1) the Assumption That Preferences Are Complete Means That

ECON 303 Fall 2002 Midterm 1 Dr. Cary Deck

This exam consists of 20 multiple-choice questions each worth 2 points. The remaining 60 points come from the three written problems. Your exam should contain 7 pages. Please write your name on the top of each page. Answer each question as best you can. Where appropriate you must show work in order to receive full credit. The exam is closed book. If you have any questions please raise your hand and someone will come to you. There is no talking allowed during the exam. The use of electronic devices other than approved calculators is prohibited. You have one hour and twenty minutes to complete this exam. Exams will not be accepted after the end of the exam has been announced.

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1 D1) The assumption that preferences are complete means that a. more is better than less. b. for any bundle there is a bundle nearby that is at least as good. c. if bundle a is better than bundle b and bundle b is better than c then a is better than c. d. when comparing two bundles one is at least as good as the other.

C2) The marginal utility of a good is a. the additional money that a person must spend to achieve an extra unit of utility. b. the utility a person receives over and above the utility for which the person pays. c. the additional utility a person receives from consuming one more unit of a good. d. the amount of a good that a person must consume to gain a unit of utility.

B3) An inferior good is a good for which a. the income elasticity is positive. b. the income elasticity is negative. c. the cross price elasticity is positive. d. the cross price elasticity is negative.

B4) Which of the following describes a Giffen good? a. The income effect is smaller than the substitution effect. b. As price falls less of the good is consumed. c. The substitution effect is negative. d. As income falls less of the good is consumed.

C5) If a 20% increase in the price of a good leads to a 10% reduction in the quantity, then demand is said to be a. elastic b. unit elastic. c. inelastic d. spastic

B6) If a person has preferences given by u(x,y)=x3y7 then the MRS is a. 3x/7y b. 3y/7x c. 7x/3y d. 7y/3x

B7) Little George currently has 7 cookies and 3 glasses of milk. His utility is given by u(c,m)=cm. Which of the following trades would Little George be willing to make? a. give up 2 cookies for 1 glass of milk. b. give up 3 cookies for 3 glasses of milk. c. give up 2 glasses of milk for 7 cookies. d. give up 1 glasses of milk for 3 cookies.

2 A8) There is an income effect associated with a price change because a. the amount of utility a person can achieve changes. b. the relative prices change. c. the nominal income the person has changes. d. the person chooses a new bundle so as to change their MRS.

B9) If Px=4, Py=7, and Pz=3, which of the following (x,y,z) bundles is the cheapest? a. (3,3,3) b. (4,2,3) c. (2,4,2) d. (3,2,4)

C10) Which of the following describes the transitive property of preferences? a. a }a b. a }b or b }a c. if a }b and b }c then a }c d. if a ~ b then b~a.

B11)Suppose you sell good a. If Jan has u(a,b)=3a+4b and the cost of good b is 1, what is the maximum price you could charge for a unit of a and still make a sell? a. 0.49 b. 0.74 c. 0.99 d. 1.33

D12) Which of the following is a definition for diminishing marginal rate of substitution? a. the marginal utility of consuming an additional unit decreases as income increases. b. as more of a good is consumed holding the other good fixed utility diminishes. c. as more of a good is consumed holding the other good fixed marginal utility diminishes. d. the more of one good a person consumes the less of the other good that person is willing to give up to consume more of the first good.

B13) If a person has preferences given by u(x,y)=x3y2 and $50. How many units of good y should this person purchase if Px=1 and Py=5? a) 2 b) 4 c) 5 d) 10

B14) Imposing a tax of 5% would have the greatest impact on which of the following behaviors? a) smoking cigarettes (Ed= -.35) b) drinking wine (Ed= -.88) c) drinking beer (Ed= -.26) d) eating (Ed= -.21)

3 C15) A person is considering buying a bundle with some x and some y that uses all of their income. This bundle is such that Mux/Px>Muy/Py. In order to maximize their utility this person should a. spend less money. b. buy more of both goods. c. buy more x and less y. d. buy more y and less x.

B16) If Px=4 and Py=6. How many unit of x would a person have to forego in order to consume 2 more units of good y? a. 2 b. 3 c. 4 d. 6

C17) Consumer surplus is a. the area under the demand curve. b. total utility a person receives from consuming the good. c. zero when demand is perfectly elastic. d. zero when demand is perfectly inelastic.

A18) Two goods are compliments if a. an increase in the price of one causes consumption of the other to fall. b. a decrease in the price of one causes consumption of the other to fall. c. the income effect works in the same direction as the substitution effect. d. the income effect works in the opposite direction from the substitution effect.

A19) Everything lying to the northeast of the budget constraint is a. more expensive than the optimal bundle b. preferred to the optimal bundle. c. less expensive than the optimal bundle. d. dispreferred to the optimal bundle.

C20) Which of the following sets of bundles is not indifferent to a person with u(x,y)=min(3x,2y)? a. (3,2) and (2,2) b. (4,3) and (2,5) c. (6,4) and (3,3) d. (7,6) and (4,7)

4 WP#1 Biker Bob likes Blues (b) and Barbecue (q). In fact they are the only things that give him utility and his preferences are captured by u(b,q)=bq. For his ride into Fayetteville last weekend, Biker Bob brought $160. Last year Blues cost $2 and Barbecue cost $4, but this year Blues cost $8 while the price of Barbecue remained unchanged. How much did the price increase impact Biker Bob’s Blues consumption? (4 points)

Use MRS=ratio of the prices and the BC. Initially, q/b=2/4 so 2q=b and 160=2b+4q. Therefore b=40 and q=20. Initially, q/b=8/4 so q=2b and 160=8b+4q. Therefore b=10 and q=20. The total impact on b is 40-10 =30.

