Question for Critical Thinking 2
Mary-Ann R. Foster
Liberty University
November 2, 2014
QUESTION FOR CRITICAL THINKING 2 1
QUESTION FOR CRITICAL THINKING 2 2
Salvator
8a. If the price increases by 10 percent, by how much does the quantity of household ( a)
natural gas and ( b) electricity change in the short run and in the long run? (Hint: use the
price- elasticity values in table 4- 3.)
If E= %∆Q/%∆P
=%∆Q=E*%∆P
Based on table 4-3
Elasticity of natural gas is 1.40 and 2.10 therefore;
In the short run elasticity of natural gas =
=%∆Q=E*%∆P
=1.40*10%
=14%
Elasticity in the long run
=%∆Q=E*%∆P
=2.10*10%
=21%
In the short run elasticity of natural gas will be 14 % and elasticity in the long run will be 21%
8b. Using the same equation above we can determine the elasticity of electricity.
=%∆Q=E*%∆P
=0.13*10%
=1.3%
Elasticity in the long run
=%∆Q=E*%∆P
=1.89*10%
=18.9%
In the short run elasticity of electricity will be 1.3 % and elasticity in the long run will be 18.9%
QUESTION FOR CRITICAL THINKING 2 3
10. Agricultural commodities are known to have a price- inelastic demand and to be
necessities. How can this information allow us to explain why the income of farmers falls
(a) after a good harvest? (b) In relation to the incomes in other sectors of the economy?
A. It is common knowledge that if prices increase in a product the demand will decrease and vise
versa. If supply and demand is not affected there is an inelastic demand. After harvest, the farmer
may have a positive outcome. Since harvest is not based on just one farmer in the agricultural
world, it would be implied that all farmers had a positive harvest therefore cost of agriculture;
(the product) would decrease. Another way to look at it is if majority of farmers produced apples
and in 2010 all or most farmers had a positive harvest, farmer A will not be able to sell apples at
$5 because other famers would be selling at $2 to get rid of the apples.
B. In relation to the incomes in other sectors of the economy; if income increases then demand
for agriculture commodities will also increase. Since the farmers’ income is unaffected the
demand increase will only affect prices slightly and farmers’ income/revenue will not increase.
To better explain, even is agriculture was 1cent individuals will only buy what they need because
the agriculture will go to waste (spoil), where as if shoes or gold were to reduce in price
individuals may purchase more than they need and save for a later time or in the event that prices
were to rise in the future. Such individual will have the option to re-sell making a profit. Profits
in agriculture will only increase if the community increases or customers increase.
3. Starting with the estimated demand function for Chevrolets given in problem 2, assume
that the average value of the independent variables changes to n = 225 million, i = $ 12,000,
p f = $ 10,000, p g = 100 cents, a = $ 250,000, and p i = 0 ( i. e., the incentives are phased
out).
(a) Find the equation of the new demand curve for Chevrolets.
QUESTION FOR CRITICAL THINKING 2 4
QC=100,000-100PC+2000N+50I+30PF-1000PG+3A+40000PI
QC=100,000-100PC+2000(225) +50(12000) +30(10,000)-1000(100) +3(250000) +40,000(0)
QC=2,100,000-100PC
B. plot this new demand curve, d' c , and, on the same graph, plot the demand curve for
Chevrolets, d c , found in problem 2( d).
7. The total operating revenues of a public transportation authority are $ 100 million while
its total operating costs are $ 120 million. The price of a ride is $ 1, and the price elasticity
of demand for public transportation has been estimated to be - 0.4. By law, the public
transportation authority must take steps to eliminate its operating deficit.
( a) what pricing policy should the transportation authority adopt? Why?
Based on the information given
Total revenue = $100m
Total cost= $120m
Price = $1
And elasticity =-0.4
One can conclude that the absolute value is inelastic because it is less than 1, (the price
elasticity of demand for public transportation has been estimated to be - 0.4). Therefore a
large increase in price will result in the decline in demand. Rides will decrease while prices will
increase.
( b) what price per ride must the public transportation authority charge to eliminate the
deficit if it cannot reduce costs?
To eliminate the deficit if it cannot reduce cost the public transportation authority should charge .
50c more per ride.
To match total operating cost of 120m there should be a 20% increase
%∆TR=120/100-1
=0.2
QUESTION FOR CRITICAL THINKING 2 5
Or 0.4*50% =20%
Price increase is .50 cents therefore the price should increase from $1 to $1.50
9. A researcher estimated that the price elasticity of demand for automobiles in the United
States is - 1.2, while the income elasticity of demand is 3.0. next year, u. s. automakers
intend to increase the average price of automobiles by 5 percent, and they expect
consumers’ disposable income to rise by 3 percent.
(a) if sales of domestically produced automobiles are 8 million this year, how many
automobiles do you expect u. s. automakers to sell next year?
Based on the information provided
E= -1.2
%∆Q=E*%∆P+ᶯ*%∆Y
=-1.2*5%+3.0*3%
=-6%+9%
=3%
Therefore sales volume increase would be 3%.
(b) By how much should domestic auto-makers increase the price of automobiles if they
wish to increase sales by 5 percent next year?
If sales were to be increased by 5%
%∆Q=E*%∆P+ᶯ*%∆Y
=5%
-1.2*%∆P+3.0*3%
=5%
1.2%∆P
=4%
%∆P=3.33%
14. suppose that a firm maximizes its total profits and has a marginal cost ( mc) of
QUESTION FOR CRITICAL THINKING 2 6
production of $ 8 and the price elasticity of demand for the product it sells is (-) 3. Find the
price at which the firm sells the product.
