Economics 172

Spring 2006

Due Friday Feb 17

NOTE: EXAM Wednesday Feb 22

The solution set for this will be posted over the weekend.

Chapter 5

Questions: 8, 10, 11 (hint: What will the budget lines look like?), 14, 19, Problems: 20(use calculus)

8. Relatively more low quality navel oranges will be sold in California than in New York. See solved problem 5.2 for the answer. Suppose low quality oranges cost $1 and high quality oranges cost $1.50 in California. High quality oranges are 50% more expensive. Suppose it costs 25 cents to ship an orange from California to NY. Low quality oranges cost $1.25 and high quality oranges cost $1.75. The ratio of high quality to low quality oranges is 1.75/1.25 so the slope of the budget line is 1.4, which is less steep. High quality oranges are only 40% more expensive in NY so we expect more to be sold in NY and therefore relatively fewer low quality oranges to be sold in NY.

10. Ximing is spending $400 on new college texts which cost $50 each. Used books cost $30. The new texts now cost $60 each, a 20% price rise. Used books are now $33, 10% more expensive. His father sends him $80. But due to the substitution effect, Ximing will not buy all 8 books new. He will substitute used books for new books as his budget line shifts and he will be better off with $80.

Suppose he bought all 8 books new. Then the $80 will make him whole and he will have spent $480. But if he buys any number of used books he will be better off. Suppose he buys all 8 books used. That will cost him $33 x 8 = $264. He will be $216 better off. As long as he buys at least one used book, he will be better off.

11. Draw an original budget line with slope w (wage). The plan will give the person $L if he works 0 hours but the wage will be 1/2w if she does work. The y intercept (composite good intercept) of the new budget line will be ½ the level of the old intercept.

Money Income

Composite Good

Original Budget Line

CG1

1/2 CG1

New Budget Line

Leisure

24 hours

Now look at the indiference curves, which represent tastes. Suppose we look at person A, who does not accept the $L subsidy. His indifference curve on the original budget line is U1 and the one that gets him onto the new budget line is U2, which is clearly below U1 and therefore makes him worse off. He will not accept the subsidy.

Money Income

Composite Good

Original Budget Line

CG1

1/2 CG1

New Budget Line

Leisure

24 hours

However, the person below will accept the subsidy because he is better off. The subsidy, even with the tax, allows him to be on a higher indifference curve because he enjoys leisure a lot more than the other person.

14. Jerome has a kinked budget line. For the first 8 hours of work, he will choose the higher paying job with wage w. If he wants to work more than 8 hours, he will work the additional hours at the job paying w*.

19. A wealthy person would more likely prefer $100 in cash since an addition to their income would be much more preferable to a $100 addition to their food consumption. The poor person would be more likely to spend most of the money on food.

20. We did this in class, but here it is. U = 10R²C

The MU of spare ribs is ∂U/∂R = 20RC

If the price of ribs is $10 and chicken is $5 what is her optimal consumption bundle?

The optimum must occur where MRS = MRT. MRS = (∂U/∂R)/(∂U/∂C) We know the numerator and the denominator is

∂U/∂C = 10R²

MRT = Pr/Pc which = 10/5

MRS = 20RC/10R² = 2C/R

MRS = MRT means 2C/R = 2 which means R=C

How much of each will she consume? The budget line Y=10R + 5C and we know R=C so Y = 10R+5R = 15 R so R = Y/15 and therefore C=Y/15 as well.

1. Left and right shoes are perfect complements for most people. If only the price of right shoes increased, what would be the substitution effect of such a price change on the typical consumer’s consumption of right shoes (assume that the only two goods that the consumer cares about and can consume are left and right shoes)? What about the income effect? Show graphically and explain.

Right

Shoes

BL1

IC1

BL2

IC2

BL3

Left Shoes

The original indifference curve is IC1 with budget line BL1. The person consumes 4 left and 4 right shoes. When right shoes get more expensive, the new budget line is BL2, the dotted line. The new equilibrium point is on a lower indifference curve IC2 where the person consume 3 left and 3 right shoes. To find the substitution effect, draw a new dotted line budget line tangent to the original indifference curve IC1. That’s tangent at the same spot, so there is no substitution effect. The intuition is that you can’t substitute left for right shoes if right shoes are more expensive. The income effect is the same as the total effect.

2. Francis consumes only three different goods: Pepsi, 7 Up, and Vitamin Water. To Francis, Pepsi and 7 Up are inferior goods. Must Vitamin Water be a normal good? Explain.

If Pepsi and 7 Up are both inferior, that means that if Francis’s income goes up, she consumes fewer units of Pepsi and 7 Up. That means she must consume more vitamin water. It must be normal.

3. You go to a carnival in town intending to purchase rides for your children. When you get there they have an offer where everyone's first two rides are free and then after that you pay. The carnival organizers obviously hope that the free rides will end up earning them more revenues (ie people would buy more rides) in the long run than if they charged for all rides.

a. First, show on an indifference curve and budget line graph a solution that would make the free rides a bad idea for the company.

2 Carnival Rides

The budget line is shaped so that the first two rides are free, which means that there is a kink at the budget line at 2 rides. The maximum amount of the CG is still the same as it was if there was a charge for rides. This person buys only two rides.

b. On a new graph, show a possible situation that would make the giveaway a success that should be repeated.

This person buys more than 2 rides.