What are the income and substitution effects associated with this price change? (3 points each?)

Use the new prices and old level of utility. Thus q=2b and u=40*20=800. Hence qb=200 or 2b2=800. Thus b=20 and q=40. The SE is 20-40=-20 and the IE is 10-20=- 10.

How much more money would Biker Bob need to have brought to Fayetteville to be as happy this year as he was last year? (4 points)

Uses old utility and new prices so the bundle is (20,40), which costs 8*20+4*40=320. As Bob had 160 he needs an extra 320-160=160.

Suppose the reason for this price hike was a noise tax that was collected in order to compensate the people who live near Dickson Street and don’t want to hear the Blues. How much money would Biker Bob pay in the tax? (2 points)

The tax is $6 and he buys 10 units so he would pay $60.

How much money would Biker Bob be willing to pay these people in order to avoid the tax? (4 points)

This uses the after price change utility and the old prices. 2q=b and bq=20*10=200. Hence q=10 and b=20 which costs 2*20+4*10=80. Thus he would be willing to give up 160-80=80.

5 WP#2 Glenda the Goblin makes a special potion from snails and children. She uses this potion to create happiness for herself, which is given by the utility function u(s,c)=min(s,3c). Sketch a graph of Glenda’s Indifference Curves for utility levels of 6 and 9. (2 points each)

These are L shaped ICs. The corner for u=6 curve is at (6,2) and the corner for the u=9 curve is at (9,3).

If snails cost $5 and children cost $5, what would be the equation for Glenda's budget constraint if she had $40. (2 points)

BC: 40=5s+5c. The s intercept is at 8 and the c intercept is at 8.

Draw her budget constraint on your graph above. (2 points). If Glenda had $40 to spend, how many children would she purchase (2 points) and how much utility would she receive? (1 point)

Use BC and optimal condition. 40=5s+5c and s=3c. Thus s=6 and c=2. Glenda’s utility would be min(6,3*2)=6.

If Glenda had $80 to spend, how many children would she purchase? (2 points) How much utility would she receive? (1 point)

Use BC and optimal condition. 80=5s+5c and s=3c. Thus s=12 and c=4. Glenda’s utility would be min(12,3*4)=12.

Calculate the Income Elasticity of children associated with income increasing from $40 to $80. (2 points)

% change Q/% change income = [(4-2)/3]/[(80-40)/40]=1

Are children a normal good? (1 point) Explain. (1 point)

Yes, the income elasticity is positive, which means as income increases Glenda consumes more c.

Find the equation for Wanda's income expansion path in terms of children. (2 points) Hint: Since you are looking for the relation between income and the optimal number of children, solve the optimization problem leaving in I for income and c for children.

I=5c+5s from the BC. s=3c from the optimal condition. Therefore, I=5c+5(3c)=20c. The equation for the income expansion path in terms of c is c=I/20. This is known as an Engle curve.

6 WP #3 Winkin, Blinkin and Nod are Opie's three birds that eat worms and insects and this makes them happy. In fact Winkin's utility is given by u(w,i)=w+i, Blinkin's utility is given by u(w,i)=3w+i and Nod's utility is given by u(w,i)=3w+2i. Worms cost 2 and insects cost 1. If Opie has $15 and is going to spend the same amount of money on food for each bird, how many worms should he buy? (4 points)

Opie is going to spend $5 per birs so each will either get (2.5,0) or (0,5). W: u(2.5,0)=2.5; u(0,5)=5. W consumes no worms. B: u(2.5,0)=7.5; u(0,5)=5. B consumes 2.5 worms. N: u(2.5,0)=7.5; u(0,5)=10. N consumes no worms. The total number of worms Opie should buy is 0+2.5+0=2.5

How much money in total would Opie need to make each bird achieve a level of happiness equal to 12? (4 points)

Need to buy cheapest corner of the level 12 IC. W: The corners are (12,0), costing 2*12=24 and (0,12), costing 1*12=12. Needs $12. B: The corners are (4,0), costing 2*4=8 and (0,12), costing 1*12=12. Needs $8. N: The corners are (4,0), costing 2*4=8 and (0,6), costing 1*6=6. Needs $6. Therefore Opie needs 12+8+6=$26.

Suppose that Opie spends $5 on each bird, which birds would be made worse off if the price of worms increased? (3 points).

Only Blinkin would be made worse off since the price of worms was already to high for the other given that insects cost 1.

What is the equation for each bird's demand for worms? (2 points each)

With linear preferences one should consume I/Px if MUx/Px>MUy/Py and 0 otherwise. W: 1/Pw > 1/1 if Pw<1. W’s demand is given by 5/Pw for Pw<1 and 0 otherwise. B: 3/Pw > 1/1 if Pw<3. B’s demand is given by 5/Pw for Pw<3 and 0 otherwise. W: 3/Pw > 2/1 if Pw<1.5. N’s demand is given by 5/Pw for Pw<1.5 and 0 otherwise.

Graph the market demand for worms? (3 points)

For prices above 3, market demand is 0. For prices between 3 and 1.5, market demand is 0+5/Pw+0=5/Pw. For prices between 1.5 and 1, market demand is 0+5/Pw+5/Pw=10/Pw. For prices below 1, market demand is 5/Pw+5/Pw+5/Pw=15/Pw.