ECON 323 Exam 1

Suppose Good X and Good Y are perfect substitutes to each other. The marginal rate of substitution of X for Y is equal to 0.5. The price of Good X is $1 and the price of Good Y is $3. The consumer has a wealth level of 900. In the consumer's utility maximization market basket, what is the quantity of Good X?

900 MRS=0.5 and PX/PY=1/3. The consumer's indifference curves are steeper than price ratio. By plotting an indifference map with straight indifference curves which are steeper than the budget line, it is easy to see that the consumer should spend all his income on Good X. Hence, he will buy I/PX=900/1=900 units of Good X.

Jane has utility function U(x,y)=x4y5. The marginal utility of Good X is MUX(x,y)= 4x3y5 and the marginal utility of Good Y is MUY=5x4y4. The price of Good X is PX, the price of Y is PY, and Jane's income is I. What is the function of her Engel curve of Good X if PX=4 and PY=5?

QX(I)= I/9 Let (x,y) be the maximizers. The tangency rule is: MRSxy(x,y)=PX/PY. Recall that, MRSxy(x,y)=MUX(x,y)/MUY(x,y)=(4x3y5)/(5x4y4)=(4y)/(5x). Thus, (4y)/(5x)=PX/PY, and consequently, y=(5Px x)/(4Py). Since (x,y) is on the budget line, then Pxx+Pyy=I. Then, Pxx+Py(5Px x)/(4Py)=I. Which is, 9Pxx/4=I. Thus, x=(4I)/(9Px). Plug in PX=4. We have Qx(I)= I/9.

The quantity of Good X is denoted by the number on the horizontal axis and that of Good Y is denoted by the number on the vertical axis. Anne has utility function U(x, y)=5x+7y and Bella has utility function U(x, y)=10x+15y. Then which of the following statement is correct?

Anne's indifference curves are steeper than Bella's. We can plot the indifference curves of Anne and Bella that give them utility level of 1 for example. Then Anne's indifference curve has function 5x+7y=1, which is equivalent to y=(-5/7)x+(1/7). So Anne's MRS=5/7=0.714. Bella's indifference curve has function 10x+15y=1, which is equivalent to y=(-10/15)x+(1/15). So Bella's MRS=10/15=0.667 As Anne's MRS is larger, her indifference curves are steeper.

Let the horizontal axis denote acceleration of a vehicle and the vertical axis denote the space of a vehicle. Among the following two indifference maps, one belongs to a Ford Explorer owner who cares more about large space, and one belongs to a Mustang owner who cares more about acceleration. Among (a) and (b), which one is more likely to belong to a Ford Explorer owner? (Hint: Use the meaning of MRS)

B

Consider the following three market baskets: Basket A: 6 units of food and 3 units of clothing, Basket B: 8 units of food and 5 units of clothing, Basket C: 5 units of food and 8 units of clothing. If preferences satisfy all four basic assumptions (completeness, transitivity, more is better than less, diminishing marginal rate of substitution), which of the following statement is correct?

B is preferred to A. The assumption of more is better tells us that B is preferred to A. No other conclusions can be made without additional information.

Jose works for the economic research department of the local utility company in his city. He is interested in the effect of a price increase in the demand for their services. He calculates that the price elasticity for the demand is -2.3. This means:

Demand will fall approximately by 2.3% if price increases by 1%. Price elasticity measures the relative change in consumption in proportion to the relative change in price. Thus, demand will fall approximately by 2.3% if price increases by 1%.

Jane has utility function U(x,y)=x4y5. The marginal utility of Good X is MUX(x,y)= 4x3y5 and the marginal utility of Good Y is MUY=5x4y4. The price of X is PX, the price of Y is PY, and Jane's income is I. What is the function of her demand curve of Good X when I=100 and PY=5?

QX(PX)= 400/(9PX) Let (x,y) be the maximizers. The tangency rule is: MRSXY(x,y)=PX/PY. Recall that, MRSxy(x,y)=MUX(x,y)/MUY(x,y)=(4x3y5)/(5x4y4)=(4y)/(5x). Thus, (4y)/(5x)=PX/PY, and consequently, y=(5Px x)/(4Py). Since (x,y) is on the budget line, then Pxx+Pyy=I. Then, Pxx+Py(5Px x)/(4Py)=I. Which is, 9Pxx/4=I. Thus, x=(4I)/(9Px). Plug in I=100. We have Qx(Px)= (400)/(9Px).

Suppose the price of Good Y doubles and the price of Good X remains unchanged, then which of the following statement is correct about the budget line (Good X is on the horizontal axis, and Good Y is on the vertical axis)?

Its y-intercept should be reduced by half and x-intercept is unchanged. The original x intercept is I/PX, and the original y intercept is I/PY. Now the price of Y doubles, and thus the new y intercept becomes I/(2PY)=0.5I/PY. Hence, the new y intercept should be half of the original level.

Jane's Engel curve for the consumption of food shows:

Jane's consumption of food as a function of income, all the other constant Engel curve shows the relationship between the consumption of food and income.

Suppose the figure below shows the demand curve of pizzas for an individual. What is his/her willingness to pay for the 100th pizza?

