1. The following two
linear functions represent a market (thus one is a supply function, the other a
demand function). Circle the answer closest to being correct. Approximately what will the equilibrium price
be? Q = 100 – 4.6P and
Q = 75 + 6.2P
2. There has been a
change in the market (represented in 1 above).
The change is represented by the following two equations. Circle the one correct conclusion that
describes the market change.
Q
= 90 – 4.6P and Q = 75 + 6.2P
3. Circle the function
on the answer sheet that represents the marginal revenue (MR) function for this
demand function: Q = 90 – 4.6P
4. Circle the
quantity that maximizes total revenue (TR) for the marginal revenue (MR)
function selected in number three (3).
5. If supply
increases and demand also increases, we can conclude that the new equilibrium:
The multivariate demand function (below) is needed for
questions 6 – 12.
Setting: U.S. Auto
manufacturers are trying to develop a multivariate function with which to estimate
the demand for their gas-electric hybrid compact cars. Here is one that Motors General developed for
its Jolt:
Qj = 65000 – 20Pj + 20Pf + 35Pt – 5Pb + 0.2Tc + 0.05Y + 10Mg
+ 0.04A
Where:
Qj = the number of
Jolts demanded per week.
Pj = the price of
each new Jolt (in $).
Pf = the price of each new Ford gas-electric hybrid (in $).
Pt = the price of each new Toyota gas-electric hybrid (in
$).
Pb = the price of replacement batteries for the Jolt (in $).
Tc = the amount of tax credit incentive offered with the
purchase of a new hybrid (in $).
Y = average weekly
disposable income of a typical Jolt purchaser (in $).
Mg = the miles per gallon of gas rating of the Jolt (in
miles per gallon).
A = average weekly
Jolt advertising expenditure (in $).
6. If all variables
remain unchanged except that the price of Jolts (Pj) increases by $1000, then
the quantity demanded of Jolts will:
7. If all variables
remain unchanged except that the average weekly disposable income (Y) increases
by $350 then demand for Jolts will:
8. You can tell by
looking at the sign of the price of Toyota hybrids (Pt) that they are
considered:
9. The partial
derivative of the demand for Jolts with respect to the price of replacement
batteries (Pb) is:
10. Enter the
following values into your Jolt demand function (be very careful with the
calculation because the resulting quantity of Jolts demanded will be used in
several questions to follow). Circle
your answer on the answer sheet. Pj =
$35000 Pf = $35000 Pt = 45000
Pb = $10000
Tc = $10000 Y = $1000
Mg = 50 A =$10000
11. What is the point
income elasticity of Jolt demand with respect to (Y) of $1000? Work out completely, show the sign (+ or -)
and carry out to six decimal places.
12. What is the point
cross-price elasticity of Jolt demand with respect to replacement battery price
(Pb) of $10000? Work out completely,
show the sign (+ or -) and carry out to three places.
Answers
to the following problems do not depend on any information from above.
13. If a 20% increase
in the price of gas causes a 35% decrease in the demand for standard sized
autos, then the cross-price elasticity of demand is:
14. If the price
elasticity of demand of gasoline is 0.9, then a 15% increase in quantity
demanded is caused by a:
15. A 10% increase in
the price of 40 inch LCD televisions which have a price elasticity of 0.6 will
cause a:
16. A business
newscast claims that the median home price of existing homes fell from $275000
to $195000. Over the same time period
the quantity of these homes sold also fell from 3150000 to 2950000. Using the arc elasticity formula, calculate
the arc elasticity implied.
17. The demand for a
product is income elastic with an elasticity coefficient of 2.4. If there is a 20% increase in income, what
must the increase in demand be?
18. The cross price
elasticity of biscotti demand with respect to the price of Lattes is -1.5
(Lattes and biscotti are complementary goods).
If the price of Lattes increases
20% what would you expect to happen to biscotti demand?
19. Write your first
derivative of the following function in the space on the answer sheet.
Y
= 2X2 +5X3 –X +10
20. Write your first
derivative of the following function in the space on the answer sheet.
Y
= 3X1/3 +4X5/4 -2X2 +10X
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