ECON 350 questions

Jasmine is a T-ball coach with homothetic preferences. When her income was $3,500.00, she bought 24.00 balls and 36.00 bats. If her income increases to $5,250.00 and prices do not change, she will buy _____ balls and ________ bats. (Assume it's okay to buy fractional balls and bats. Round your answer to two decimal places if necessary.)

36, 54 (Chapter 6 Question 11)

At prices (𝑝1,𝑝2)=(1,4)(p1,p2)=(1,4), Bob consumes the bundle 𝑋=(3,6)X=(3,6), while at prices (𝑝′1,𝑝′2)=(2,2)(p1′,p2′)=(2,2), he chooses bundle 𝑌=(𝑦1,4)Y=(y1,4). For which values of 𝑦1y1 is the WARP violated?

5 is less than or equal to y1 which is less than or equal to 11 (Chapter 7 Question 10)

Kasey has income of $20.00. She always consumes 2 ounces of cream cheese with one bagel. If the price of cream cheese is $1.00 per ounce and the price of a bagel is $2.00, Kasey will maximize her utility by purchasing ___ bagels and ___ ounces of cream cheese.

5,10 (Chapter 5 Question 9)

Given the different consumption bundles in the graph below (and assuming that we always choose a bundle that (1) maximizes our utility and (2) uses all income), which of the following are true?

A is revealed as preferred to B. A is revealed as preferred to C. A is indirectly revealed as preferred to D. B is revealed as preferred to C. (Chapter 7 Question 6)

Using the diagram below, answer the following questions. Both 𝑥1x1 and 𝑥2x2 are "goods." Which of the labeled bundles on the diagram are affordable (i.e., would not cost more than the consumer's income)? Which of the labeled bundles would be the most preferred bundle for the consumer (regardless of income)? Which labeled bundle is the most preferred bundle the consumer can afford?

A, C, E B C (Chapter 5 Question 2)

Which types of preferences will always result in an interior optimum for utility maximization (assuming income is greater than $0)?

Cobb-Douglas, Perfect Complements (Chapter 5 Question 3)

Which of the situations shown in the figures below violate the WARP? (The bundle chosen at a given budget set is drawn with the same color as the budget set.)

D (Chapter 7 Question 8)

The diagram below shows the budget line and consumption choices for Darrin, Gene, and Katelyn. An increase in the price of salads would cause everyone to decrease their salad consumption except

Darrin (Chapter 2 Question 8)

Which of the following statements are true?

If the SARP is satisfied, then the WARP is satisfied too. If the WARP is violated, then the SARP is violated too. (Chapter 7 Question 17)

Tammie has income of $150. The price of hats is $7 each, the price of gloves is $6, and the price of scarves is $5. The quantity of items in each bundle can be represented by the set (𝑥1x1, 𝑥2x2, 𝑥3x3), where 𝑥1x1 is the quantity of hats, 𝑥2x2 is the quantity of gloves, and 𝑥3x3 is the quantity of scarves. Sort the bundles below into those that are in the budget set and those that are not.

In budget set: (8, 7, 6) (8, 8, 8) (5, 9, 10) (10, 10, 4) Not in budget set: (10, 10, 5) (11, 9, 4) (3, 15, 10) (Chapter 2 Question 7)

Consider the below diagram. Assuming points Y and Z identify optimal points of consumption for different levels of income and prices, is this consumer's behavior consistent with the Weak Axiom of Revealed Preference (WARP)? From the prior part, if the WARP was indeed violated, drag point Y to a point along the budget constraint that would be consistent with WARP. If WARP was not violated, then take point Y and drag it to the origin (0,0).

No, because point Z is revealed as preferred to point Y and point Y is revealed as preferred to point Z. look at graph (Chapter 7 Question 18)

Assume you're in the market for a new Wintendo Nii gaming system. Which of the following events would shift your demand for the Nii gaming system?

Prices for Nicrosoft's Ybox gaming system decrease. A new study comes out touting the health benefits of playing simulated sports video games. Middle East turmoil causes a disruption in the global oil supply, decreasing the value of your stock portfolio. (Chapter 6 Question 15)

Good 𝑥x is a mystery good. Demand for good 𝑥x is given by the following function:𝑥=18𝑚−3𝑝𝑦+36𝑝𝑥 Which of the following goods might be good x? Which of the following might be good y?

basic meals prepared at home meals at nice restaurants (Chapter 6 Question 7)

Nicole spends all her income on books and pencils. If the prices of books and pencils double, which statements are true about her budget line?

The budget line makes a parallel shift inward. The vertical and horizontal intercepts both decrease by 50%. (Chapter 2 Question 13)

The following graph shows the choices made by an individual at three different prices. Which of the following statements are correct?

The choices violate the WARP. The choices violate the SARP. (Chapter 7 Question 19)

Will's utility function can be written as u = 6G + M, where G represents pairs of gloves and Mrepresents pairs of mittens. Based on Will's utility function, which of the following statements are true?

Will is willing to trade 6 pairs of mittens for 1 pair of gloves. For Will, gloves and mittens are perfect substitutes. (Chapter 4 Question 6)

The graph below shows three consumer's choices at three different prices. Which of the following statements are correct?