$20 The demand curve reflects the consumer's willingness to pay. For the 100th pizza, the willingness to pay is $20. For the 50th pizza, the willingness to pay is $30.

Refer to the figure below. When the price of pizza is $20, total expenditure and consumer surplus are, respectively:

$2000; $1000 Expenditure=20*100. Consumer surplus is the area of the triangle above $20, so it is 100*(40-20)*0.5=1000.

Suppose Aaron has utility function U(x, y)=x+2y. Which of the following consumption bundle does he like most?

(1,3) Plug in the values of (x, y) into the utility function, and find the bundle with the highest utility level.

Suppose Larry's budget on fruit is $20 and he consumes apples and bananas only. The price of bananas is fixed to be $2 per pound. When price of apples is equal to $0.5, $1, and $2 respectively, Larry's utility maximizing market basket is (20 pounds of apples, 5 pounds of bananas), (12 pounds of apples, 4 pounds of bananas), and (4 pounds of apples, 6 pounds of bananas) respectively. Then which of the following point (Qapple, Papple) is on Larry's demand curve of apples (when I=$20 and Pbanana=$2)?

(20, 0.5) The question essentially asks you how to derive the demand curve of apple from the price consumption curve.Fixing the income level and the price of banana, when price of apple is $0.5, the quantity demanded of apple is 20 (the number 20 comes from the utility maximizing market basket (20 apple, 5 banana), but you only need to focus on the quantity of apple and can ignore the quantity of banana in this problem); when price of apple is $1, the quantity demanded of apple is 12; when price of apple is $2, the quantity demanded of apple is 4. Hence, the following three points (Q,P) are on the demand curve of apple: (20,0.5), (12,1), and (4,2). You can only find one correct option — (20,0.5).

Denote the consumption of food by x and the consumption of all other goods by y. The demand for food as a function of prices and income is given by: Qx(Px,Py,I)=(3I)/(4Px). What is the price elasticity for the consumption of food when income I=100, PX=3, and PY=5?

-1 (dQx/dPx)(Px/Qx)=(-3I/4P2x)(Px/(3I/4Px))=-1.

When the market demand function is given by Q(P)=100/P, the demand elasticity of price is given by __.

-1 E=Q'(P)*(P/Q)=(-100/(P2))*(P/(100/P))=(-100/(P2))*(P*(P/100))=-1.

Linda has an income of $100, which she spends completely on two goods: x and y. The price of x is $20 and the price of y is $12. Which of the following is the slope of her budget constraint (in a graph where x is measured in the horizontal axis and y in the vertical axis)?

-5/3 The slope of the budget constraint is -px/py=-20/12=-5/3.

Consider the following indifference curve. The marginal rate of substitution between points C and D is roughly equal to ____.

0.5 Between points C and D, MRSSH=|Delta H/Delta S|=|(2-3)/(6-4)|=0.5.

Suppose there are two goods: X and Y. Nick's indifference curves regarding X and Y are L-shaped. The kinks are along the y=2x straight line. Then we know that ____.

1 unit of good X can perfectly complement 2 units of good Y When indifference curves are L-shaped, the two goods are perfect complements. If the kinks of indifference curves are along the y=2x straight line, then for x unit of good X, we need y=2x units of good Y so that X and Y can perfectly complement each other. So 1 unit of good X can perfectly complement 2 units of good Y.

Suppose the marginal utility of good x is denoted by MUx =8xy3 and MUy=12x2y2. What is the value of MRSxy(x, y) when x=2 and y=1?

1/3 MRSxy(x,y)=MUx(x,y)/ MUy(x,y). Then, MRSxy(x,y)=(8xy3)/(12x2y2)=(2y)/(3x).

Bob views apples (a) and oranges (o) as perfect substitutes in his consumption. When we put apples on the horizontal axis and oranges on the vertical axis, MRSao = 0.5 for all combinations of the two goods in his indifference map. Suppose the price of apples is $2 per pound, the price of oranges is $3 per pound, and Bob's budget is $30 per week. Given Bob's budget constraint, what is his utility maximizing choice?

10 pounds of oranges and no apples As MRSao =0.5, indifference curves are downward sloping and the absolute value of the slope is 0.5. The magnitude of the slope of budget line is Pa/Po=2/3. Thus, the budget line is steeper than indifference curves. The consumer is optimized by buying oranges only. Total income is 30. Hence, Bob will buy is 30/3=10 pounds of oranges.

Suppose Good X and Good Y are perfect complements to each other. The kinks of indifference curves are along the y=0.5x straight line. The consumer has a wealth level of 700. The price of good X is $2 and the price of good Y is $10. In the consumer's utility maximization market basket, what is the quantity of Good X?

100 We need to set up the following two equations: (1) y=0.5x (2) 2x+10y=700. Plug (1) into (2), then we have 2x+10*(0.5x )=7x=700, which yields x=100.

Lisa consumes food (F) and clothing (C) only. Per unit of food has a price $10 and per unit of clothing has a price of $50. Lisa has an income of $200. Then her budget line has the function of ____.

10F+50C=200 Her budget line has function PF*F+PC*C=Income, i.e., 10F+50C=200.

