Ashford 5: - Week 4 - Instructor Guidance
Class, I'm going to start with helping you with problem 2. This is the most difficult
problem and if I can get you through this one hopefully Problem 1 won't be so bad.
Problem 2 NOTE: “constant” just means the number you calculate from given
values.
1.
To derive the demand curve for Western states, substitute the values for
advertising, income and prices and derive function for the price. Add up the constant
terms to get
Qe=(coefficient)P + constants
or if this looks more familiar Q=a+bP, (Q/b)-(a/b) = P, a/b reduces to a constant and
Q/b= 1/b*(Q) where 1/b is a number
2.
Solve for P to get the inverse demand curve, i.e. rearrange the equation above to
get
Qe/coefficient - constants/coefficient = P
Just divide the constants by the coefficient to get a new constant. You can
express the first term as 1/coefficient * Q where 1/coefficient will divide out to be
a number.
3.
Similar for the Eastern states.
Qe = [coefficient] Pge + [constant] – [constant] +[constant]
Pge=[constant] -Qe/ [constant] is the derived demand curve
b) Let us start with the Western market:
TRw=(Pw)*Qw
Note that because P= a+b(Q) when you multiply times Q you'll get TR=aQ+b(Q)^2
MR is the first derivative of that equation. The book shows you some ways to get it
without calculus but lets just say the rate of change of aQ is just a and the rate of
change of Q^2 is 2Q so:
MRw=[constant] – 2*Qw/[constant]
For the Eastern market, we have:
TRe=(Pe)*Qe
from the total revenue equation TR = PQ
MRe=[constant] -2*Qe/ [constant]
The cost information is the same for both markets:
TVC=755.363Q+0.005*Q^2
MC=755.363+2*0.005*Q
We create some values for Q and derive the respective values for MC, and for P and
MR in each market. Then we plot the functions for each market:
Q
Pgw
MRw
MC
Pge
MRe
0 3498.725 3498.725 755.363 2179.875 2179.875
3000
6000 2510.524 1522.323 815.363 1984.874 1789.874
9000
12000
15000
18000
21000 40.02214
Western Market
534.1226
875.363
1692.374
1009.874
-3418.68 965.363 1497.374 814.8733
It is clear from the graph that the optimal solution is where MR and MC intersect, which
from the graph seems to be for quantity between _____? and _____? units.
[you can also just set MC = MR and solve for Q as below in c.]
Eastern Market
For the Eastern states, the price is lower and quantity is just under _____?
c) We can calculate quantity exactly by setting MR=MC and solving for Q and
then using that Q value to find P from the demand curve:
For the Western market:
Qw*=_____?
Pgw*=$_____?
For the Eastern market:
Qe*= ________?
Pge*=$______?
d)The price elasticity of demand in the western states is:
Elasticity (Western) = (dQw/dPw)*(Pw/Qw) = [Note: eQw/dQw is just the coefficient of
Pw given above, and you just solved for Pw/Qw so just plug in the numbers]
Elasticity (Eastern) = (dQe/dPe)*(Pe/Qe) =
[Remember: if the absolute value (forget the - sign) is less than one it is inelastic, if >1 it
is elastic. So recall how revenue changes depending on the price elasticity of demand]
With _______? demand, it makes sense for price to be _________ so as to _________
sales. This indicates that the GGC strategy to ?_____ prices for the Eastern states is
?__________.
e) As the competitor is charging $2100 in both markets, it appears that GGC’s pricing
strategy is ?______ in the Eastern markets as it will ?______ its sales and allow it to
more than double its sales there. The pricing in the Western markets is very similar to
its competitor’s pricing.
Market Structures and Pricing Decisions Applied Problems.
Please, complete the following 2 applied problems in a Word or Excel document. Show
all your calculations and explain your results. Submit your assignment in the drop box
by using the Assignment Submission button.
Week 4 Assignment Study Guide
1. A small business which produces plastic vacuum-suction covers for round
household dishes has a monopoly that is protected by a utility patent. The market
demand curve for this product is estimated to be: Q = 6009 – 25P where Q is the
number of plate covers per year and P is in dollars. Cost estimation processes
have determined that the firm’s cost function is represented by TC = 120 +
2500Q -0.25*Q2.
(i)
What is the profit-maximizing price and
output level? Solve this algebraically for equilibrium P
and Q and also plot the MC, D and MR curves and
illustrate the equilibrium point.
(ii)
What profit do you expect that the firm will make in
the first year?
(iii)
Do you expect this profit level to continue in
subsequent years? Why or why not?
2. Greener Grass Company (GGC) competes with its main rival, Better Lawns and
Gardens (BLG), in the supply and installation of in-ground lawn watering systems
in the wealthy western suburbs of a major east-coast city. Last year, GGC’s price
for the typical lawn system was $1,995 compared with BLG’s price of $2,100.
GGC installed 9,130 systems, or about 55% of total sales and BLG installed the
rest. (No doubt many additional systems were installed by do-it-yourself
homeowners since the parts are readily available at hardware stores.) GGC has
substantial excess capacity—it could easily install 25,000 systems annually, as it
has all the necessary equipment and can easily hire and train installers.
Accordingly, GGC is considering expansion into the eastern suburbs, where the
homeowners are less wealthy. In past years, both GGC and BLG have installed
several hundred systems in the eastern suburbs but generally their sales efforts
are met with the response that the systems are too expensive. GGC has hired
you to recommend a pricing strategy for both the western and east¬ern suburb
markets for this coming season. You have estimated two distinct demand
functions, as follows:
Qw = 1,035.548 - 6.07164Pgw + 2.83Pbw + 2,100Ag - 1,500Ab + 0.2348Yw
for the western market and
Qe = 49,714.29 - 30.7692Pge + 6.984Pbe + 1,180Ag - 950Ab + 0.0825Ye
for the eastern market, where Q refers to the number of units sold; P refers to
price level; A refers to advertising budgets of the firms (in millions); Y refers to
average disposable income levels of the potential customers; the subscripts w
and e refer to the western and eastern markets, respectively; and the subscripts
g and b refer to GGC and BLG, respectively. GGC expects to spend $1.5 million
on advertising this coming year and expects BLG to spend $1.2 million on
advertising. The average household disposable income is $55,000 in the western
suburbs and $25,000 in the eastern suburbs. GGC does not expect BLG to
change its price from last year, since it has already distributed its glossy
brochures (with the $2,100 price stated) in both suburbs, and its TV commercial
has already been produced. GGC’s cost structure has been estimated as TVC =
755.363Q + 0.005Q2 where Q represents single lawn watering systems.
a.
Derive the demand curves for GGC’s product in each market.
b.
Plot graphically the demand and MR curves for each market, and
curve. Show graphically the quantities that should be produced and
sold, and the prices that should be charged, in each market.
c.
Confirm your quantity and price results algebraically.
d.
Calculate the price elasticities of demand in each market and
discuss these in relation to the prices to be charged in each market.
e.
Add a short note to GGC management outlining any reservations
and qualifications you may have concerning your price
recommendations