X is directly revealed preferred to Y. X is indirectly revealed preferred to Z. Y is directly revealed preferred to Z. (Chapter 7 Question 7)

Place the indifference curve diagrams in the appropriate category.

look at graphs (Chapter 3 Question 12)

Rob is always willing to trade one Reese's Piece for one M&M. For Rob, Reese's Pieces and M&M's are __ Use the line tool to draw an indifference curve based on Rob's preferences that passes through the point shown on the diagram below.

perfect substitutes look at graph (Chapter 3 Question 8)

Bundle C is strictly preferred to bundle B, and bundle B is strictly preferred to bundle A. If the utility associated with B is 53, which of the following are possible utility levels for bundle C and bundle A? (The first element in the ordered pair represents the utility for bundle A, the second element in the ordered pair represents the utility for bundle B, and the third is for bundle C.)

(44, 53, 63) (Chapter 4 Question 1)

Burritos (𝑥1x1) cost $18.00 each. A cup of coffee (𝑥2x2) costs $3.00. Jerry's income is $510.00, and his preferences are represented by the utility function 𝑥0.81𝑥0.12.x10.8x20.1. Henry's income is $690.00, and his preferences are represented by the utility function 𝑥0.11𝑥0.82x10.1x20.8. Assuming that both Jerry and Henry are maximizing their utility, what is Jerry's marginal rate of substitution? Round your answers to two decimal places. What is Henry's marginal rate of substitution?

-6 -6 (Chapter 5 Question 13)

Each week, Beth purchases 5.00 pizzas, 10.00 bottles of soda, and 4.00 donuts. These purchases completely exhaust her income. The price of donuts is $2.00 each. If Beth buys one fewer pizza, she can buy 4.00 more bottles of soda or 6.00 more donuts. The price of pizza is $ ___ Based on the same information given in Part 1, the price of a bottle of soda is $__

12.00 and 3.00 (Chapter 2 Question 6)

For Sharon, brownies (𝑥1x1) and cookies (𝑥2x2) are perfect substitutes, as shown in the diagram below. Sharon's income is $120. If the price of one brownie is $10 and the price of one cookie is $2, she will purchase_____ brownies and ______cookies.

0 60 (Chapter 5 Question 7)

What is the marginal rate of substitution at point A in the diagram shown above? What is the marginal rate of substitution at point B in the diagram shown above?

0 infinity (Chapter 4 Question 12)

Suppose prices in period one (base period) are (4, 4) and the consumer chooses (2, 4). In period two (current period), prices are (4.00, 2.00) and the consumer updates her optimal consumption bundle and chooses (5.00, 6.00). The Laspeyres price index of prices in period two relative to period one is ____

0.67 (Chapter 7 Question 16)

Mary likes to watch football and volleyball. Suppose we can observe how many times she goes to see a match in a given year and the price of entry tickets for both sports. In year 𝑏b (for baseline), the price of a football match is $25 and the price of a volleyball match is $18. Mary goes to see three football matches and six volleyball matches. In year 𝑡t, the price of a football match is $20 and the price of a volleyball match is $15. Mary goes to see five football matches and seven volleyball matches. The Paasche price index for Mary's choices is The Laspeyres price index for Mary's choices is The index of the change in total expenditure is Given your previous answers, Mary is better off in year 𝑡t because

0.817 0.819 1.12 Ln<M (Chapter 7 Question 14)

The diagram below shows Steve's indifference curve for bananas and all other goods. All other goods are measured in dollars. At point A, the slope of his indifference curve is -1. If Steve is currently consuming at point A, what is the most he would be willing to pay for one more banana? $__

1 (Chapter 3 Question 13)

The diagram below shows Maria's indifference curve. Bundle 𝑥1x1 includes three units of good 1 and four units of good 2. If Maria is currently consuming at point 𝑥1x1, but would like to consume an additional unit of good 1, how many units of good 2 can she give up and still remain indifferent between the consumption bundle 𝑥1x1 and the new consumption bundle with one additional unit of good 1? Maria is currently consuming at point 𝑥1x1, with 1 unit of good 1 and 12 units of good 2. If she would like to consume an additional unit of good 1, how many units of good 2 can she give up and still remain indifferent between the consumption bundle 𝑥1x1 and the new consumption bundle with one additional unit of good 1?

1 6 (Chapter 3 Question 7)

Devon's utility function can be written as 𝑥0.751𝑥0.252x10.75x20.25, where 𝑥1x1 is the quantity of hamburgers consumed and 𝑥2x2 is the quantity of milk shakes. His income is $2,400.00. Hamburgers cost $8.00 each and the price of one milk shake is $4.00. If he is maximizing his utility, how much will Devon spend on hamburgers? $___ he price of hamburgers decreases to $7.37 each. Now, how much will Devon spend on hamburgers if he is maximizing his utility? $___

1,800 1,800 (Chapter 5 Question 11)

Mary likes to watch football and volleyball. Suppose we can observe how many times she goes to see a match in a given year and the price of entry tickets for both sports. In year 𝑏b (for baseline), the price of a football match is $25, and the price of a volleyball match is $18. Mary goes to see three football matches and six volleyball matches. In year 𝑡t, the price of a football match is $20, and the price of a volleyball match is $15. In year 𝑡t, Mary goes to see five football matches and seven volleyball matches. The Paasche quantity index for Mary's choices is ____ The Laspeyres quantity index for Mary's choices is ____ Which of the following statements is true?