Monica consumes only goods X and Y. Suppose that her marginal utility from consuming good X is equal to 1/x, and her marginal utility from consuming good Y is 1/y. If the price of X is $0.50, the price of Y is $4.00, and the Monica's income is $120.00, how much of good X will she purchase?

120 MRSXY= MUX/MUY. When she maximizes her utility, the following two equations should be satisfied: MRSXY =PX/PY and PX*x+ PY*y = Income. The two equations become y/x=0.125 and 0.5x+4y=120. Solve the system of equations. We have x=120 and y=15.

Suppose there are two goods: X and Y. Nick's indifference curves regarding X and Y are downward sloping with a slope of -0.5. Then we know that ____.

2 units of good X can perfectly substitute 1 unit of good Y When indifference curves are downward-sloping straight lines, the two goods are perfect substitutes. If the slope of each indifference curve is equal to -0.5, then when x increases by 1 unit, Nick can decrease y by 0.5 unit without affecting his utility level. This means that 1 unit of good X can perfectly substitute 0.5 units of good Y, or 2 units of good X can perfectly substitute 1 unit of good Y.

A local retailer has decided to carry a well-known brand of shampoo. The marketing department tells them that the quarterly demand by an average man is: Qm = 3 - 0.25P and the quarterly demand by an average woman is: Qw = 4 - 0.5P. The market consists of 10,000 men and 10,000 women. How many bottles of shampoo can they expect to sell if they charge $6 per bottle?

25,000 Plug in $6 and then compute the individual demand. Then aggregate the individual demand.

Suppose the price of good x is $10, the price of good y is $15, and Katrina's income is $30. What is the equation of Katrina's budget constraint? (You may need to simplify the function of the budget line you get initially.)

2x + 3y = 6 The budget constraint is pxx+pyy=Income. Here it is: 10x+15y=30. Simplifying, 2x+3y=6.

Suppose good X and good Y are perfect complements to each other. The kinks of indifference curves are along the y=2x straight line. The consumer has a wealth level of 12. The price of good X is $2 and the price of good Y is $1. What is the consumer's utility maximization market basket?

3 units of good X and 6 units of good Y By observing the indifference map, you should see that the utility maximization market basket is the intersection of y=2x and the budget line: 2x+y=12. By solving the system of equations, we have x=3, y=6.

Consider the utility function U(x, y)=4x+2y. A consumer who has this utility function prefers which of the following baskets?

3 units of x and 1 unit of y. Evaluate the utility of each option and the one with greatest utility will be the preferred basket.

The price elasticity of demand for gasoline is estimated by some researchers to be -0.02. Approximately, what percentage change in the price of gasoline induces an increase of 1% in its consumption?

50% decrease -0.02=(1% change in consumption)/(percentage change in price). Hence, percentage change in price =1%/(-0.02)= -50%.

Sue views hot dogs and hot dog buns as perfect complements in her consumption, and the corners of her indifference curves follow the 45-degree line. Suppose the price of hot dogs is $5 per package (8 hot dogs), the price of buns is $3 per package (8 hot dog buns), and Sue's budget is $48 per month. What is her optimal choice under this scenario?

6 packages of hot dogs and 6 packages of buns Sue's indifference curves are right angles. The corner fall on the 45 degree line. By observing the indifference map, you should find that Sue's utility maximization market basket is always along the 45-degree line. This means that Sue will always choose to buy the same number of packages of hot dogs and buns. When buying 1 packet of hot dog and 1 packet of buns, the cost is $8. By spending all $48, Sue will buy 48/8=6 packages of hot dogs and 6 packages of buns.

Suppose your utility function for food (F) and clothing (C) is u(F, C) = F + 4C. If you reduce your clothing consumption by 2 units, how much do you have to increase your food consumption in order to maintain the same utility level?

8 units Suppose we put F on the horizontal axis and C on the vertical axis. We can find any indifference curve, for example, the one passing (F, C)=(1, 1) and compute its equation: F+4C=5. Then C=-0.25F+1.25. MRSFC=0.25=|Delta C/Delta F|=|-2/Delta F |. Hence, |Delta F|=8.

(In this question we denote income by Y, not by I as in the textbook). The following figure shows the consumption of x and y for two market situations. The income effect of a change in price of x from px to px' is?

Negative and dominates the substitution effect. Negative and dominates the substitution effect. The total effect is negative, and the substitution effect (when there is a decrease in px) is always positive.

(In this question we denote income by Y, not by I as in the textbook). The following figure shows the consumption of x and y for two market situations. The income effect of a change in price of x from px to px' is?

Negative and is dominated by the substitution effect. Negative and is dominated by the substitution effect. The total effect is positive and is less than the substitution effect which is positive. So the income effect is dominated by the substitution effect.

Which of the following statement is correct?

No matter a consumer maximizes utility or not, MRSXY=MUX/MUY. MRSXY=MUX/MUY holds everywhere, no matter utility is maximized or not. It can be viewed as an alternative definition of MRS. MRSXY=PX/PY characterizes the utility maximization solution only when preferences are smooth, and when the solution is interior.

