## 2Z03: Practice Questions for Midterm 1

微观经济学代考 His current utility is min 1, 2(2) = 1. Bundle C gives the same utility because min 1, 2(1) = 1. The other bundles give utility 2.

### 1)Consideralinear market demand function *Q*^{d}* *= 10 *−** ** *and a linear market supply function *Q*^{s}* *=What is the equilibrium price? 微观经济学代考

^{d}

^{s}

a.1

b.3

*c.−*2

d.6

e.none of theabove

2)Considerthe inverse market demand function *p*(*Q*) = 12 2*Q*. For what values of *p *is the demand function demand elastic with respect to price?

*a.p >*4

*b.p <*4

*c.p >*3

*d.p <*6

*e.p >*6

Demand function: *Q *= 6 *− *0*.*5*p*. Elasticity equals *E*(*p*) = Elasticity equals *−*1 when *p *= 12 *− **p*, i.e. *p *= 6. Demand is elastic when *|**E*(*p*)*| **> *1, i.e. *p > *6.

#### 3)Ifthe price elasticity of demand is *−*5, then a 100% increase in price will lead to

a.20% increase in quantitydemanded

b.20%decrease in quantity demanded

c.500%increase in quantity demanded

d.500% decrease in quantitydemanded

e.none of the above

Price increased by 100%, so quantity decreases by 5 *× *100% = 500%.

4)Supposethe consumer’s income is 60, and the price of potatoes is If the consumer buys 10 potatoes, what should the price of burgers be so that the consumer can afford 4 or more burgers? 微观经济学代考

a. 10

b.15

30

c.morethan one of the above

d.none of the above

10 potatoes cost 20, which leaves income of 40. If the price is 10, then 4 burgers are exactly affordable. The other prices are higher, so 4 burgers are not affordable.

### 5)The prices of good 1 and 2 are given by *p*_{1}= 3, *p*_{2} = 6. What is the slope of the budget line when the consumption of good 1 is on the horizontal axis?

a.1

b. *−*1

c.2

*d.−*2

e.none of theabove

Slope is *− * = *−*1*/*2.

6)A consumer has the utility function *u*(*x*_{1}*, **x*_{2}) = min *x*_{1}*, *2*x*_{2}. He currently has a bundle (*x*_{1}*, **x*_{2}) =(1*, *2). Which of the following bundles will give him the same level of utility? 微观经济学代考

a.(3*,*2)

b.(5*,*2)

c. (1*,*1)

d.morethan one of the above

e.none of theabove

His current utility is min 1*, *2(2) = 1. Bundle C gives the same utility because min 1*, *2(1) = 1. The other bundles give utility 2.

#### 7)A consumer has the utility function *u*(*x*_{1}*, **x*_{2}) = min *x*_{1}*, *2*x*_{2}.

The prices of the goods are *p*_{1} = $1,*p*_{2} = $2. Currently, he has the bundle (*x*_{1}*, **x*_{2}) = (5*, *2). If he was given an additional dollar, it would be optimal to

a.spendit entirely on good 1

**b**. spenditentirely on good 2

c.spendsome of it on good 1 and some of it on good 2

d.notspend it as he cannot increase his utility

e.none of theabove

At the current bundle *x*_{1} = 5 *> *4 = 2*x*_{2}. Additional income will go first to good 2 until *x*_{1} = 2*x*_{2}. An additional dollar buys 0.5 units of good 2 making *x*_{2} = 2*.*5. At this point *x*_{1} = 5 = 5 = 2*x*_{2}, thus the consumer spends the additional dollar entirely on good 2. If he were given another dollar he would spend it on both goods to increase utility. 微观经济学代考

8)A consumer has the utility function *u*(*x*_{1}*, **x*_{2}) = min *x*_{1}*, **x*_{2}. The prices of the goods are *p*_{1} = 3*, p*_{2} = 5, and his income is *m** *= What is the optimal bundle for this consumer?

a. (1, 1)

b. (8, 0)

c. (0, 4.8)

d. (3, 3)

e. none of the above

The optimal bundle has *x*_{1} = *x*_{2} and exhausts the budget, i.e. *p*_{1}*x*_{1} + *p*_{2}*x*_{2} = 24. Thus, 3*x*_{1} + 5*x*_{1} = 24, and *x*_{1} = *x*_{2} = 3.