1.367 1.372 Mary is better off at time 𝑡t because the Paasche quantity index is greater than 1. (Chapter 7 Question 13)

Suppose prices in period one (base period) are (2, 2) and the consumer chooses (4.00, 5.00). In period two (current period), prices are (3.00, 4.00) and the consumer updates his optimal consumption bundle and chooses (2, 2). The Paasche price index of prices in period two relative to period one is ___

1.75 (Chapter 7 Question 15)

Susan's preferences can be represented by the utility function 𝑥0.51𝑥0.52x10.5x20.5, where 𝑥1x1 is pounds of chocolate and 𝑥2x2is pounds of bologna. The price of chocolate is $3 per pound, and the price of bologna is $4 per pound. With income of $1200, Susan currently maximizes her utility by purchasing 200.00 pounds of chocolate and 150.00 pounds of bologna. The government imposes a tax of $2 per pound on chocolate. How many pounds of chocolate will Susan purchase if she maximizes her utility with the tax in place? How much tax revenue will the government collect from her? What dollar amount of an income tax, instead of the quantity tax, would leave Susan equally well off?

120 240 270.57 (Chapter 5 Question 14)

When the government imposes an ad valorem tax on all goods at rate 𝜏τ, the price of goods increases from 𝑝p to (1+𝜏)𝑝(1+τ)p. If the consumer's budget line was 𝑝1𝑥1+𝑝2𝑥2=𝑚p1x1+p2x2=m before the tax, the budget line becomes (1+𝜏)𝑝1𝑥1+(1+𝜏)𝑝2𝑥2=𝑚(1+τ)p1x1+(1+τ)p2x2=m. This same budget equation can be rewritten as 𝑝1𝑥1+𝑝2𝑥2=𝑚(1+𝜏)p1x1+p2x2=m(1+τ), indicating that the application of an ad valorem tax is the equivalent of an income reduction. An ad valorem tax of 20% is the equivalent of an income reduction of __ %

16.67% (Chapter 2 Question 15)

Christina enjoys salads and subs for weekday lunches, and she prefers a mix of both to extreme amounts of either one. Specifically, her utility over subs and salads can be represented by the function 𝑢(𝑥1,𝑥2)=u(x1,x2)=10𝑥1𝑥2x1x2 , where 𝑥1x1 is the number of subs she eats per month and 𝑥2x2 is the number of salads. What utility would Christina receive from consuming four subs and four salads in a month? If Christina consumes 16 salads, how many subs will she consume to achieve the same utility as (4,4)? All bundles that provide the utility you found in part 1 lie on the same indifference curve. The equation for this curve can be found by simply setting the utility value equal to the function; it is the curve where u=10 𝑥1𝑥2x1x2. 𝑥2x2 = __/X1 Now graph this equation. Start by plotting the two points you have from Part 1 ((4,4) and the point with 16 salads) as well as the point (16,1). Then use the curve tool to plot the indifference curve through all three points. Suppose that Christina has one sub and 16 salads. Her friend Latoya offers to trade her two subs for 10 salads. Will Christina accept the trade? Suppose Latoya has three subs she is willing to trade. What is the maximum number of salads Christina would give up for three subs?

160 1 16/X1 look at graph yes 12 (Chapter 4 Question 5)

When prices are (8, 1), Ezra chooses the bundle (𝑥1,𝑥2) = (8, 5). When prices change to (𝑝1,𝑝2), he updates his consumption bundle to (7, 7). For his preferences to satisfy the Weak Axiom of Revealed Preference (WARP), it must be true that 𝑝1 > ___ P2

2 (Chapter 7 Question 11)

Zuniga is currently consuming 10 burritos and five bags of chips. If the price of chips falls and we assume that chips are a Giffen good, which one of the following could be Zuniga's new consumption of burritos and chips? You can assume that each of the answers below is affordable.

20 burritos and four bags of chips (Chapter 6 Question 9)

Curtiss lives in a two-good world, where the only goods are cappuccinos and pistachio nuts. Answer the following questions about Curtiss's budget constraint. The price of cappuccinos is $4.00 each. The price of pistachios is $1.00 per pound. If Curtiss has income of $35.00 and purchases 7.00 cappuccinos, how many pounds of pistachios can he buy? The price of cappuccinos is $4.00 each, and pistachios are $1.00 per pound. If Curtiss buys one fewer cappuccino, how many more pounds of pistachios can he buy?

7.00 and 4.00 (Chapter 2 Question 1)

In a two-good world, which condition(s) would prove that good 2 is inferior?

As income increases, demand for good 2 decreases. As income decreases, demand for good 2 increases. (Chapter 6 Question 2)

Refer to the following indifference curve diagrams to answer the questions below. Which indifference curve has a diminishing marginal rate of substitution (MRS)? Which indifference curve has an MRS of 0 and infinity? Which indifference curve has a constant MRS? Which indifference curve has an MRS equal to 0 (everywhere)?

D A both B and C C (Chapter 3 Question 14)

The diagram below shows various bundles of good 1 and good 2. John's indifference curve passes through points A and B. His preferences for good 1 and good 2 are strictly nonconvex. Which of the points labeled C through J could be on John's indifference curve with A and B?

D, E, H (Chapter 3 Question 16)

Isabel currently has 6 graham crackers and 2 smoothies. Determine whether the bundles shown below would be equally preferred, more preferred, or less preferred than what Isabel currently has.

Equally preferred: (6 graham crackers, 3 smoothies ) (9 graham crackers, 2 smoothies ) More Preferred: (9 graham crackers, 3 smoothies ) Less Preferred: (9 graham crackers, 1 smoothie ) (3 graham crackers, 2 smoothies ) (Chapter 3 Question 11)

Friedrich has income of €300. He spends his income on clothing and food. A recession caused his income to fall by 10%, but the prices of clothing and food have also fallen by 10%. Which of the following statements is true?