Alfred derives utility from consuming iced tea and lemonade. For the bundle he currently consumes, the marginal utility he receives from iced tea is 16, and the marginal utility he receives from lemonade is 8. Instead of consuming this bundle, Alfred should:

None of the other options is necessarily correct. When he maximizes his utility and the solution is interior, it must be true that: MRSXY =PX/PY. Without knowing price ratio, we do not know whether he has maximized his utility or not.

Consider the following graph that describes three indifference curves and the budget line. Which point gives this consumer the highest utility level within the budget constraint?

Point A A is the point on the budget line that reaches the furthest indifference curve.

(In this question we denote income by Y, not by I as in the textbook). The following figure shows the consumption of x and y for two market situations. The income effect of a change in price of x from px to px' is?

Positive and reinforces the substitution effect. Positive and reinforces the substitution effect. The total effect is positive and the substitution effect is always positive. Income effect reinforces substitution effect.

The horizontal dotted line below is a/an ___.

Price-consumption curve When price of one good (X) changes, the line tracing utility maximization market baskets is the price-consumption curve.

Jane has utility function U(x,y)=x4y5. The marginal utility of Good X is MUX(x,y)= 4x3y5 and the marginal utility of Good Y is MUY=5x4y4. The price of X is PX, the price of Y is PY, and Jane's income is I. What is the expression of her consumption of Y as a function of prices and income (her optimal consumption is determined by the tangency rule)?

Qy(Px, Py, I)= (5I)/(9Py). MRSXY(x,y)=PX/PY. Recall that, MRSxy(x,y)=MUX(x,y)/MUY(x,y)=(4x3y5)/(5x4y4)=(4y)/(5x). Thus, (4y)/(5x)=PX/PY, and consequently, y=(5Px x)/(4Py). Since (x,y) is on the budget line, then Pxx+Pyy=I. Then, Pxx+Py(5Px x)/(4Py)=I. Which is, 9Pxx/4=I. Thus, x=(4I)/(9Px). Thus, y=(5Px x)/(4Py)=(5I)/(9PY).

Suppose an Engel curve is upward-sloping at low income level and downward-sloping at high income level. Then one can conclude that at low income level (upward-sloping portion of the Engel curve), the good is ___.

a normal good Upward sloping Engel curves means that more income leads to more consumption. In this case, the good is normal. Downward sloping Engel curve means that more income leads to less consumption. In this case, the good is inferior.

Suppose that initially the prices of Good X (on horizontal axis) and Good Y (on vertical axis) are the same. If the price of Good X doubles, the price of Good Y triples, and income is held constant, then the budget line:

becomes flatter If the price of Good X doubles, the price of Good Y triples, and income is held constant, the x intercept I/PX will be half of before, and the y intercept I/PY will be a third of before. Hence, the budget line becomes flatter.

Suppose that initially the prices of x and y are the same. If the price of good x doubles and the price of good y triples, while income is held constant, the budget line (x is measured in the horizontal axis and y in the vertical axis):

becomes flatter. The slope of the budget constraint is initially -px/py=-1. Then it becomes -2px/3py=-2/3. That means is less negative and the line is flatter.

Suppose the demand function of Good X is QX=I/(PX+PY) and that of Good Y is QY=I/(PX+PY). The two goods, X and Y, are:

complements As the increase in price of Y decreases the consumption of Good X, and vice versa, the two goods are complements.

In the upward-sloping portion of the curve that connects points A, B and D, the two goods, food and clothing, are:

complements When price of food decreases, from B to D, the consumption of clothing increases. By definition, they are complements.

According to the following graph, Good X and Good Y are ____.

complements When the price of Good X decreases, the budget line rotates counter-clockwise around the y intercept so that the x intercept is larger. According to the price-consumption curve given in the graph, when the price of Good X decreases, the consumption of Good Y increases. Hence, price of X and quantity of Y move in the opposite directions, which means that the two goods are complements.

If Evan does not know if he likes ice cream cone more, he likes ice cream sandwich more, or he is indifferent between an ice cream cone and an ice cream sandwich, then we say Evan's preference violates the assumption of ____.

completeness The definition of completeness means that given any consumption bundles A and B, one of the following must be true: A is preferred to B, B is preferred to A, and A and B are indifferent. If a consumer cannot does not know the relationship between A and B, then his/her preference is incomplete.

The difference between what a consumer is willing to pay for a unit of a good and what must be paid when actually buying it is called:

consumer surplus. This is the definition of consumer surplus.

If preferences satisfy all four basic assumptions (completeness, transitivity, more is better than less, diminishing marginal rate of substitution), then consumer's indifference curves are ____.

downward sloping parallel thin curves that bend in towards the original If preferences satisfy all four basic assumptions (completeness, transitivity, more is better than less, diminishing marginal rate of substitution), then consumer's indifference curves are downward sloping parallel thin curves that bend in towards the original.

Suppose good x and y are perfect substitutes to Nicholas, then the indifference curves of Nicholas looks are ____.

downward sloping straight lines When the indifference curves are perfect substitutes, the indifference curves look like downward sloping straight lines.

