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Assignment
Algebra
“Exponential growth drives resource usage” See the syllabus for the “rules” on all assignments
Part 1 (work to be included in your portfolio – written requirement in questions 1-5) The work is to be
typed.
1a. A student’s grade is based on four exams. If the student wants a grade of B that requires an average score of 85 in
the exams, then what will the minimum score on the fourth exam if the average on the first three exams is 83? (Last
names beginning with A-H)
1b. A student’s grade is based on three exams. If the student wants a grade of B that requires an average score of 85 in
the exams, then what will the minimum score on the third exam if the average on the first two exams is 88? (Last names
beginning with I-Z)
2. It has been estimated that average attendance at a Water fire event in Providence is 40,000 and that the Public Works
Department must clean up 5 tons of garbage left by the crowds. How many pounds did the average partygoer leave?
What will be the total tonnage of garbage if an advertising campaign increases attendance by 10%?
3a. Use the equation V = P*Q/M to solve for M (Last names beginning with A-H)
3b. Use the equation V = P*Q/M to solve for Q (Last names beginning with I-Z)
4a. Assume you need to rent a car for one day and that you compare that cost at two different agencies. The cost (in $)
at agency A is given by C = 30 + 0.22m, where m is the number of miles you drive. Similarly, the cost at agency B is
given by C = 12 + 0.40m. (Last names beginning with A-H)
.
a. If you drive only a few miles (say, less than 20 miles), which agency costs less, A or B?
b. How far would you need to drive in order for the other agency to become less expensive?
4b. Assume you are trying to make a choice between two machines based on costs. The cost (in $) of machine A is
given by C = 3300 + 0.3X, where X is the number of units of output (in 1000s). The cost of machine B is given by C =
2000 + 0.5X. (Last names beginning with I-Z)
.
a. The fixed costs are higher for which machine – and what is it?
b. The marginal costs are higher for which machine – and what is it?
c. What is the average cost of the two machines if output is projected to be 100,000?
d. If the level of production is scheduled to be 100,000, which is the least cost machine?
5a. We have heard much about the price of gas in recent years, and the price swings have had a big impact on the US
economy. One sector where it has had an impact is on the auto industry. A recent econometric study of SUV demand in
the US has produced the following equation: (Last names beginning with A-H)
Q = 6100 - 50*P + 2.1*i + .025*Y + 34*Pg
a.
b.
c.
Where: Q = SUV sales P = price of SUVs i = interest rate Y = median income Pg = price of gas
Are the signs on the coefficients what you would expect? Explain.
How would the demand equation for Canada differ if SUV demand was more sensitive to interest rates than in
the US?
Draw on one graph the curves relating demand for SUVs (Q) to interest rates (i) for the two countries.
5b. The New Economy has focused attention on Investment spending. A recent econometric study of investment
spending in the US has produced the following equation: (Last names beginning with I-Z)
I = 6100 + 2.1*i + .25*ΔY + 4.5*U
a.
b.
c.
Where: I = investment
i = interest rate ΔY = change in GDP U = unemployment rate
Are the signs on the coefficients what you would expect? Explain.
How would the investment demand equation for Canada differ if investment demand were more sensitive to
changes in income in Canada;
Draw on one graph the curves relating investment demand (I) to changes in Income (ΔY) for the two
countries. Please put both curves on the same graph.
Part 2 (work to be included in your portfolio – written requirements in questions 1-5)
1. A flight from Boston to LA the number of first-class seats available is N1 and they are sold at the price P1 and the
number of coach seats available is Nc and they are sold at the price Pc. Assuming all seats are sold, express the equation
for revenue ( R ) in terms of these parameters.
2a. The demand for electricity (Qd) in any municipality is dependent upon the price of electricity (P), population (POP),
and median income (Y). (Last names beginning with A-H)
a. Assume that the demand function is linear in all the variables and construct an equation for the demand
function.
b. Describe the expected restrictions on the parameters in the equation based on your knowledge of economic
theory (what size and sign should the coefficients be?)
c. Describe how the equation change if in Hartford demand is more responsive to price changes than in
Providence?
2b. The demand for hybrids (Qd) in the US depends upon median income (Y), the price of the hybrids (P), population
(POP), and the price of gas (Pg). (Last names beginning with I-Z)
a. Assume that the demand function is linear in all the variables and construct an equation for the demand
function.
b. Describe the expected restrictions on the parameters in the equation based on your knowledge of economic
theory (what size and sign should the coefficients be?)
c. Describe how the equation would change if in Europe demand is less responsive to price changes than in the
US?
3a. Below is some data on population and energy use in 2008. You should use it to answer the following questions.
(Last names beginning with A-H) [You can find this table in the spreadsheet 306_Spread_Ex1 on the A2_P1_2 tab that
is in Sakai resources.
Population (bil.)
China
1.317
India
1.141
US
0.304
World
6.701
Quadrillion = 1,000,000,000,000,000
a.
b.
c.
d.
e.
Consumption Per capita
Million. BTUs)
64.6
17.1
330.4
73.6
Consumption
(quadril.Btus) *
What is China’s energy consumption and share of world energy consumption in 2008?
What is the US share of the world's population and energy consumption in 2008?
How much more energy does the average American consume than the average Indian?
What will consumption per capita be in China in 20 years if it grows at 7% a year?
What would energy consumption be in China and India if per capita consumption were 50% of the US
average?
3b. Below is some data on population in 2000 and 2010. You should use it to answer the following questions. (Last
names beginning with I-Z)] [You can find this table in the spreadsheet 306_Spread_Ex1 on the A2_P1_3 tab that is in
Sakai resources.
Total population
Hispanic or Latino
Not Hispanic or Latino
White
Black or African American
Asian
a.
b.
c.
d.
e.
2000 Population
281,421,906
35,305,818
246,116,088
194,552,774
33,947,837
10,123,169
2010 Population
308,745,538
50,477,594
258,267,944
196,817,552
38,929,319
14,674,252
How much did the US population grow in the decade ending in 2010?
Which racial / ethnic group grew the fastest in the decade – and how fast?
Which racial / ethnic group grew the most in the decade – and how much?
What was the annual growth rate in the US population in this decade?
What will the Hispanic population be in 20 years if it continues to grow at that rate? What about the White
population?
4. Answer the following questions using the PV analysis.
a. How much will college cost in 20 years if it costs $30,000 now and it continues to rise at 5% a year?
b. How much would I need to invest today if I wanted to use the money to pay for a year of college for my
granddaughter who will be entering school in 13 years and I expect to earn 3% a year over that period?
c. College costs rose from $23,000 to $52,000 in ten years, what was the average yearly growth rate?
5a. Here is a simple algebraic version of a market. You are to solve this for the equilibrium price (P) and quantity (Q).
(Last names beginning with A-H)
Qd = 100 – 4P
Qs = 10 + 2P
Qs = Qd
5b. Here is the information on the production functions for two goods (X & Y) that can be produced with one input (L).
You are to use this information to solve for the equation of the production possibility curve. (Last names beginning with
I-Z)
X = 4*Lx
Y = 2*Ly
Lx+Ly - 100