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Suppose that Sally's preferences over baskets containing coffee (good x), and milk (good y), are described by the utility function U(x,y) = 40x+y. Sally's corresponding marginal utilities are MUx=40 and MUy=1. The price of coffee is Px = $4 per cup, and the price of milk is Py = $1 per litre. Sally's income is I = $200.

Question 1: Without deriving the optimal consumption basket, show that the basket with x = 25 cups of coffee, and y = 50 liters of milk, is NOT optimal. (3 Marks)

Question 2: Derive the expression for Sally's marginal rate of substitution. (1 Mark)

Question 3: Find Sally's optimal consumption basket. (3 Marks)

Question 4: Find Sally's new optimal consumption basket if the price of coffee increases to Px = $5 per cup. (3 Marks)

Question 5: Is coffee a Giffen good for Sally? Briefly explain. Your answer must reference the consumption baskets you found in questions 3 and 4. (3 Marks)

Question 6: Find the income and substitution effects associated with an increase in the price of coffee from $4 to $5 a cup. (4 Marks)

Question 7: Describe the relationship between Sally's demand for coffee and her income. Your answers must reference your previous answers AND use the correct term to describe the relationship. (3 Marks)

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Retselisitsoe Pokothoane
Retselisitsoe PokothoaneLv10
28 Sep 2019

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Related questions

Michael spends all of his income on coffee and donuts. A coffee costs $2.50 and a donut costs $2.00. At his current consumption level, the marginal utility for coffee is 30 utils, and the marginal utility for a donut is 60 utils. Which statement best describes what Michael needs to do to maximize his utility?

Question 1 options:

1)

buy less of both coffee and donuts.

2)

buy less coffee and more donuts.

3)

buy more coffee and less donuts.

4)

spend the same amount on coffee as he does on donuts.

Question 2

What is it called when the marginal utility derived from the last dollar spent on each good is the same across all goods and the last dollar spent uses all of the available budget for the purchase of those goods?

Question 2 options:

1)

the optimal consumption bundle.

2)

the optimal production bundle.

3)

diminishing marginal utility.

4)

optimal point.

Question 3 (1 point)

What does the economic theory of marginal utility infer?

Question 3 options:

1)

consumers naturally know which consumption choices will maximize their utility.

2)

consumers who watch market trends are better at maximizing their utility than are those who do not watch those trends.

3)

one cannot maximize utility without taking an economics class that explains utility theory.

4)

one cannot maximize utility without doing the math of calculating the ratios of marginal utility divided by price.

Question 4

Kate is addicted to chocolate and does not care how much it costs. In fact, she spends more than $20 a week on chocolate. What can be concluded about elasticity in her buying decisions?

Question 4 options:

1)

Her income elasticity of demand for chocolate is equal to one.

2)

Her income elasticity of demand for chocolate is equal to zero.

3)

Her price elasticity of demand for chocolate is equal to one.

4)

Her price elasticity of demand for chocolate is equal to zero.

Save

Question 5 (1 point)

Why does the demand for a good become relatively more elastic?

Question 5 options:

1)

substitutes for the good become more available.

2)

substitutes for the good become less available.

3)

the good becomes more of a necessity.

4)

the time allowed for adjustment is shortened.

Save

Question 6 (1 point)

Assume the price of chicken per pound is $3.49 and that Americans purchase 10 million pounds per chicken every month. If the price of chicken increases to $5.49 per pound, identify what will occur to consumer surplus?

Question 6 options:

1)

consumer surplus increases.

2)

consumer surplus decreases.

3)

consumer surplus creates incentive to save.

4)

consumer surplus creates incentive to spend.

Question 7 (1 point)

What is another name for the difference between the price that consumers are willing to pay for a good and a lower price that they may actually have to pay?

Question 7 options:

1)

profit.

2)

revenue.

3)

consumer utility.

4)

consumer surplus.

Question 8

Adam, Brian, Robert, and Sam all want to attend a football game. The admission price is $48. Adam is willing to pay $59 for the ticket. Brian is willing to pay $39. Robert is willing to pay $45, and Sam is willing to pay $55. Based on this information, who will go to the game?

Question 8 options:

1)

Adam, Brian, Robert, and Sam.

2)

Brian and Robert.

3)

Adam and Sam.

4)

Brian, Robert, and Sam.

Save

Question 9 (1 point)

Lily is willing to pay $10 for one bracelet and $5 for a second. Patty is willing to pay $12 for one bracelet and $2 for a second. If the price is currently $8 per bracelet, identify what is the total consumer surplus after Lily and Patty make their purchases?