Envision a graph with meat on the horizontal axis and vegetables on the vertical axis. Vivian loves vegetables more and Mike likes meat more. Vivian's indifference curves should be ____ than those of Mikes.

flatter As Vivian is not willing to give up too much vegetable in exchange for one extra unit of meat consumption, her indifference curve should be flatter.

Bill currently uses his entire budget to purchase 5 cans of Pepsi and 3 hamburgers per week. The price of Pepsi is $1 per can, the price of a hamburger is $2, Bill's marginal utility from Pepsi is 4, and his marginal utility from hamburgers is 6. Bill could increase his utility by:

increasing Pepsi consumption and reducing hamburger consumption. Marginal utility per dollar for Pepsi is 4/1=4. Marginal utility per dollar for hamburger is 6/2=3. Since marginal utility per dollar for Pepsi is higher and Bill has already used his entire budget, he can only benefit from increasing consumption of Pepsi and decreasing that of hamburger.

Suppose the demand function of Good X is QX=0.5I/PX and that of Good Y is QY=0.5I/PY. The two goods, X and Y, are:

independent As the change in price of Y does not change the consumption of Good X, and vice versa, the two goods are independent.

Assume that beer is a normal good. If the price of beer rises, then the substitution effect results in the person buying ________ of the good and the income effect results in the person buying ________ of the good.

less; less When the price of beer rises, beer is becoming relatively more expensive. The substitution effect leads the consumer to buy less beer. When the price of beer rises, the real purchasing power decreases. Since beer is a normal good to the consumer, the consumer buys less beer.

Assume that wheat is a Giffen good. If the price of wheat increases, then the substitution effect results in the person buying ___ of the good and the income effect results in the person buying ___ of the good. Overall, the person will buy ___ of the good.

less; more; more Since wheat becomes more expensive, the consumer will buy less of wheat and more of the other good which is relatively cheaper. Hence, the substitution effect makes the consumer buy less wheat. When the price of wheat increases, the consumer's real purchasing power decreases. Since beer is Giffen good (a very inferior inferior good) and the consumer's real purchasing power decreases, the income effect makes the consumer buy more wheat. Since the good is Giffen good, when the price of wheat increases, the person buys more wheat. So the total effect is more wheat.

The assumption that preferences are complete:

means that the consumer can compare any two market baskets of goods and determine that either one is preferred to the other or that she is indifferent between them. By definition of completeness, two market baskets are either indifferent or strictly comparable.

Assume that rice is a Giffen good. If the price of rice falls, then the substitution effect results in the person buying _ of the good and the income effect results in the person buying __ of the good. Overall, the person will buy __ of the good.

more; less; less When the price of rise falls, substitution effect results in an increase in the consumption of rice. This is true no matter the good in normal or inferior or Giffen. As the price of rice falls, there is an increase in real purchasing power, and thus the real income increases. However, a Giffen good is an inferior good. Hence, the income effect results in the person buying less of the rice. Overall, the income effect dominates for the Good to be Giffen.

If a consumer prefers market basket A to C and C to B, then according to transitivity, the consumer should ____.

prefer A to B. When a consumer prefers market basket A to C and C to B, then by transitivity, the consumer should prefer A to B.

Suppose that an agent has utility function U(x, y)=x+2y. What information is necessary to calculate the agent's optimal consumption of Good X?

price of Good X, price of Good Y, and income When U(x, y)=x+2y, the agent may spend all his/her income on Good X, all his/her income on Good Y, or have multiple optimal solutions, depending on the relation of MRSXY and PX/PY. If the consumer spends all income on X, the quantity of X is I/Px. If the consumer spends all income on Y, the quantity of X is 0. Thus, we have to know PX, PY, and I to determine the exact consumption of X.

An individual demand curve can be derived from the ________ curve.

price-consumption We construct a demand curve from the price-consumption curve. We construct an Engel curve from the income-consumption curve.

In the graph below, the downward sloping curve that passes through points P1, P2, P3 is a/an ____.

price-consumption curve Since the budget lines are rotations of each other around the y intercept, the only thing that changes among the different budget lines is the price of Good X. The curve that traces different utility maximizing market basket under different budget lines with different PX is the price-consumption curve of Good X.

Suppose Martha can make one bread with 1 teaspoon of yeast and 2 cups of flour. Martha likes to make as much bread as possible, but leftover yeast/flour alone is not useful to her. In this case, her indifference curves look like ____.

right angles

Suppose good x and y are perfect complements to Nicholas, then the indifference curves of Nicholas looks are ____.

right angles When the indifference curves are perfect complements, the indifference curves look like right angles.

Suppose price elasticity of demand of artichoke is equal to -0.5. When the price of artichokes is increases slightly, the total expenditure by consumers on artichokes will ________ and the number of artichokes sold will ________.

rise; fall The demand is inelastic. Thus, as the price falls, the quantity demanded increases but at a smaller percentage. Thus, the expenditure increases.

Suppose laptops are evaluated based on two features: power of the processor and portability. Put the score of the processor on the horizonal axis and the score of portability on the vertical axis of an indifference map. A gamer cares more about a powerful processor and a business traveler cares more about portability. The indifference curve of a gamer is most likely to be ___ that of a business traveler.

steeper This problem asks the economic and graphical definitions of MRS. A game cares a lot about processor, so he is willing to give up a lot of portability score to increases the processor score by 1 point. So a game's MRS is quite large, which means that his indifference curve is quite steep.

