problem 1: Robert’s New Way Vacuum Cleaner Company is a newly started small business which generates 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. The Cost estimation processes have determined that the firm’s cost function is symbolized by TC = 1500 + 20Q + 0.02Q^2.
Show all of your computations and processes. describe your answer for each problem in complete sentences, whenever it is required.
a) What are the profit-maximizing price and output levels? Describe them and compute algebraically for equilibrium P (price) and Q (output). Then, plot the MC (marginal cost), D (demand) and MR (marginal revenue) curves graphically and describe 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 following years? Why or why not?
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 main 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 around 60% of total sales and BLG installed the rest. (No doubt most of the additional systems were installed by do-it-yourself homeowners as the parts are readily available at hardware stores.)
GGC has substantial excess capacity–it could simply install 25,000 systems annually, as it has all the essential equipment and can simply 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 however usually their sales efforts are met with the response which 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 shown below:
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, correspondingly; 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 doesn’t expect BLG to change its price from last year as it has already distributed its glossy brochures (with the $2,100 price stated) in both suburbs and its TV commercial has already been generated. GGC’s cost structure has been estimated as TVC = 750Q + 0.005Q^2, where Q represents single lawn watering systems.
Show all of your computations and processes. Describe your answer for each item below in complete sentences, whenever it is essential.
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 which must be produced and sold, and the prices that must be charged, in each market.
d) Compute the price elasticities of demand in each market and describe 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 might have concerning your price recommendations.