Friedrich's budget set will be unchanged (Chapter 2 Question 11)

The diagram above shows Gisela's indifference curves for housing and all other goods. Which of the following statements regarding Gisela's preferences and utility function is true?

Gisela's preferences are quasilinear. (Chapter 4 Question 9)

Without knowing information on price and income levels, assume that you first optimize at point A. After a change in the market conditions, you re-optimize at point B. And again at point C. And finally, after market conditions change for a third time, you settle on optimizing at point D. Which of the following statements is true?

Good 2 is normal and good 1 transitions from a normal good to an inferior good. (Chapter 6 Question 4)

Both Ellory and Horace have one box of popcorn (𝑃)(P), one box of candy (𝐶)(C), and one movie ticket (𝑀)(M). Ellory's preferences are accurately captured by the utility function 𝑢=𝑃12𝐶12𝑀12u=P12C12M12. Horace's preferences are accurately represented by the utility function 𝑢=2𝑃34𝐶34𝑀34u=2P34C34M34. Based on this information, which of the following statements is correct?

It is not possible to make meaningful comparisons of Ellory's and Horace's happiness based on their respective utility functions. (Chapter 4 Question 2)

The admissions office at State University is looking for students who are smart, hardworking, and dedicated to the community. When ranking potential students, they determine that if potential student A is better than potential student B in two out of the three characteristics, A will be ranked higher. Similarly, if B is better than A on at least two out of the three characteristics, then B will be ranked higher. Otherwise, the admissions office remains indifferent. • Sally Smartypants is very smart, quite lazy, and has average dedication to the community. • Dedicated DeAndre is fairly smart, extremely hardworking, and not at all dedicated to the community. • Happy Harry is not smart, has an average work ethic, and is extraordinarily dedicated to the community. Whom does the admissions office prefer between Sally Smartypants and Dedicated DeAndre? Whom does the admissions office prefer between Dedicated DeAndre and Happy Harry? Whom does the admissions office prefer between Sally Smartypants and Happy Harry? Are the preferences of the admissions office transitive? In an attempt to improve the student body, the admissions office decides to adjust its ranking criteria. Under the new criteria, student A is ranked higher than student B only if A is smarter, more hardworking, and more dedicated to the community. If students A and B are equally smart, hardworking, and dedicated to the community, then the admissions office is indifferent between them. In all other cases, the office simply states that A and B are not comparable. Are the new preferences over students complete, reflexive, or transitive?

Sally Smartypants Dedicated DeAndre Happy Harry no They are reflexive, They are transitive. (Chapter 3 Question 4)

There are many examples of goods that go together in a particular proportion, such as left and right shoes, or hats with scarves. The utility function that represents preferences for such goods takes a form such as 𝑢(𝑥1,𝑥2)=min{8𝑥1,24𝑥2}u(x1,x2)=min{8x1,24x2}. Demand based on this function cannot be found using the normal method of setting the MRS equal to the price ratio. However, with inspection, it quickly becomes clear that the optimal bundle with such a function must occur where the two terms inside the min function are equal. Otherwise, one constrains the other. It is possible to solve for demand functions using this information. Find the demand functions for 𝑥1x1 and 𝑥2x2 based on the given utility function for any prices 𝑝1p1 and 𝑝2p2 and any income 𝑚m. Demand for 𝑥1x1 is given by __________. Demand for 𝑥2x2 is given by __________. Are 𝑥1x1 and 𝑥2x2 normal goods? Based on the demand function for 𝑥1x1 from Part 1, what is the relationship between goods 1 and 2?

X1 = 3m/3P1+P2 X2= m/3p1/P2 Both are normal goods. They are complements because 𝑥1 is inversely related to 𝑝2. (Chapter 6 Question 14)

Consider the following diagram, which shows an indifference curve and eight additional bundles of good 1 and good 2, labeled 𝑥1x1 through 𝑥9x9. The set of bundles weakly preferred to 𝑥1x1 includes the following: The set of bundles strictly preferred to 𝑥1x1 includes the following:

X1, X2, X3, X5, X6, X7, X8, X9 X2, X5, X6, X7, X8, X9 (Chapter 3 Question 5)

In the graph below, you initially maximize utility at point A relative to the B1 budget constraint. Your income changes, which puts you on a new budget constraint (B2). If good 1 is normal and good 2 is inferior, then point _____ is the new optimal bundle of consumption.

Z (Chapter 6 Question 3)

An army officer is charged with managing the food budget efficiently and appropriately. The officer is aware that there are two main suppliers that produce meals ready to eat (MREs) for soldiers in war zones. One supplier specializes in Mexican-themed MREs that feature hot sauce and corn, while the other specializies in Italian-inspired MREs that contain spaghetti and sauce. The main difference, however, is that the Mexican-themed MREs offer twice as many calories, designed either for sharing or to account for two meals when time to eat is limited. The officer thinks both options are equally valid; his preferences over MREs can be represented by 𝑢(𝑥1,𝑥2)=12𝑥1+6𝑥2u(x1,x2)=12x1+6x2, where 𝑥1x1 is Mexican-style MREs and 𝑥2x2 represents Italian-style MREs. The current price of 𝑥1x1 is $27, and the price of 𝑥2x2 is $9. Find demand for 𝑥1 and 𝑥2 at the current prices for any level of income 𝑚. Demand for 𝑥1x1 is given by __________. Demand for 𝑥2x2 is given by __________. Are 𝑥1x1 and 𝑥2x2 normal goods? If the demand function for a good has an inverse relationship with the price of another good, those goods are complements. If there is a direct relationship between the demand for one good and the price of another, those goods are substitutes. In this problem, what is the relationship between goods 1 and 2?

