Market Structures and Pricing Decisions Applied Problems
Please complete the following two applied problems:
Problem 1:
Robert’s New Way Vacuum Cleaner Company is a newly started
small business that produces vacuum cleaners and belongs to a monopolistically
competitive market. Its demand curve for the product is expressed as Q = 5000 –
25P where Q is the number of vacuum cleaners per year and P is in dollars. Cost
estimation processes have determined that the firm’s cost function is
represented by TC = 1500 + 20Q + 0.02Q2.
Show all of your calculations and processes. Describe your
answer for each question in complete sentences, whenever it is necessary.
a. What are
the profit-maximizing price and output levels? Explain them and calculate
algebraically for equilibrium P (price) and Q (output). Then, plot the MC
(marginal cost), D (demand), and MR (marginal revenue) curves graphically and
illustrate the equilibrium point.
b. How much
economic profit do you expect that Robert’s company will make in the first
year?
c. Do you
expect this economic profit level to continue in subsequent years? Why or why
not?
Problem 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 $1,900 compared
with BLG’s price of $2,100. GGC installed 9,960 systems, or about 60% of total
sales and BLG installed the rest. (No doubt many additional systems were
installed by do-it-yourself homeowners because the parts are readily available
at hardware stores.) A total system installed is 16,614. – GH
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 eastern suburb markets for this coming season. You have estimated
two distinct demand functions, as follows:
Qw =2100 – 6.25Pgw + 3Pbw + 2100Ag – 1500Ab + 0.2Yw
for the western market and
Qe = 36620 – 25Pge + 7Pbe + 1180Ag – 950Ab + 0.085Ye
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 (use Ag = 1.5) on advertising this
coming year and expects BLG to spend $1.2 million (use Ab = 1.2) on
advertising. The average household disposable income is $60,000 in the western
suburbs and $30,000 in the eastern suburbs. GGC does not expect BLG to change
its price from last year because 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 =
750Q + 0.005Q2, where Q represents single lawn watering systems.
Show all of your calculations and processes. Describe your
answer for each item below in complete sentences, whenever it is necessary.
a. Derive
the demand curves for GGC’s product in each market.
b. Derive
GGC’s marginal revenue (MR) and marginal cost (MC) curves in each market. Show
graphically GGC’s demand, MR, and MC curves for each market.
c. Derive
algebraically the quantities that should be produced and sold, and the prices
that should be charged, in each market.
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.