(P-MC)/P=1/e
(P-8)/P=1/-3
1/-3
(=-0.333...
8-0.33...)
P=7.67
$7.67
Froeb et al
Individual problems:
6- 1. Elasticity of t- shirt sales George has been selling 5,000 t- shirts per month for $ 8.50.
When he increased the price to $ 9.50 he sold only 4,000 t- shirts.
What is the demand elasticity?
{(5000-4000)/ (5000+4000)}/ {(8.50-9.50)/ (8.50+9.50)}
= (1000/9000)/ (-1)/18
=0.11/-.056
Therefore demand elasticity =-1.964
If his marginal cost is $ 4 per shirt, what is his desired markup and what is his initial actual
markup?
=1/-1.964
==-.509164969450102
=-0.51
Desired mark up would be -0.51
Initial Mark up=
(P-MC0/P
QUESTION FOR CRITICAL THINKING 2 7
P=8.50
MC=4
=8.50-4/8.50
=4.50/8.50
=0.529411764705882
=0.53
Initial Mark-up =0.53
C. Was raising the price profitable?
Based on the above information raising the price is not profitable.
6- 3 Increasing movie ticket prices to conduct an experiment, amc increased movie ticket
prices from $ 9.00 to $ 10.00 and measured the change in ticket sales. Using the data over
the following month, they concluded that the increase was profitable. However, over the
subsequent months, they changed their minds and discontinued the experiment.
How did the timing affect their conclusion about the profitability of increasing prices?
As in any product the months that follow (short term) there will be a profit as consumers decide
whether they should continue buying at the higher price or find alternatives to the product. In the
case of movie tickets consumers accepted the increase in prices short term as they researched
other options. Therefore in the long term unless consumers absolutely have to purchase movie
tickets, movie ticket sales will continue decrease because of other options such as Netflix.
6- 5 Promotional pricing an end- of- aisle price promotions changes the price elasticity of a
good from – 2 to – 3.
If the normal price is $ 10, what should the promotional price be?
(P-MC)/P
=10/-2
QUESTION FOR CRITICAL THINKING 2 8
=-5
MC=5
Promotional price =
P-5/P
=1/-3
=-3P-15=P
-3P-15=P
-4P=15
P=3.75
The promotional price would be 3.75
Salvatore’r Chapter 5:
8. In a study published in 1980, b. b. Gibson estimated the following price and income
elasticities of demand for six types of public goods:
(a) Do these public goods conform to the law of demand?
According to the law of demand when demand increases price also increases. Based on the
information given all of the state activities price elasticity is negative therefore they all qualify or
adhere under the law of demand. When prices begin to raise demand will decrease.
For which public goods is demand price elastic?
Based on the information provided; Demand price is elastic in Parks and recreational areas,
Highway construction and maintenance.
(b) What types of goods are these public goods?
All of the state activities have a positive elasticity of demand. The activities can be divided into
two groups’ necessities and luxury services or goods. Services with elasticity income of greater
than one are considered luxury goods the others are necessities.
QUESTION FOR CRITICAL THINKING 2 9
( c) if the price or cost of college and university education increased by 10 percent and, at
the same time, incomes also increased by 10 percent, what would be the change in the
demand for college and university education?
The change in demand for college and university education would be
-0.87*10%
=8.7%
If income were to increase by 10%
=0.92*10%
=9.2%
If they occurred together it would be
=9.2-8.7
0.5%
15. integrating problem starting with the data for problem 6 and the data on the price of a
related commodity for the years 1986 to 2005 given below, we estimated the regression for
the quantity demanded of a commodity ( which we now re-label q ˆ x ), on the price of the
commodity ( which we now label p x ), consumer income ( which we now label y), and the
price of the related commodity ( p z ), and we obtained the following results. (if you can,
run this regression yourself; you should get results identical or very similar to those given
below.) q ˆ x = 121.86 – 9.50p x + 0.04y – 2.21p z (– 5.12) (2.18) (– 0.68) r2 = 0.9633 f =
167.33 d– w = 2.38 (a) explain why you think we have chosen to include the price of
commodity z in the above regression.
(b) Evaluate the above regression results.
Based on the information on page 211,
R^2=0.9633
=96.33%
Or 96%
Based on the F-stat if,
F-stat is greater than F-crit then the regression equation is statistically significant.
(c) What type of commodity is z? Can you be sure?
(c) Graph both the actual data and the forecast using the graphing tool. Does the forecast
vary much from the actual data?
QUESTION FOR CRITICAL THINKING 2
10
Because Z has a negative slope and the slope is not statistically significant a legitimate
connection cannot be made.
2. (a) estimate the regression in problem 5 based on table 5- 6 using excel’s regression
function in the data analysis menu.
Revenue=32.82+3.44Q
= (2.61) (0.49)
R^2=0.86
F-stat= 48.89
Y23456789
F sales39.6843.1246.5650.0053.4456.8860.3263.76
C:\Users\Mary-Ann\Documents\quest 15 part a.xlsx
(b) Using the coefficients found in the regression estimate; enter a formula based in cells c6
through j6 to forecast the sales revenue when quality control goes from $ 2 million to $ 9
million a year.
The on the attached spreadsheet the forecast value of sales are shown in C6-J6 (see above
attachment.
For Zsales revenue =
Y=32.8125+3.4375*Z