X1=0 X2=m/P2 At current prices, 𝑥2x2 is normal while 𝑥1x1 is not. However, if the price ratio were to drop below 2, 𝑥1x1 would be normal while 𝑥2x2 would not. While their demand functions do not contain the prices of the other good, they are contingent on the price ratio. If the price ratio crosses a threshold, demand for one good can go to zero. This is the special case of perfect substitutes. (Chapter 6 Question 16)

Suppose we've observed several consumption bundles chosen at different prices and calculated the cost of each in Table 1. Recall that the diagonal terms in this table measure how much money the consumer spends at each choice. The other entries in each row measure how much the consumer would have spent if she had purchased a different bundle. Are there any bundles that are indirectly revealed as preferred to another bundle? According to the above data, do the consumer's preferences satisfy the Strong Axiom of Revealed Preference (SARP)?

Yes, bundle 3 is indirectly revealed as preferred to bundle 2. No, because there is at least one instance where bundle x is (directly or indirectly) revealed as preferred to bundle y and bundle y is (directly or indirectly) revealed as preferred to bundle x. (Chapter 7 Question 12)

Consider three goods 𝑥x, 𝑦y, and 𝑧z with corresponding prices 𝑝𝑥px, 𝑝𝑦py, and 𝑝𝑧pz. If a consumer has income m, her budget equation can be written as 𝑝𝑥𝑥+𝑝𝑦𝑦+𝑝𝑧𝑧=𝑚pxx+pyy+pzz=m. Can we graph this budget set? Suppose that 𝑝𝑥px= 6, 𝑝𝑦py= 3, 𝑝𝑧pz = 6, and 𝑚m = 340. If 𝑧 is fixed at a quantity of 3, simplify and complete the budget equation below: __X+__Y=__

Yes. Three-dimensional graphs are possible but challenging to graph by hand and may be less intuitive to use than two-dimensional graphs. 6X+3Y=322 (Chapter 2 Question 12)

The budget line is represented by the equation 𝑝1𝑥1+𝑝2𝑥2=𝑚p1x1+p2x2=m, where: 𝑥1x1 is the quantity of good 1, which is plotted on the horizontal axis; 𝑝1p1 is the price of good 𝑥1x1; 𝑥2x2 is the quantity of good 2, which is plotted on the vertical axis; 𝑝2p2 is the price of good 𝑥2x2; and 𝑚m is income. Which of the following occurrences would cause a budget line to become flatter?

a per-unit tax on 𝑥2x2 an increase in 𝑝2p2 a decrease in 𝑝1p1 (Chapter 2 Question 14)

In addition to finding the optimal bundles given prices and income, utility maximization can be used to find individual demand functions at any prices and income. Setting up the problem and solving it are the same, except that the prices of each good and the income will be left in variable form (economists call these parameters or exogenous variables). Perfect substitutes almost always have boundary solutions, which are found in a different way than interior optima. The demand functions from perfect substitutes are contingent; specifically, they depend on the slopes of the indifference curves and the budget line. Consider a utility function 𝑢(𝑥1,𝑥2)=𝑎𝑥1+𝑏𝑥2u(x1,x2)=ax1+bx2 and a general-form budget line 𝑝1𝑥1+𝑝2𝑥2=𝑚p1x1+p2x2=m. If the absolute value of the slope of the indifference curve, 𝑎/𝑏a/b, is greater than the absolute value of the slope of the budget line, 𝑝1𝑝2p1p2, the consumer will find it optimal to consume In such a case, demand for good 1 is 𝑥∗1(𝑝1,𝑝2,𝑚)= and demand for good 2 is 𝑥∗2(𝑝1,𝑝2,𝑚)x2∗(p1,p2,m) = If the reverse were true, 𝑎𝑏<𝑝1𝑝2ab<p1p2, demand for good 1 would be 𝑥∗1(𝑝1,𝑝2,𝑚)=x1∗(p1,p2,m)= and demand for good 2 would be 𝑥∗2(𝑝1,𝑝2,𝑚)=x2∗(p1,p2,m)=

all of good 1 she can afford and none of good 2. m/p1 0 0 m/p2 (Chapter 5 Question 5)

Consider a consumer with a utility function of 𝑢(𝑥1,𝑥2)=2𝑥1+𝑥2u(x1,x2)=2x1+x2 defined over the quantities of two goods (𝑥1x1 is the quantity of good 1 and 𝑥2x2 is the quantity of good 2). The prices of these goods are 𝑝1p1 (for good 1) and 𝑝2p2 (for good 2). If the prices of the two goods are equal (i.e., 𝑝1=𝑝2p1=p2), then the consumer will spend her entire income on _________ and her income-offer curve will be ___________ Finally, the Engel curve for good 1 will be (assume the horizontal axis represents the amount of good 1 and the vertical axis represents the amount of good 2)

good 1, a horizontal a line through the origin with a slope of p1 (Chapter 6 Question 6)

Peter is very particular about how he dresses. He likes nice suits and nice shoes, but only if they match perfectly. He wants as many matching combinations as possible, but he is not made happier at all by either extra shoes that match no suit or extra suits that match no shoes. Let 𝑥x represent pairs of shoes and 𝑦y represent suits. On the graph below, use the straight-line tool to plot indifference curves for Peter if he has three matching sets and five matching sets, respectively.

look at graph (Chapter 3 Question 10)

