ECO100Y5 Lecture Notes - Lecture 6: Costco, Indifference Curve, Substitute Good

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Income is m = 4, px = 4, py = 2. What is the most you would pay to join costco. = x , 1 = y, haic: fee = m cost b, U = xy , mrs(slope) = y/x, B: xy=1/2: zy = x} y=1/2 x=1 cost = : less than , is the correct answer, , , more than , utility is u = x + y. Indifference curves are linear with mrs = 1. Income is m=6, px = 3, py = 2. Mrs = ocost: 1 = 3/2, x = 6/2, y = 6/3. Px:ocost 1/2: less than , , = the answer, means youll be spending all your money on good x, cost : x =3, px =1, , more than , utility is u=x^2 + y^2. Income is m=6, px = 6, py=3/ crackco offers members a discounted px=1, but charges a membership fee.

Related Questions

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) = x^ay^b (Cobb-Douglas utility function)

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

John M. Keynes: U(x,y) = x + y^b (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 p_x and p_y respectively.

d. Now assume that a=1/2, b = 1/4, I = 600, p_x = 10 and p_y = 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, s_x, is defined as

(p_x 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.

aquamarinescorpion997

1. (Law of Diminishing Marginal Utility) Some restaurants offer âall you can eatâ meals. How is this practice related to diminishing marginal utility? What restrictions must the restaurant impose on the customer in order to make a profit? (Answers may vary)

2. (Marginal Utility) Is it possible for marginal utility to be negative while total utility is positive? If yes, under what circumstances is it possible?

3. (Role of Time in Demand) In many amusement parks, you pay an admission fee to the park but you do not need to pay for individual rides. How do people choose which rides to go on? (Answers may vary)

4. What is the diamonds-water paradox, and how is it explained? Use the same reasoning to explain why bottled water costs so much more than tap water.

5. Please read Jane Katzâs âThe Joy of Consumption: We Are What We Buy,â in the Federal Reserve Bank of BostonâsRegional Review at http://www.bos.frb.org/economic/nerr/rr1997/winter/katz97_1.htm and briefly discuss/summarize the evidence that Katz cites about how the rising value of time has affected consumer spending patterns.

6. Suppose that marginal utility of Good X = 100, the price of X is $10 per unit, and the price of Y is $5. Assuming that the consumer is in equilibrium and is consuming both X and Y, what must the marginal utility of Y be? (Hint: Please apply the formula: MUx/Px = MUy/Py)

7. What is consumer surplus? What happens to consumer surplus as price level falls?

8. Do you think any good which does not exhibit the law of diminishing marginal utility?

1. What is the capitalized value of an infinite series of $1,000 biennial (every two years) payments? MARR = 10%

		$4,950
		$4,025
	.	$4,350
		$4,762

2. Frank West Enterpises would like to choose one of the following plans for expansion. Using present worth analysis, find the best alternative among the three alternatives and the Do-Nothing.

	Alt. A	Alt. B	Alt. C
Initial Cost	$10,000	$21,000	$8,000
EUAB	$6,000	$7,000	$4,000
EUAC	$1,500	$1,000	$2,000
Salvage Value	$2,000	$8,000	$3,000
Life	2 Years	3 Years	2 Years

Use a MARR of 10%.

	.	Do-Nothing
	.	Alt. C
	.	Alt. B
	.	Alt. A

U. S. Engineering is investigating the possibility of acquiring new automated packaging equipment at a cost of $12,000. It is expected that the equipment will have a salvage value of $1,000 at the end of its useful life of 10 years. It is determined by the plant engineering department at the company that the operation and maintenance cost will be $500 in the first year and will gradually increase every year starting year 2 at the rate of $50 until the equipment is retired. Determine the equivalent uniform annual cost (EUAC) if MARR for the company is 10%.

		$2,575.95
		$2,150.50
	.	$2,176.60
	.	$2,184.40

The cash flows given in table below are for two different alternatives. MARR =10%

Data	C	D
Initial Cost	$20,000	$80,000
Uniform Annual Benefits	$6,000	$10,000
Salvage Value	$5,000	$20,000
Useful Life in years	5	infinity

The equivalent uniform annual worth (EUAW) of alternative N is ______________.

Hint: Assume the Salvage Value is never realized since N is infinite.

		$2,000
		$1,920
		$1,762
		$2,476

Compare the following plans using a MARR of 6%.

Data	Plan X	Plan Y
Equipment First Cost	$50,000	$75,000
Annual Operation & Maintenance Cost	$3,000	$2,500
Salvage Value	$10,000	$0
Service Life, Years)	25	50

		$6,728; $7,255
		$7,255; $9,000
	.	$6,728; $7,728
	.	$6,728; $8,200

LAEP, Inc. wants to evaluate two methods of shipping their products. The following cash flows are associated with each alternative:

Data	Method
	A	B
Life (Years)	10	10
First Cost	$700,000	$1,512,000
M&O Cost	$18,000	$9,000
M&O Cost Gradient	$900	$775
Annual Benefit	$154,000	$303,000
Salvage Value	$142,000	$210,000

Annual profits are based on amount of products which can ordinarily be shipped each year as a function of the amount of vehicles or service purchased with the first cost and the M&O costs.

Using a MARR of 15%, calculate the equivalent uniform annual cash flow (EUAB - EUAC) for each alternative.

Determine the most desirable alternative based on the results.

		$389.57, $445.90; Method A
		$445.90, $389.57; Method A
	.	$445.90, $389.57; Method B
	.	$389.57, $445.90; Method B

For the cash flow diagram shown, which of the following equations properly calculates the uniform equivalent (A)?

n	0	3	6	9	12	15
Dollars	$100	$100	$100	$100	$100	$100

		A=100(A/P,i,15)+ 100(A/F,i,3)
		A=100(A/P,i,15)
		A=100(A/F,i,3) + 100(A/F,i,15)
		A=100(A/P,i,3) + 100(A/F,i,3)

Three different alternatives shown in table below are being considered by U. S. Engineering systems.

Assume that alternatives X and Z are replaced at the end of their lives.

Data	Alternative X	Alternative Y	Alternative Z
Initial Cost	$6,000	$1,000	$1,500
Uniform Annual Benefits	$810	$125	$ 230
Useful Life in Years	20	infinite	10
MARR	12%

The NPW for alternative

ECO100Y5 Lecture Notes - Lecture 6: Costco, Indifference Curve, Substitute Good

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