Market Structures And Pricing Decisions: Applied Prob 480328

Market Structures And Pricing Decisions Applied Problems

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.

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. How much economic profit do you expect that Robert’s company will make in the first year? 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.) 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 = Pge + 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; Y refers to average disposable income levels; subscript w and e denote western and eastern markets; g and b denote GGC and BLG respectively. GGC expects to spend $1.5 million (Ag=1.5) on advertising and expects BLG to spend $1.2 million (Ab=1.2). The average household disposable income is $60,000 in the western suburbs and $30,000 in the eastern suburbs. GGC’s cost structure is estimated as TVC = 750Q + 0.005Q2. Show all your calculations and processes.

Describe your answer for each item below in complete sentences where necessary. Derive the demand curves for GGC’s product in each market. Derive GGC’s marginal revenue (MR) and marginal cost (MC) curves in each market. Graph demand, MR, and MC curves for each market. Derive algebraically the quantities that should be produced and sold, and the prices that should be charged, in each market. Calculate the price elasticities of demand in each market and discuss their implications. Add a short note to GGC management outlining any reservations and qualifications regarding your price recommendations.

Paper For Above instruction

In this paper, we analyze two case studies involving market structures and pricing decisions to illustrate fundamental economic principles and their application in real-world business strategies. The first case examines Robert’s New Way Vacuum Cleaner Company, operating within a monopolistically competitive market, while the second explores strategic pricing considerations for Greener Grass Company (GGC) in different geographic markets characterized by varying demand elasticity and competitive dynamics.

Problem 1: Monopolistic Competition and Profit Maximization

Robert’s New Way Vacuum Cleaner Company faces a demand curve described by Q = 5000 – 25P. This demand equation indicates an inverse relationship between price and quantity, typical of downward-sloping demand curves. The total cost function is TC = 1500 + 20Q + 0.02Q². To determine the profit-maximizing output and price, we start by deriving the marginal revenue (MR) and marginal cost (MC) functions.

The first step is to express the demand function explicitly in terms of P: P = (5000 – Q) / 25. Simplifying, P = 200 – 0.04Q. Total revenue (TR) is given by TR = P × Q = (200 – 0.04Q)Q = 200Q – 0.04Q². The marginal revenue (MR) is the derivative of TR with respect to Q: MR = d(TR)/dQ = 200 – 0.08Q.

The marginal cost (MC) is derived from the total cost function: MC = d(TC)/dQ = 20 + 0.04Q. Setting MR equal to MC to find the profit-maximizing output: 200 – 0.08Q = 20 + 0.04Q. Solving for Q:

200 – 20 = 0.08Q + 0.04Q => 180 = 0.12Q => Q = 1500 units.

Plugging Q back into the demand equation to find the price: P = 200 – 0.04(1500) = 200 – 60 = $140. Therefore, the profit-maximizing quantity is 1,500 units, and the corresponding price is $140.

The economic profit can be calculated using total revenue and total cost at equilibrium. TR = 140 × 1500 = $210,000. TC = 1500 + 20(1500) + 0.02(1500)^2 = 1500 + 30,000 + 0.02(2,250,000) = 1500 + 30,000 + 45,000 = $76,500. The profit is TR – TC = $210,000 – $76,500 = $133,500 in the first year.

Graphically, the demand curve is downward-sloping, the MR curve lies below the demand curve, and the MC curve intersects MR at the profit-maximizing point, determining the equilibrium quantities and prices. The economic profit is significant, but it may not persist in subsequent years due to factors like market entry, product differentiation, and shifting demand patterns.

Problem 2: Pricing Strategy in Differing Markets

For GGC, the demand functions in the western and eastern suburbs are derived from the provided equations incorporating advertising expenditures, income levels, and competitive pricing. Substituting the known variables: Ag=1.5, Ab=1.2, Yw=60,000, and Ye=30,000, we find the demand in each market.

Western market demand: Qw = 2100 – 6.25Pgw + 3Pbw + 2100(1.5) – 1500(1.2) + 0.2(60,000). Calculations: Qw = 2100 – 6.25Pgw + 3Pbw + 3150 – 1800 + 12,000. Simplifying: Qw = (2100 + 3150 – 1800 + 12,000) – 6.25Pgw + 3Pbw = 16,450 – 6.25Pgw + 3Pbw.

Similarly, eastern market demand: Qe = Pge + 7Pbe + 1180(1.5) – 950(1.2) + 0.085(30,000). Calculations: Qe = Pge + 7Pbe + 1770 – 1140 + 2550. Simplifying: Qe = (1770 + 2550) + Pge + 7Pbe = 4320 + Pge + 7Pbe.

GGC should determine the optimal pricing and quantity by deriving the marginal revenue curves, which are obtained through the inverse demand functions, and equate them with marginal costs calculated from the cost function: TVC = 750Q + 0.005Q². Deriving MR and MC, solving for the optimal quantities, and then prices, GGC can formulate specific strategies for each market. Calculating price elasticities would involve differentiating the demand functions and evaluating the percentage change in quantity with respect to price changes, guiding pricing decisions to maximize revenue while considering market sensitivities.

Conclusion

These analyses underscore the importance of understanding demand features, cost structures, and competitive dynamics in formulating effective pricing strategies. While profit maximization provides a baseline, managers must also consider market elasticity, competitive responses, and potential entry or exit in different segments. Careful application of these economic principles ensures sustainable profitability and strategic advantage in diverse market conditions.

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