Midterm Examination, Economics 101, July 12, 2002
Below, “Question 1, dealing with material from chapter 2, Answer: False” is abbreviated 1\2\A F, and similarly for all the short format questions (Parts A and B)
Part A. True-False questions.
1\2\A F If all prices double and income triples, then the budget line will become steeper.
2\3\A F The marginal rate of substitution measures the distance between one indifference curve and the next one.
3\4\A T Angela's utility function is U(x1,x2)=3(x1+x2). Her indifference curves are downward-sloping, parallel straight lines.
4\4\A F Maximilian consumes two goods x and y. His utility function is U(x,y)= max(x,y). Therefore x and y are perfect substitutes for him
5\5\A F Josephine buys 3 quarts of milk and 2 pounds of butter when milk sells for $2 a quart and butter sells for $1 a pound. Wilma buys 2 quarts of milk and 3 pounds of butter at the same prices. Josephine's marginal rate of substitution between milk and butter is greater than Wilma's.
6\5\A F If a consumer doesn't consume any snails, but does consume Big Macs, then his marginal rate of substitution between snails and Big Macs (when his snail consumption is zero) must be equal to the ratio of the price of snails to the price of Big Macs.
7\6\A T If two goods are substitutes, then an increase in the price of one of them will increase the demand for the other.
8\8\A T A Giffen good must be an inferior good.
9\8\A T If the Engel curve slopes up, then the demand curve slopes down.
10\8\A F When the price of a good rises and income remains constant, there is a substitution effect on demand but there cannot be an income effect.
11\15\A T A good is a luxury good if the income elasticity of demand for it is greater than 1.
1\2\A C In year 1, the price of good x was 4, the price of good y was 2, and income was 60. In year 2, the price of x was 17, the price of good y was 8, and income was 60. On a graph with x on the horizontal axis and y on the vertical, the new budget line is:
A. flatter than the old one and lies below it.
B. flatter than the old one and lies above it.
C. steeper than the old one and lies below it.
D. steeper than the old one and lies above it.
2\2\A A If you could exactly afford either 5 units of x and 17 units of y, or 8 units of x and 5 units of y, then if you spent all of your income on y, how many units of y could you buy?
3\4\A B If there are only two goods, if more of good 1 is always preferred to less, and if less of good 2 is always preferred to more, then:
A. indifference curves slope downwards.
B. indifference curves slope upwards.
C. indifference curves may cross.
D. indifference curves could take the form of ellipses.
4\4\A C In Professor Mean's class, the first midterm exam and the second midterm exam are weighted equally toward the final grade. With the first midterm's score on the horizontal axis, and the second midterm's score on the vertical axis, indifference curves between the two exam scores are
A. L-shaped with lines extending upward and to the right.
B. L-shaped with lines extending downward and to the left.
C. straight lines with slope -1.
D. straight lines with slope 2.
5\4\A D Charlie has the utility function U(xA,xB)=xAxB. His indifference curve passing through 32 apples and 8 bananas will also pass through the point where he consumes 4 apples and:
A. 16 bananas.
B. 32 bananas.
C. 72 bananas.
D. 64 bananas
6\5\A D Clara's utility function is U(X,Y)=(X+2)(Y+1). If Clara's marginal rate of substitution is -2 and she is consuming 11 units of Good X, how many units of good Y is she consuming?
7\5\A C Coke and Pepsi are perfect substitutes for Mr. Drinker and the slope of his indifference curves is minus 1. One day he bought 2 cans of Coke and 20 cans of Pepsi. (The cans of both drinks are the same size.) You may conclude that:
A. Coke is less expensive than Pepsi.
B. Coke is more expensive than Pepsi.
C. Coke and Pepsi cost the same.
D. Mr. Drinker prefers Pepsi to Coke.
8\6\A A Mary has homothetic preferences. When her income was $1,000, she bought 40 books and 60 newspapers. When her income increased to $1,500 and prices did not change, she bought:
A. 60 books and 90 newspapers.
B. 80 books and 120 newspapers.
C. 60 books and 60 newspapers.
D. 40 books and 120 newspapers.
9\6\A B The demand function is described by the equation q(p)=210-p/4. The inverse demand function is described by:
10\8\A B Rob consumes two goods, x and y. If the price of good x increases and his substitution and income effects change demand in opposite directions:
A. good x must be a Giffen good.
B. good x must be an inferior good.
C. good x must be a normal good.
D. there is not enough information to judge whether good x is a normal or inferior good.
11\14\A D George loves pretzels. His inverse demand function for pretzels is p(x)=49-6x, where x is the number of pretzels that he consumes. He is currently consuming 8 pretzels at a price of $1 per pretzel. If the price of pretzels rises to $7 per pretzel, the change in George's consumer surplus is:
12\14\A B Sir Plus has a demand function for mead that is given by the equation D(p)=100-p. If the price of mead is 65, how much is Sir Plus's (net) consumer surplus?
13\15\A C A peck is 1/4 of a bushel. If the price elasticity of demand for millet is -0.60 when millet is measured in bushels, then when millet is measured in pecks, the price elasticity of demand for millet will be:
14\15\A D The inverse demand function for nectarines is described by the equation p=185-3q, where p is the price in dollars per crate and where q is the number of crates of nectarines demanded per week. When p=$20 per crate, what is the price elasticity of demand for nectarines?
Part C: Problems:
1. Briefly explain in a sentence or two (each) how you could tell:
a) whether a good is a normal good or an inferior good.
b) whether a good is a luxury or a necessity.
c) whether two goods are complements or substitutes.
In your answers, mention the things that need to stay fixed, the things that need to change, and in which direction these things need to change.
a) If prices are left constant and income rises, demand for a normal good will rise and demand for an inferior good will fall.
b) If prices are left constant and income rises, expenditure on a good will rise more than proportionately if the good is a luxury, and less than proportionately if the good is a necessity.
c) Two goods are complements if a rise in the price of one of them decreases demand for the other. Two goods are substitutes if a rise in the price of one of them increases demand for the other
2. The demand for sandwiches is given by q=20-2p.
a) By how much does the quantity demanded change for every $1 increase in price?
b) If the price (p) is 4, what is the price elasticity of demand? I’m looking for a numerical answer.
3. In this question, parts (a) through (d) ask for general expressions, or functions. Parts (f) through (i) ask for numerical answers.
Joe is a graduate student, so he consumes only the essentials: he consumes only wine and cheese. His utility function is U(xw, xc)= xw xc. The prices are pw per bottle of wine, pc per pound of cheese, and his income is m.
a) Draw Joe’s budget line, with cheese on the vertical axis. Shade in his budget set. In general terms, if he bought no wine, how many pounds of cheese could he buy?
b) What is the slope of his indifference curve?
c) What equation must be satisfied if his indifference curve is tangent to his budget line?
d) What is Joe’s demand (function) for wine?
What is his demand (function) for cheese?
Xw=m/2pw and Xc=m/2pc
e) If his income is $12,000, the price per bottle of wine is $6, and the price per pound of cheese is $4. How many bottles does he consume?
How many pounds of cheese?
1,000 and 1,500
f) The price of wine falls to $3 per bottle. How and by how much would his income need to be adjusted so that he could just afford the old bundle? With the adjusted income (what is it?), how much wine would he consume?
adjustment: -$3,000; adjusted income $9,000; Xw(pw,pc,m)=Xw(3,4, 9000)=1,500
g) Now put his income back to its original level (12,000), and keep pw=3, pc=4. How much wine would he consume?
h) What is the substitution effect (of this price decrease)? What is the income effect of this price decrease? What is the total effect? I’m looking for numerical answers.
The income effect is (an increase in the demand for wine by) 500.
Therefore the total effect is (an increase in the demand for wine by) 1,000.