Question 9 options:

1)

$8

2)

$6

3)

$7

4)

$5

Question 10 (1 point)

Manfred is willing to shovel one driveway for $25, a second for $30, and a third for $35. Assume that the market rate for shoveling driveways is $32. How many driveways will Manfred shovel, what will be his total revenue, and what will be his producer surplus?

Question 10 options:

1)

Manfred will shovel two driveways for a total revenue of $64 and his producer surplus will be $9.

2)

Manfred will shovel three driveways for a total revenue of $75 and his producer surplus will be $12.

3)

Manfred will shovel three driveways for a total revenue of $96 and his producer surplus will be $5.

4)

Manfred will shovel four driveways for a total revenue of $125 and his producer surplus will be $18.

Save

Question 11 (1 point)

What would the difference between the price that producers receive and the lower price at which they are willing to sell the good be called?

Question 11 options:

1)

producer shortage.

2)

producer surplus.

3)

consumer shortage.

4)

consumer surplus.

Save

Question 12 (1 point)

What will happen when there is an increase in the price of eBook downloads?

Question 12 options:

1)

It reduces the marginal utility derived from each dollar spent on eBooks.

2)

It reduces the marginal utility derived from each hardcopy book purchased.

3)

There will not be a substitution effect.

4)

There will not be a change in the number of eBooks in the set of consumption possibilities.

Save

Question 13 (1 point)

When is price elasticity of demand utilized to measure how an individual changes the quantity they demand?

Question 13 options:

1)

when supply changes.

2)

when product quality changes.

3)

when marketing changes.

4)

when price changes.

Save

Question 14 (1 point)

Assume Mary consumes only tea and pastries. A cup of tea costs 5 euros and a pastry costs 8 euros. Her weekly income is 450 euros. Mary always drinks 2 cups of tea for every pastry she consumes. What is Mary’s optimal weekly consumption bundle?

Question 14 options:

1)

25 cups of tea and 50 pastries.

2)

50 cups of tea and 25 pastries.

3)

58 cups of tea and 20 pastries.

4)

60 cups of tea and 30 pastries.

Save

Question 15 (1 point)

When is producer surplus a positive value?

Question 15 options:

1)

the price the producer is willing to charge equals the market price.

2)

there is no tax applied to the good.

3)

the price the producer is willing to charge is less than the market price.

4)

the price the producer is willing to charge is greater than the market price.

Please explain the steps to get to the answers. I already have just the answers.

Adam and Eve are consumers in a 2-consumer, 2-good exchange economy. The price of X is Px, and the price of Y is $1. Each one has an initial endowment of (X=6, Y=6); therefore, each one has a "budget line" of X*Px+ Y*Py = 6*Px + 6. Adam's utility function is U = XY. The expression for Adam's marginal rate of substitution (i.e.   ) is Y/X, which at his initial endowment of (6, 6) has the value of 1. Adam's demand for X as a function of the price of X is X = 3 + 3/PX.

If Eve's utility function is,  

find: (i) the expression for Eve's marginal rate of substitution.

(ii) the value of Eve's marginal rate of substitution at her initial endowment.

(iii) Eve's demand for X as a function of the price of X.

(iv) What is the price of X in equilibrium?

PROBLEM 1 (This one is designed to give you lots of math practice!)

Consider the following individual utility functions:

Adam Smith: U(x,y) = xy

Jeremy Bentham: U(x,y) = xayb (Cobb-Douglas utility function)

Alfred Marshall: U(x,y) = ln x + ln y

John M. Keynes: U(x,y) = x + yb (Quasi-linear utility function)

Joan Robinson: U(x,y) = aX + bY (linear; perfect substitutes)

a. Solve for the MRS(XY) for each of the gentlemen (i.e., all but Joan Robinson). Show that Mr. Smith, Mr. Bentham, and Mr. Marshall all have diminishing MRS(XY), but that if a=b=2, their preferences exhibit constant, increasing, and decreasing marginal utility respectively. (Fortunately, diminishing MRS is the condition that guarantees convex indifference curves, so we can solve for their optimal consumption!)

 

b. What is the general formula for Mrs. Robinsons (constant) MRS?

c. Find demand functions for x and y for Smith, Bentham, Marshall, and Keynes. Assume that each man has income I and that the prices of x and y are px and py respectively.

d. Now assume that a=1/2, b = 1/4, I = 600, px = 10 and py = 20. Use these values to find the utility-maximizing quantities of x and y consumed by each man.

e. Find an expression for the share of income Mr. Bentham and Mr. Marshall each devote to the consumption of good x, where this share, sx, is defined as

(px x)/I.

f. Find expressions for the income elasticity of demand for good x for Mr. Bentham and Mr. Marshall. Find expressions for the (own) price elasticity of demand for good y for these two men.

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