax it would pay would be less than 10% of its 2008 payroll. Alternatively, if the price in 2009 were 10% greater than in 2008, as pictured in figure 2, then the firm would not shut down in 2009 as the price would still be at least as great as the minimum average cost in 2009. Furthermore, the firm would produce the same level of output as in 2008, denoted as Q₀ in figure 2, and hence would hire the same amount of labor in 2009 as 2008. Therefore, its payroll would be the same in 2009 as 2008 and its tax would equal 10% of its 2008 or equivalently 2009 payroll.

Figure 1

Figure 2

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

[4] 9. False

[4] 10. True

[5] 11. True

[6] 12. True

[5] 13. False

[6] 14. False

[7] 15. True

3. The increase in the price of oil from 2002 to July 2008 was attributed in class to the income growth in the economies of China, India, and the Middle East at around 10% per year. Assuming an income elasticity of demand for oil products of 1, the income growth would be translated into a 10% per year growth in the demand for oil. Such a rate of increase would not only require the price of oil to rise to balance world supply and demand but would also induce producers to defer some of their production to later years, further increasing the price of oil.

If the income elasticity of demand for products manufactured from oil increased to 1.5 as of July 2008, it would cause world demand for oil to increase even further as a result of the growth in income of China, India, and the Middle East. This would put additional upward pressure on the price of oil. If the price elasticity of demand for products manufactured from oil decreased to .1, a larger increase in the price of oil would be required to reduce world demand sufficiently to balance supply and demand. If U.S. and European economies have been in a recession since July 2008, demand for oil would decrease, which would contribute to a fall in the price of oil since July 2008. If OPEC reduced its production of oil since July 2008, this would reduce the world supply of oil, which would contribute to a rise in the price of oil since July 2008. Last, if the U.S. and Europe increased their tax on gasoline in 2009, the demand for gasoline and hence oil in these countries would decline in 2009. This would contribute to a decline in the price of oil in 2009. If oil producers anticipated this would occur as of July 2008, they would shift some of their 2009 production to the rest of 2008, which would cause the price of oil to fall after July 2008.

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

[4] 16. False

[5] 17. False

[3] 18. True

[3] 19. False

[5] 20. True