When riding his bicycle, Jeremy always consumes bottles of water and granola bars in fixed proportions. His utility function is 𝑢=min{𝑊,12𝐺}u=min{W,12G}, where 𝑊W is the number of bottles of water and 𝐺G is the number of granola bars. Based on Jeremy's utility function, use the line tool to draw the indifference curves where 𝑢=1u=1and 𝑢=2u=2. Note that you will need to use two line segments for each indifference curve and extend the line segments to the border of the graphing region.

look at graph (Chapter 4 Question 8)

Jeanine has $20 in her pocket and faces prices (𝑝1,𝑝2)(p1,p2) = (4, 2) for apples and oranges, respectively. Consider two possible consumption bundles, point A = (2, 5) and point B = (3, 4). Use the straight line tool to graph Jeanine's budget constraint and then use the point plotting tool to plot these two potential consumption bundles. Assume that Jeanine spends all of her income when maximizing utility. What can we say about Jeanine's preferences between points A and B?

look at graph She prefers point B, even though point A is affordable. (Chapter 7 Question 3)

Susan likes to attend live sporting events. Specifically, she likes both football games and basketball games, and she has convex preferences over both. The graph below shows Susan's indifference curve that goes through the bundle (3,3), which represents Susan's attendance at three football games and three basketball games last year. She would prefer attending four of each, and she is indifferent between (4,4), (1,16), and (16,1). Using the point tool, plot those bundles, and then use the curved-line tool to graph Susan's indifference curve through them. Using the indifference curves on the graph in Part 1, evaluate the following statements as true or false. (2,8) is weakly preferred to (4,4). (1,16) is strictly preferred to (4,4). (16,1) is at least as good as (3,3). (3,3)~(1,9) (9,1)~(2,8)

look at graph true false true true false (Chapter 3 Question 6)

Label the slope and intercept terms on the budget diagram, in terms of 𝑝1p1, 𝑝2p2, and 𝑚m, where 𝑝1p1 is the price of 𝑥1x1, 𝑝2p2 is the price of 𝑥2x2, and 𝑚m is income.

look at graph (Chapter 2 Question 2)

Consider the budgeting decisions of a consumer who spends money on gasoline and other goods. The consumer has income of $250. The price of gasoline is $2.50 per gallon. If the other good is a composite good, use the line tool to draw the budget line for this consumer.

look at graph (Chapter 2 Question 4)

Mike's income is $240. If the price of a shirt is $15 and pants cost $30 each, use the line tool to draw Mike's budget line. Mike's income increases to $300. The price of a shirt drops to $10 and the price of pants decreases to $25. Redraw Mike's budget line.

look at graphs (Chapter 2 Question 9)

It's time to practice graphing budget lines. Suppose 𝑝1=2p1=2, 𝑝2=3p2=3, and 𝑚=30m=30. Use the line tool to graph the budget line. Suppose 𝑝1=2p1=2, 𝑝2=2p2=2, and 𝑚=40m=40. Use the line tool to graph the budget line. Suppose 𝑝1=2p1=2, 𝑝2=0p2=0, and 𝑚=10m=10. Use the line tool to graph the budget line. Now suppose 2𝑝1=𝑝22p1=p2 and 𝑚=8𝑝2m=8p2. Use the line tool to graph the budget line.

look at graphs (Chapter 2 Question 3)

The utility-maximizing bundle of 𝑥1x1 and 𝑥2x2 may, in some instances, be found at a point of tangency between the budget line and an indifference curve. In other instances, the utility-maximizing bundle will be found at a corner point—that is, where the quantity consumed of one good is zero. For which types of indifference curves shown below will the utility-maximizing bundle definitely be found at a corner point?

look at graphs (A, B) (Chapter 5 Question 10)

Eddie has a new hybrid car that can use either gasoline or electricity. Eddie doesn't care which source of energy he uses; he cares only about how many miles he is able to drive. Let x represent miles driven using gasoline and y represent miles driven using electricity. On the graph below, use the straight-line tool to draw indifference curves for Eddie when he drives 200 miles in a month and 300 miles in a month. What is Eddie's marginal rate of substitution (MRS) between miles driven with gasoline and miles driven with electricity?

look at the graph -1 (Chapter 3 Question 9)

In addition to finding the optimal bundles given prices and income, utility maximization can be used to find individual demand functions at any prices and income. Setting up the problem and solving it are the same, except that the prices of each good and the income will be left in variable form (economists call these parameters or exogenous variables). Consider a utility function that represents preferences over perfect complements: 𝑢(𝑥1,𝑥2)=min{50𝑥1,25𝑥2}u(x1,x2)=min{50x1,25x2}. What are the demand functions 𝑥∗1(𝑝1,𝑝2,𝑚)x1∗(p1,p2,m) and 𝑥∗2(𝑝1,𝑝2,𝑚)x2∗(p1,p2,m)? 𝑥∗1(𝑝1,𝑝2,𝑚)= 𝑥∗2(𝑝1,𝑝2,𝑚)=x2∗(p1,p2,m)=

m/p1+2p2 2m/p1+2p2 (Chapter 5 Question 6)

Tammie strictly prefers bundle A, which is 4 bottles of water and 3 hamburgers, to bundle B, which is 4 bottles of water and 2 hamburgers. She strictly prefers bundle B to bundle C, which is 3 bottles of water and 1 hamburgers. If 𝑥1x1 is the quantity of bottles of water and 𝑥2x2 is the quantity of hamburgers, which of the following utility functions would NOT represent Tammie's preferences?