### 9)A consumer has the utility function *u*(*x*_{1}*, **x*_{2}) = *x*_{1}+ 3*x*_{2}. The prices of the goods are *p*_{1} = 7*, p*_{2} = 4. What is his marginal rate of substitution? 微观经济学代考

a.1

**b**. *−*1

c.3

*d.−*3

e.none of theabove

The marginal utilities are MU_{1} = 1 and MU_{2} = 3. The marginal rate of substitution is .

10)A consumer has the utility function *u*(*x*_{1}*, **x*_{2}) = *x*_{1}+ 3*x*_{2}. The prices of the goods are *p*_{1} = 7*, p*_{2} = 4. What is the consumer’s optimal choice?

a.spendhis entire income on good 1

b. spendhisentire income on good 2 微观经济学代考

c.spendsome of his income on good 1 and some on good 2

d.wecannot determine (a), (b), or (c) without knowing his

e.none of the above

Preferences are perfect substitutes, so the consumer spends his income on the good(s) with the highest marginal utility-to-price ratio. MU_{1} = 1 and MU_{2} = 3, so

#### 11)A consumer has the utility function *u*(*x*_{1}*, **x*_{2}) = *x*_{1}+ 3*x*_{2}. He currently has a bundle (*x*_{1}*, **x*_{2}) = (18*, *6). What is the maximum number of units of good 2 he would give up to receive an additional unit of good 1?

a.1

b.1

c.3

d.6

e.givingup any number of units of good 2 will decrease his utility.

Receiving an additional unit of good 1 will increase utility by 1 (because of perfect substitutes this is independent of the current bundle the consumer has). Giving up 1 units of good 2 will decrease utility by 1 (3) = 1 matching the utility increase. 3

12)Aconsumer has the utility function *u*(*x*_{1}*,** **x*_{2}) = *x** *4 *x** *4 .Which one of the following statements is true for the optimal bundle (*x** ^{∗}*1

*,*

*x*

*2)?*

^{∗}a.Themarginal utilities of both goods are equal at (*x** ^{∗}*1

*,*

*x*

*2). 微观经济学代考*

^{∗}b.Theslope of the budget constraint equals the marginal rate of substitution at (*x** ^{∗}*1

*,*

*x*

*2).*

^{∗}c.Theconsumer spends half his income on good 1, and half his income on good 2.

d.morethan one of the above

e.neither of theabove

Part b is true because preferences are Cobb-Douglas. Answers a and c are false in general without knowledge of the ratio of prices.

### 13)Themarginal rate of substitution of a consumer with Cobb-Douglas preferences

a.is constant

b. depends on the bundle(*x*_{1}*, **x*_{2})

c.depends on theprices

d.morethan one of the above

e.none of theabove

It depends only on the bundle, and not on the prices.

14)The demand function for good 1 of a consumer with utility function *u*(*x*_{1}*, **x*_{2}) = *x *3 *x *3 when pricesare

These are Cobb-Douglas preferences. The consumer spends 1*/*3 of his income on good 1. 微观经济学代考

15)TheEngel curve plots the demand for a good as a function of

a.itsprice

b.theprice of the other good

c.its marginalutility

d.income

e.none of theabove

### 16)A consumer considers potatoes an inferior good. What is true of the Slutsky income (IE), and total (TE)effects of a decrease in the price of potatoes on this consumer’s demand for potatoes? 微观经济学代考

*a.IE **> *0 and *T E >*0

*b.IE **> *0 and *T E <*0

*c.IE **< *0 and *T E >*0

*d.IE **< *0 and *T E <*0

e.Cannot be determined without further

An inferior good has an income effect which goes in the opposite direction of the substitution effect.Here, the price of potatoes decreases so the substitution effect is positive, meaning that the income effect is negative. However, without further information the sign of the total effect cannot be determined, as the income and substitution effects go in opposite directions. This is unlike the case of a Giffen good, where we know the sign of the total effect (which here would be negative).

