[solution]: The standards for direct labor for a product are 3.5 hours at \$5

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Hi! I need help with questions 2 and 3 under the "Part II: Problem" section.
Microeconomics (Spring 2016)

Problem Set 3: Consumer Choice, Elasticity, And Consumer Surplus

Submit in Recitation or Lecture, Feb 29-Mar 1, whichever comes ?rst

? day and time of your recitation

1. The graph below shows the relationship between vehicle ownership and average income in the USA, Germany,

Japan and South Korea. Based on this graph, are vehicles a normal or inferior good? What would the graph

look like in theFigure 1. Vehicle Ownership and Per-Capita Income for USA, Germany, Japan, and

opposite case?

South Korea, with an Illustrative Gompertz Function, 1960-2002

1000

USA

2002

800

USA

Vehicles

per 1000

people

1960-2002 400

Japan

USA

1960

Germany

S.Korea

2002

200

Japan

1960

0

Gompertz

function

2002

600

Germany

1960

S.Korea

0

10

20

30

per-capita income, 1960-2002 (Real \$ PPP, thousands)

Figure 2. Vehicle Ownership and Per-capita Income for South Korea, Brazil, China, and

2. In the third quarter India, with the Same Illustrative Gompertz Function, increase in their subscription fees. As a result,

of 2011, Net?ix announced a 60% price 1960-2002

the total number of subscribers decreased from 24.59 million at the end of the second quarter to 23.79 million

1000

by the end of the third quarter. Based on these numbers, what is the estimated price elasticity of demand for

Net?ix subscriptions? Based on this calculation, does it seem like this price change was a good idea? Explain.

S.Korea 2002

Brazil 2002

100

Brazil

Brazil 1960

Vehicles

per 1000

10

people

1960-2002

India

China

2002

Gompertz

function

S.Korea 1960

1

China

1962

0.1

S.Korea

India 2002

India

1960

0

1

10

per-capita income, 1960-2002 (Real \$ PPP, thousands)

6

1

Part II: Problem

1. Suppose there are two type of customers for a comic book store. The owner has conducted interviews and

concluded that there are around 50 customers each with a demand curve P = 20 - 5Q and another 20 each

with demand curve P = 20 - Q, where P is the price and Q is the quantity demanded.

(a) What is the total bookstore?s demand function?

(b) Draw a graph of the total bookstore?s demand.

(c) If the seller set the price to \$5, what is the total quantity demanded?

(d) What is the elasticity of demand at the above bundle?

(e) If the owner slightly increases the price, would the total expenditure of customers increase or decrease?

Explain.

(f) Show the total consumer surplus at P = 5 on the graph.

2. Justin likes to have chocolate chip cookies and milk for breakfast. When the price of a chocolate chip cookies

is \$1 and price of a glass of milk is \$1, he consumes 10 chocolate chip cookies and 6 glasses of milk each week.

Suppose the price of a chocolate chip cookies increases to \$2. Consequently, Justin buys some of each of the

two goods.

(a) What happens to the MRS at the point he chooses? Explain.

(b) Suppose when the price of cookies increases to \$2, the bundle he purchases is 6 chocolate chip cookies

and 4 glasses of milk. Are chocolate chip cookies and milk substitutes or complements? Explain.

(c) From the numbers in the previous part, can we conclude that chocolate chip cookies are normal or inferior

3. Suppose that utility of goods x and y are given by u(x,y) = xy+x. Let the price of x be 1 and and the price

of y be 4. Income is 36.

(a) What is MRS at the optimum?

(b) Use this to write the optimal x as a function of y.

(c) Solve for x and y.

2

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