In the downward-sloping portion of the curve that connects points A, B and D, the two goods, food and clothing, are:

substitutes When price of food decreases, from A to B, the consumption of clothing decreases. By definition, they are substitutes.

If an increase in the price of one good leads to an increase in the quantity demanded of another, the two goods are:

substitutes. The two goods are substitutes by definition.

Indifference curves are convex to the origin (namely, bow in towards the origin) because of:

the assumption of a diminishing marginal rate of substitution. The magnitude of slope of the indifference curve is the marginal rate of substitution (MRS). When x increases, under the assumption of diminishing MRS, the curve becomes flatter.

Suppose the assumption of more is better is satisfied. If indifference curves cross, then:

the assumption of transitivity is violated. If indifference curves cross, then either the assumption of transitivity is violated or the assumption of more is better is violated.

A change in consumption of a good resulting from an increase in purchasing power, with relative prices held constant, is referred to as:

the income effect. When real purchasing power changes, the change in consumption of a good is described by the income effect.

Suppose the indifference curves are smooth and the utility maximization solution is interior. When a person consumes two goods (A and B), that person's utility is maximized when the budget is allocated such that:

the ratio of the marginal utility of A to the price of A equals the ratio of the marginal utility of B to the price of B. When utility is maximized, MRSXY= PX/PY. Since MRSXY = MUX/MUY, the previous equation implies that MUX/MUY= PX/PY. By rearranging, we have MUX/PX =MUY/PY.

From the information on the figure below, we can obtain:

two points on a downward-sloping individual demand curve. Similar to Figure 4.1 in the textbook. From B to D, when price of food decreases, (the budget line becomes flatter), the utility maximization market basket includes more food. This gives two points on an individual demand curve of food.

Suppose Anne's indifference curve has MRSXY=2 everywhere. By increasing the consumption of Good X by 2 units and decreasing the consumption of Good Y by 1 unit, Anne ____.

will be better off Since MRS=2 everywhere, if Anne increases consumption of X by 1 unit and decreases Y by 2 units, she will be indifferent. Namely, if Anne increases X by 2 units and decreases Y by 4 units, she will be indifferent. Now she increases X by 2 and only decreases Y by 1, she will be better off.

Consider an economy with good X and good Y. Good X is on the horizontal axis and good Y is on the vertical axis. Suppose the marginal rate of substitution of X for Y is equal to 3. If Noah decreases his consumption of Y by 4 and increases his X by 1. Then his utility will ___.

will decrease MRS=3 means that if Noah decreases consumption of Y by 3 and increases X by 1, his utility is unchanged. Now if he decreases Y by 4 and increases X by 1, he should be worse off.

Consider an economy with good X and good Y. Good X is on the horizontal axis and good Y is on the vertical axis. Anne currently consumes 50 units of good X and 30 units of good Y, where her MRS of X for Y is equal to 2 everywhere. If she decreases her consumption of Y by 2 and increases her consumption of X by 1, her utility level ____.

will stay at the same level Since MRSXY=2, she is willing to give up 2 units of Y to increase X by 1 and this change will make her utility stay at the same level.

Fanny's marginal utility of X is given by MUX =8xy3 and that of Y is MUY=12x2y2. If she has income I=$120, PX=$2, and PY=$4, what is her utility maximization market basket? Notice that the preference is smooth and the utility maximization solution is interior.

x = 24 and y = 18 MRS=(8xy3)/(12x2y2)=(2y)/(3x). We set up the following two equations to solve the utility maximizing (x,y) (1) MRS=(2y)/(3x)=PX/PY, which is equivalent to (2y)/(3x)=1/2. By solving for y, we have y=3x/4. (2)PXx+PXy=I, which is equivalent to 2x+4y=120. Plugging y=3x/4 into 2x+4y=120, we have 2x+4(3x/4)=120. This simplifies into (2+3)x=120 and thus x=24. Plug x=24 into y=3x/4, we have y=3*(24)/4=18.

Jane' marginal utility of consuming good x is given by MUx =2xy3 and that of y is MUy=3x2y2. If she has income W=$1000, px=$50, and py=$25, what is her utility maximization market basket given that the solution is interior?

x = 8 and y = 24 Let (x*,y*) be Jane's optimal market basket. We know that when maximization happens at an interior point, it must be the case that MRSxy(x*,y*)=px/py=50/25=2. We know that MRSxy(x,y)=MUx(x,y)/MUy(x,y)= (2xy3)/(3x2y2)=(2y)/(3x). Thus, (2y*)/(3x*)=2 and y*=3x*. Now, we know that Jane will consume all her income, so 50x*+25y*=1000. Thus, 50x*+25(3x*)=125x*=1000 and x*=8. Thus, y*=3x*=24.

(In this question we denote income by Y, not by I as in the textbook). The following figure shows the consumption of x and y for two market situations. We can conclude that:

x is a Giffen good for some market situation. The consumption of x decreases when the price of x decreases from Px to Px': x is a Giffen good.