#### 17)Consider a consumer with preferences *u*(*x*_{1}*,** **x*_{2}) = min*{*2*x*_{1}*,** *3*x*_{2}*}*. The prices of the goods are *p*_{1} =5, *p*_{2}= His income is *m > *0.

Which of the following statements are true for the Slutsky (SIE), Hicksian (HIE) income effects, and the total effect (TE) of an increase in the price of good 1 to *p** ^{′}*1 = 10 on the demand for good 1?

*a.SIE *= *HIE *= *T E >*0

b. *SIE *= *HIE *= *T E <*0

*c.SIE *= *HIE *=0

*d.SIE **̸*=*HIE*

e.Cannotbe determined without further information about income

These are “perfect complements” preferences. In this case the substitution effect is 0, regardless of whether it is computed in the “Slutsky” or “Hicks” way. Thus, the total effect equals both types of income effects. The total effect itself is negative because the price of good 1 increased, which will cause the consumer to buy less of each good lowering his utility. 微观经济学代考

18)Mary’spreferences can be described by the utility function *u*(*x*_{1}*,** **x*_{2}) = Her income is *m** **>** *0 and *p*_{1} = *p*_{2} = 1. Suppose that *p*_{2} increases to *p*2*′** *= 2. Which of the following is true about the change in her optimal consumption of good 2 after this price increase?

a.TheSlutsky substitution effect is positive.

b.TheSlutsky income effect is equal to the total effect

c.TheSlutsky income effect is positive

d.TheSlutsky income effect is zero

e. None of theabove

Cobb-Douglas preferences like this imply that Mary considers each good a normal good. Hence, the income and substitution effects are in the same direction. In this case they are both negative because the price of good 2 increased. They are not equal because the weights in the Cobb-Douglas utility function are not equal. Both effects are positive, which can be verified generally.

### 19)Consider Mary from the previous question. Her income is *m > *0 and *p*_{1}= *p*_{2} = 1. Suppose that *p*_{2} decreases to *p*^{′}2 = 0*.* Which of the following is true about the change in her optimal consumption of good 2 after this price decrease? 微观经济学代写

^{′}

a.TheSlutsky income effect is negative

b.TheSlutsky substitution effect is zero

c.TheSlutsky substitution effect is positive

d.TheSlutsky income effect is positive

**e**. Morethanone of the above

When the price of good 2 decreases, both income and substitution effects are positive. Thus, C and D are correct.

20)Angelahas “perfect substitutes” preferences for cherries and She is always equally happy to have 3 extra strawberries or 2 extra cherries. The price of cherries is $5, while the price of strawberries is $4. Angela’s income is $10. 微观经济学代考

Suppose the price of cherries increases to $7. What is the income that would make Angela afford exactly her optimal consumption before the price increase?

a.$4

b.$10

c.$14

d.$17.5

e.None of the above

Angela’s preferences can be described by the “perfect substitutes” utility function: *u*(*c, s*) = 3*c *+ 2*s *where *c *denotes cherries, and *s *denotes strawberries. The per-dollar marginal utilities of each good are

so Angela spends her entire income of $10 on cherries which buys her = 2 cherries.

Under the new price of cherries, she needs an income of 2(7) = 14 to afford her original consumption of two cherries and no strawberries.

21)ConsiderAngela from the previous What is the Slutsky substitution effect of the increase in the price of cherries to $7?

*a.−*2*.*8

**b**. *−*2

*c.−*2*.*5

d.0

e.None of theabove

When the price of cherries increases to 7, the per-dollar marginal utility of cherries becomes

so Angela spends her entire income on strawberries under the new prices (regardless of what her income is). To find the substitution effect we need to find

consumption under new prices and adjusted income *−** *consumption under old prices and old income which equals 0 *− *2 = *−*2.