Problem Set 3 - Consumer Choice, Elasticity

Microeconomics (Spring 2017)
Problem Set 3: Consumer Choice, Elasticity, And Consumer Surplus
Submit in Lecture, Feb 27 (MW lectures)/ Feb 28 (TR lectures)
• Write your answers on separate sheets of paper. Please include:
– your name
– your recitation teacher’s name
– day and time of your recitation
Part I: Short Answer Questions
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
opposite
case?Ownership and Per-Capita Income for USA, Germany, Japan, and
1. Vehicle
South Korea, with an Illustrative Gompertz Function, 1960-2002
1000 USA
2002 800
USA Japan USA
1960 Germany
S.Korea
2002 200
Japan
1960 0 Gompertz
function 2002 Vehicles 600
per 1000
people
1960-2002 400 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
with the
Same Illustrative
Gompertz
1960-2002 in their subscription fees. As a result,
2. In the third quarter India,
of 2011,
Netflix
announced
a 60%Function,
price increase
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
Netflix subscriptions? Based on this calculation, does it seem like this price change
was
S.Korea
2002 a good idea?
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: Problems
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 $15, 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) Does your analysis for part (e) change if P = 5?
(g) Show the total consumer surplus at P = 5 on the graph, and calculate it.
2. Ramon likes to have tacos and chilaquiles for breakfast. When the price of a taco is $2 and the price of
chilaquiles is $5, he consumes 10 Tacos and 4 chilaquiles each week. Suppose the price of a taco increases to
$4. Consequently, Ramon 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 tacos increases to $4, the bundle he purchases is 6 tacos and 2 chilaquiles.
Are tacos and chilaquiles substitute or complements? Explain.
(c) From the numbers in the previous part, can we conclude that tacos are normal or inferior? What about
chilaquiles?
3. Suppose that utility of goods x and y are given by u(x, y) = ln x + ln y. Let the price of x be Px = 2 and the
price of y be Py = 4. Income is 40.
(a) What is MRS at the optimum point?
(b) Use this MRS to write the optimal x as a function of y.
(c) Solve for x and y. 2