min{x1,x2} (Chapter 4 Question 3)

The diagram below shows a budget set, bounded by the budget line. What property of well-behaved consumer preferences ensures that the utility-maximizing bundle will lie on the budget line, rather than on an interior point of the budget set?

monotonicity (Chapter 5 Question 1)

Suppose that, at prices (𝑝1,𝑝2)=(4,3)(p1,p2)=(4,3) , Alice chooses to consume the bundle(𝑥1,𝑥2)=(3,4)(x1,x2)=(3,4) . Is the bundle directly revealed preferred to the bundle(𝑦1,𝑦2)=(4,3)(y1,y2)=(4,3) ?

no (Chapter 7 Question 2)

Robert loves reading and normally buys both (paper) books and ebooks. We observe him making the following choices: When the price of books and ebooks is (𝑝𝑋𝑏,𝑝𝑋𝑒)=(7,4)(pbX,peX)=(7,4), Robert buys the bundle 𝑋=(2,4)X=(2,4) (the first number refers to the number of books, the second to the number of ebooks bought). When (𝑝𝑌𝑏,𝑝𝑌𝑒)=(4,6)(pbY,peY)=(4,6), he buys 𝑌=(2,2)Y=(2,2). Finally, when (𝑝𝑍𝑏,𝑝𝑍𝑒)=(8,5)(pbZ,peZ)=(8,5), he buys 𝑍=(1,3)Z=(1,3). Is bundle X indirectly revealed preferred to bundle Z?

no (Chapter 7 Question 5)

Anne likes to go to the cinema and to the theatre. When the prices of a cinema ticket and of a theatre ticket are (10,15), Anne goes to both the cinema and the theatre twice a month. The cinema where she normally goes introduces a special offer: all tickets will cost $7 for a month. At the same time, the local theatre decides to increase the price of a ticket to $18. At these new prices, Anne goes to the cinema three times and to the theatre only once. Do her choices violate the WARP?

no (Chapter 7 Question 9)

Juliana's optimal consumption of movie tickets is given by the function 𝑥∗1=3𝑚5𝑝1x1∗=3m5p1, where 𝑚m is her income and 𝑝1p1 is the price of a movie ticket. According to Juliana's preferences, movie tickets are a(n) ___ good Assuming her income (𝑚=m=500.00) increases by $100.00 and the price of a movie ticket is 𝑝1=p1= 2, by how many units does her consumption of movie tickets change?

normal good 30 (Chapter 6 Question 1)

Sort the following statements to match them with their respective terms:

normal: An increase in income results in an increase in the quantity of good A. inferior: A decrease in income results in an increase in the quantity of good A. complete: An increase in the price of good A results in a decrease in the quantity of good B. giffen: An increase in the price of good A results in an increase in the quantity of good A. substitut: A decrease in the price of good A results in a decrease in the quantity of good B. (Chapter 6 Question 12)

A consumer is choosing a bundle of two different goods, good 1 (𝑥1x1) and good 2 (𝑥2x2). Her utility function is given by 𝑢(𝑥1,𝑥2)=min[𝑥1,2𝑥2]u(x1,x2)=min[x1,2x2] and the prices of the two goods are 𝑝1p1 for good 1 and 𝑝2p2 for good 2. The consumer has income of 𝑚m to spend on these two goods. Based on the utility function, the consumer views goods 1 and 2 as Suppose that the price of good 1 is 𝑝1=$2p1=$2 and the price of good 2 is 𝑝2=$6p2=$6 and that the consumer has $100 to spend on the two goods. How many units of good 1 will she buy in her optimal bundle? How many units of good 2 will she buy in her optimal bundle?

perfect complements 20 10 (Chapter 5 Question 8)

Jorge consumes two goods, energy bars and bottled water. His demand for energy bars is given by 𝑥𝑏𝑎𝑟𝑠=𝑚5𝑝𝑏𝑎𝑟𝑠+𝑝𝑤𝑎𝑡𝑒𝑟xbars=m5pbars+pwater, where 𝑚m is Jorge's income, 𝑝𝑏𝑎𝑟𝑠pbars and 𝑝𝑤𝑎𝑡𝑒𝑟pwater are the prices of energy bars and bottled water, respectively, and 𝑥𝑏𝑎𝑟𝑠xbars is the number of energy bars. Given the form of Jorge's demand function, we can conclude that energy bars and bottled water are ________ to him. Suppose the price of a bottle of water is $4 and that Jorge has $100 to spend on these two goods. This means that his demand function for energy bars is and his inverse demand function is

perfect complements Xbars = 100/ 5Pbars +4 Pbars = 100-4Xbars/ 5Xbars (Chapter 6 Question 13)

The consumer is indifferent to the bundles at points A and B. We know that the consumer has strictly convex preferences. Based on this information, we can conclude that the consumer ___

pont C is tricot preferred to Point A and B (Chapter 3 Question 15)

The table below shows a consumer's yearly consumption schedule for both ramen and steak for yearly incomes between $10,000 and $100,000. According to this information, the Engel curve for ramen has what type of slope?

positive slope for low incomes, negative slope for high incomes (Chapter 6 Question 5)

Mapping the relationship between income and quantity demanded for a good, Engel curves have a ________ slope for normal goods and a ___________ slope for inferior goods.

positive, negative (Chapter 6 Question 8)

The symbol "≻≻" indicates strict preference. The symbol "≽≽" indicates weak preference. The symbol "~" indicates indifference. Ken always chooses salad and croutons for lunch rather than sushi and bottled water. Ken's preferences would be specified as __________.