Suppose the price of good x is equal to 1, the price of good y is equal to 2, and income level is equal to 10. What is the expression of the budget line?

x+2y=10 Use formula PXx+PYy=I.

Jenny has utility function U(x, y)=x4y2. Then, the equation of Jenny's indifference curve through (2,3) is ____.

y=12/x2 Since U(x, y)=x4y2, U(2, 3)=2432=144. The indifference curve passing through (2,3) has function form x4y2=144. Solving y, we have y=(144/x4)0.5=12/x2.

Mark has utility function U(x, y)=x3y. Then, the equation of Mark's indifference curve through (2,1) is ____.

y=8/x3 Mark's utility at (2,1) is 8. This his indifference curve has equation 8=x3y. Thus, y=8/x3.

The marginal rate of substitution of Good X for Good Y is MRSXY(x,y)= 9y/x. The price of Good X is PX, the price of Y is PY, and Jane's income is I. Notice that the preference is smooth and the utility maximization solution is interior. What is the function of the consumer's demand curve of Good X if income I=100 and price of Good Y is PY=0.2?

QX(PX)= 90/PX We need two equations for this problem: (1) MRSXY(x,y)= 9y/x=PX/PY (2) xPX+yPY=I From (1), we can isolate y and have y=(xPX)/(9PY). Plug it into (2), which gives us xPX+((xPX)/(9PY))PY=I. The left hand side simplifies into (1+1/9)xPX=I. Hence, x=(9I)/(10PX). Since I=100 and the expression is independent of PY, the demand curve of X is given by Q(P)=(9*100)/(10PX)=90/PX.

Suppose Good X and Good Y are perfect complements and the kinks of indifference curves fall of the line y=3x. The prices of Good X is PX =20. We also know that PY=10. The income level is denoted by I. Then the Engel curve of Good X is given by ___?

Qx (I)=I/50 The utility maximizing market basket (x, y) should satisfy that PXx+PYy=I and y=3x. Plug y=3x into PXx+PYy=I, we have that PXx+PY(3x)=I. Hence x=I/(PX+3PY). Since PX=20 and PY=10, we have that x=I/50.

Suppose Good X and Good Y are perfect complements and the kinks of indifference curves fall of the line y=3x. The price of Good X is denoted by PX . We also know that PY=10 and income level is I=200. Then the demand function of Good X is given by ___?

Qx(Px)=200/(Px+30) The utility maximizing market basket (x, y) should satisfy that PXx+PYy=I and y=3x. Plug y=3x into PXx+PYy=I, we have that PXx+PY(3x)=I. Hence x=I/(3PY+PX). Since I=200 and PY=10, we have that x=200/(30+PX).

By consuming 5 units of food and 10 units of clothing now, John spends all of his income. His marginal utility of food is 2 and marginal utility of clothing is 4. The price of food is $10 and the price of clothing is $30. Then what can he do to improve his utility without violating the budget constraint?

By consuming more food and less clothing. Suppose food is on the horizontal axis and clothing is on the vertical axis. Notice that MRSFC=2/4=0.5 and PF/PC=10/30=1/3. Since MRSFC>PF/PC, the indifference is steeper than the budget constraint. The consumer can attain a higher indifference curve by moving along with budget constraint and towards the southeast direction, which is still affordable. This means that the consumer will be better off by consuming more food and less clothing.

The curves in the following graph are indifference curve of Mike. Notice that Mike's preference violates the assumption of diminishing marginal rate of substitution. Northeast indifference curves represent higher utility level than southwest ones. The budget line is given by the downward sloping straight line. Under such an unusual preference, what is Mike's utility maximizing market basket subject to his budget constraint?

D We want to find the point on the budget line that touches the highest indifference curve, which is D.

The demand curves (for a given level of income and given prices of all the other commodities) for the consumption of Good X in town 1 and town 2 are shown below. (The figure shows a two-axis graph. In the horizontal axis we measure QX, i.e., the consumption of good X; in the vertical line we measure PX, i.e. the price of good X. There are two lines representing the demand functions in two markets. The demand for market 1 is steeper than the demand for market 2. These two lines intersect at PX=3.) Which demand is more elastic at PX=3 (that is, the one with greater price elasticity at PX=3)?

Demand in town 2. The flatter demand at PX=3 is more elastic: a proportional change in price of Good X causes a bigger proportional change in consumption of Good X.

Emma spends all her income on 80 units of Good X and 40 units of Good Y. Her current MRSXY=0.5. The prices of Good X and Good Y are equal. Which of the following statement is correct?

Emma can increase her utility by consuming more Y and less X. As MRS<PX/PY, Emma would be better off to increase Y and decrease X. This can be seen, for instance, by plotting an indifference curve and a budget line.

When the assumption "more is better" is imposed on consumer behaviors, the income effect can never be negative.

False The assumption "more is better" is satisfied, because indifference curve are downward sloping and the northeast curves represent a higher utility level. But the income effect of food is negative.

