03 Jun Question Please, complete the following 2 applied
Question
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
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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 firms
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, GGCs price for the typical lawn
system was $1,995 compared with BLGs 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 capacityit 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 eastern 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. GGCs cost structure has been estimated as TVC 5 755.363Q
1 0.005Q2 where Q represents single lawn watering systems.
a. Derive the demand curves for GGCs product in each market.
b. Plot graphically the demand and MR curves for each market, and also show
GGCs combined marginal revenue curve (MR) and its MC 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.
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