salad and croutons≻ sushi and bottled water (Chapter 3 Question 2)

Consider a budget line with daffodils on the horizontal axis (x1) and begonias on the vertical axis (x2). The town, seeking to encourage neighborhood beautification projects, offers a subsidy of $2 subsidy per begonia. The slope of the budget line will

steepen (Chapter 2 Question 10)

Joaquim always chooses pizza and soda for lunch, rather than ramen noodles and biscuits. Joaquim ___ Lenore, when confronted with the choice of pizza and soda or ramen noodles and biscuits, sometimes chooses pizza and soda and sometimes chooses ramen noodles and biscuits. Which of the following statements could be true?

strictly prefers pizza and soda over ramen Lenore weakly prefers pizza and soda to ramen noodles and biscuits. Lenore is indifferent between pizza and soda and ramen noodles and biscuits. Lenore weakly prefers ramen noodles and biscuits to pizza and soda. (Chapter 3 Question 1)

Renaldo prefers apples to parsnips and okra to apples. And, given a choice between parsnips and okra, he will always choose parsnips. Renaldo's preferences violate the assumption of __

transitivity (Chapter 3 Question 3)

Marissa always consumes 4 Oreos with 3 ounces of milk. She has no use for Oreos or milk if they are not consumed in this proportion. If Oreos are represented as 𝑅R and an ounce of milk is represented as 𝑀M, which of the following utility functions would accurately represent her preferences?

u = min {3R, 4M} (Chapter 4 Question 7)

Recall that homothetic preferences map into income offer curves that are straight lines through the origin. Which of the following functions satisfy the condition of homothetic preferences?

u=x1^6x2^2 u=7x1+4x2 u=min(5x1, 10x2) (Chapter 6 Question 10)

In what situations will the tangency condition be sufficient for utility maximization? The tangency condition means the budget line is tangent to the indifference curve. A condition is sufficient if that condition by itself ensures that utility is being maximized.

when preferences are convex (Chapter 5 Question 4)

Suppose that, at prices (𝑝1,𝑝2)=(2,3)(p1,p2)=(2,3) , Mary chooses to consume the bundle (𝑥1,𝑥2)=(3,4)(x1,x2)=(3,4) . Is the bundle directly revealed preferred to the bundle (𝑦1,𝑦2)=(4,3)(y1,y2)=(4,3) ?

yes (Chapter 7 Question 1)

The graph below shows indifference curves for perfect substitutes, which have the general-form utility function 𝑢(𝑥,𝑦)=𝑎𝑥+𝑏𝑦u(x,y)=ax+by. If an individual has the preferences represented by the indifference curves above and can afford at least one of each good, will she ever choose to consume zero of one good? The graph below shows indifference curves for perfect complements, which have the general-form utility function 𝑢(𝑥,𝑦)=min{𝑎𝑥,𝑏𝑦}u(x,y)=min{ax,by}. If an individual has the preferences represented by the indifference curves above and can afford at least one of each good, will he ever choose to consume zero of one good? The graph below shows indifference curves for Cobb-Douglas preferences, which have the general-form utility function 𝑢(𝑥,𝑦)=𝑥𝑎𝑦𝑏u(x,y)=xayb. If an individual has the preferences represented by the indifference curves above and can afford at least one of each good, will she ever choose to consume zero of one good? The graph below shows indifference curves for quasilinear preferences, of which one common general form is 𝑢(𝑥,𝑦)=𝑎𝑥‾‾√+𝑏𝑦u(x,y)=ax+by. If an individual has the preferences represented by the indifference curves above and can afford at least one of each good, will he ever choose to consume zero of one good?

yes no no yes (Chapter 4 Question 11)

Tricia is always willing to trade 5 red pencils for 1 blue pencil. If we represent red pencils as 𝑅 and blue pencils as 𝐵, we can write Tricia's utility function as 𝑢 = __________.

𝑅+5 𝐵 (Chapter 4 Question 4)

At some given prices, we observe the consumer buying bundle 𝑋 in the graph below. Suppose that preferences are strictly convex, so that for each budget set, there is a unique demanded bundle. Which of the following statements is correct?

𝑋 is directly revealed as preferred to 𝑌. (Chapter 7 Question4)

Start with the Cobb-Douglas utility function 𝑢=𝑥15.0𝑥25.0u=x15.0x25.0. If we apply the monotonic transformation 𝑧=𝑢110z=u110, the resulting utility function is 𝑧=__________.

𝑥10.5𝑥20.5x10.5x20.5 (Chapter 4 Question 10)

The table below shows Kristy's purchases of truffles (𝑥1x1) and pears (𝑥2x2) at varying levels of income. Assuming that Kristy is maximizing her utility, which utility function best represents her preferences?

𝑥1^0.80𝑥2^0.20 (Chapter 5 Question 12)

Recall that the equation for a line can be written as 𝑦=𝑚𝑥+𝑏y=mx+b, where 𝑚m is the slope of the line and 𝑏b is the vertical intercept. When working with good 𝑥1x1 on the horizontal axis and good 𝑥2x2 on the vertical axis, the equation would be written as 𝑥2=𝑚𝑥1+𝑏x2=mx1+b. Jordan has income of $460.00, the price of 𝑥1x1 is $5, and the price of 𝑥2x2 is $4. Her budget line will be written as:

𝑥2=−1.25𝑥1+115.00x2=−1.25x1+115.00 (Chapter 2 Question 5)