Natalia and her sister, Gina, have the following utility functions on the number of slices of pizza (x) and cans of soda (y) they consume in the semester. Natalia's is U(x, y)=3x+2y and Gina's is V(x, y)=4x+2y. If we plot their indifference curves with x measured in the horizontal axis and y measured in the vertical axis, we find that ____.

Gina's indifference curves are steeper than Natalia's Both sisters have linear indifference curves. Take for instance the point (1,1). The equation of Natalia's indifferent curve through (1,1) is 5=3x+2y, and the equation of Gina's indifference curve through (1,1) is 6=4x+2y. Thus for Natalia y=5/2-3x/2 and for Gina y=3-2x. Thus, Gina's indifference curves are steeper: the slope is more negative. The only point in Gina's indifference curve through (0,0) is (0,0). The utility of Natalia in her indifference curve through (3,2) is 13. Thus, (0,0) is not on Natalia's indifference curve through (0,0).

What can you tell from the income-consumption curve below?

Good Y is a normal good at low income level and an inferior good at high income level. When the income level is low, the consumption of both goods increases when income increases. Hence, when income level is low, both goods are normal. When the income level is high, increasing income leads to an increase in consumption of X and decrease in consumption of Y.

Which of the following statement is NOT true?

If Good X and Good Y are perfect complements and the kinks of your indifference curves follow the 45-degree line. You should follow the rule that MRS equals the price ratio to find the optimal market basket. When X and Y are perfect complements, the indifference curves have kinks. The utility maximization solution is where the budget line intersects with the line that connects all these kinks. The rule that MRS equals the price ratio works for the case when indifference curves are smooth and solution is interior only, and does not apply to the situation with perfect complements. When X and Y are perfect substitutes, the utility maximization consumption may be only X (if MRSXY>PX/PY), only Y (if MRSXY<PX/PY), or any combination of X and Y (if MRSXY=PX/PY).

The vertical line in the figure below is a/an _.

Income-consumption curve When the income level changes, the line tracing utility maximization market baskets is the income-consumption curve.

Which of the following is true concerning the substitution effect of a decrease in price?

It always will lead to an increase in consumption. When price decreases, substitution effect always leads to an increase in consumption of the good.

Which of the following is true regarding utility along a price-consumption curve?

It changes from point to point. Utility level changes along the price-consumption curve. This is because when the price of one good changes, the utility maximizing consumption bundle will be on different indifference curves.

Linda receives a raise at work and her income increases. How does her budget line change?

It makes a parallel shift outward. When income increases, the budget line shifts outward parallelly.

The following figure shows the budget constraint and one indifference curve of an agent whose preferences satisfy more is better. It is a two-axis graph in which the horizontal axis measures x and the vertical axis measures y. The budget constraint is a line of negative slope. It passes through the points (1,7/3) and (8/3,1). The indifference curve, in red, is a downward sloping curve that touches the budget constraint at (1,7/3) and (8/3,1). No other point in this indifference curve is on or to the southwest of the budget constraint. Then,

The agent maximizes utility, given her budget, at both (1,7/3) and (8/3,1). The agent maximizes utility at both (1,7/3) and (8/3,1). This is so because the agent maximizes utility at the points in the budget constraint that are in the indifference curve that is most to the northeast and touches it.

By which assumption, an indifference curve should be thin lines rather than thick lines?

The assumption of more is better. If the indifference curve is thick, then on the same difference curve, we can find (at least) two market baskets: a northeast one and a southwest one. The northeast market basket and the southwest one should be indifferent to each other. But this violates the more the better assumption.

By which assumption, an indifference curve should never be upward sloping?

The assumption of more is better. If the indifference curve is upward sloping, then on the same difference curve, we can find (at least) two market baskets: a northeast one and a southwest one. The northeast market basket and the southwest one should be indifferent to each other. But this violates the more the better assumption.

Suppose Andy has a utility function of U (x, y) = 2x + y and a wealth level of 12. The price of good X is 2 and the price of good Y is 1. Which of the following statement is optimal?

There are multiple optimal market baskets. Indifference curves are straight lines. MRSXY=2. The magnitude of slope of budget line is also 2. Hence, there are multiple solutions, as long as Andy spends all money on the two goods.

If prices and income in a two-good society double, what will happen to the budget line?

There will be no effects on the budget line. As both prices and the income double, the budget line is not changed.

Both Sally and Sam receive a 5% raise in a single year. Sally increases her demand for ground beef, whereas Sam decreases his demand for ground beef.

This is possible if ground beef is a normal good for Sally, and is an inferior good for Sam. This is possible if ground beef is a normal good for Sally, and is an inferior good for Sam.

Suppose the price elasticity of demand of movie tickets is equal to -1 throughout the curve. How do total expenditures on movie tickets vary along the demand curve?

Total expenditures remain the same between points along the demand curve. When demand has constant elasticity of -1, a 1% increase in price leads to a 1% decrease in quantity demanded. Hence, the expenditure/revenue does not change.

The Engel curve bends backward implies that the good is a normal good at low income level and is an inferior good at a high income level.

True

The following figure shows a demand curve of a good that is inferior for some market situation?

True An increase in Px causes an increase in Qx at some market situation, where the good is a Giffen good. All Giffen goods are inferior goods.