Market Structures And Pricing Decisions Applied Probl 257722
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. GGC had last year a price of $1,900 per system, while BLG’s price was $2,100. GGC installed approximately 9,960 systems, capturing about 60% of the market, with total sales split between the two companies. GGC has substantial excess capacity, able to install up to 25,000 systems annually.
GGC is considering expanding into the eastern suburbs, where households are less wealthy. Past sales in these areas are few, largely because of high prices, but GGC's production capacity remains high. Demand functions for the western and eastern markets are given as:
- Qw = 2100 – 6.25Pgw + 3Pbw + 2100Ag – 1500Ab + 0.2Yw
- Qe = Pge + 7Pbe + 1180Ag – 950Ab + 0.085Ye
Where Q refers to units sold; P refers to the price level; A refers to advertising budgets (in millions); Y is the average disposable income level; the subscripts w and e denote western and eastern markets, respectively; and g and b refer to GGC and BLG. GGC plans to spend $1.5 million on advertising (Ag=1.5), and expects BLG to spend $1.2 million (Ab=1.2). The average household disposable income is $60,000 in the western suburbs (Yw) and $30,000 in the eastern suburbs (Ye). GGC’s cost function is TVC = 750Q + 0.005Q².
Show all calculations and processes. Describe your answers for each item:
- 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. Show graphically the demand, MR, and MC curves for each market.
- Calculate the optimal quantities and prices in each market algebraically.
- Calculate the demand price elasticities in each market and discuss how they relate to the pricing strategies.
- Provide a brief note outlining any reservations or qualifications about the price recommendations for GGC.
Follow the grading rubric for evaluation. Submit your completed assignment through the designated platform, following the specific submission instructions provided.
Paper For Above instruction
Introduction
Market structures are fundamental to understanding how firms operate, price, and strategize within different competitive environments. Monopolistic competition and perfect competition are prevalent forms that dictate firms' pricing decisions and profit expectations. This paper explores two applied problems: one involving a monopolistically competitive vacuum cleaner business, and the other analyzing a duopoly in the lawn sprinkler market. By calculating profit-maximizing output and prices, examining economic profits, and analyzing demand elasticities in each case, this paper aims to shed light on strategic market behaviors and their implications.
Problem 1: Robert’s Vacuum Cleaner Firm Analysis
Demand Function and Cost Structure
Robert’s Vacuum Cleaner Company is operating in a monopolistically competitive market with a demand function defined as Q = 5000 – 25P. This indicates that for every dollar increase in price, the quantity demanded decreases by 25 units. The total cost function is TC = 1500 + 20Q + 0.02Q^2, representing fixed and variable costs with increasing marginal costs as output expands.
Profit Maximization: Calculations and Graphs
To determine the profit-maximizing output, we calculate marginal revenue and marginal cost. First, express the inverse demand function: P = (5000 – Q)/25. Simplify: P = 200 – 0.04Q. Total revenue (TR) is P × Q, which becomes TR = (200 – 0.04Q)Q = 200Q – 0.04Q^2. Marginal revenue (MR) is the derivative d(TR)/dQ: MR = 200 – 0.08Q.
The marginal cost (MC) is derived from the total cost function: MC = d(TC)/dQ = 20 + 0.04Q. Equilibrium occurs where MR = MC:
200 – 0.08Q = 20 + 0.04Q
Combine like terms: 200 – 20 = 0.08Q + 0.04Q → 180 = 0.12Q
Q = 180 / 0.12 = 1500 units.
Substitute Q into the demand function to find price: P = 200 – 0.04(1500) = 200 – 60 = $140.
Graphically, demand (D) shows a downward slope, MR is twice as steep as demand, and MC increases linearly with Q. The equilibrium point corresponds to Q=1500 units and P=$140.
Economic Profit Calculation
Total revenue at equilibrium: TR = 140 × 1500 = $210,000. Total cost: TC = 1500 + 20(1500) + 0.02(1500)^2 = 1500 + 30,000 + 0.02(2,250,000) = 1500 + 30,000 + 45,000 = $76,500.
Economic profit = TR – TC = $210,000 – $76,500 = $133,500 in the first year.
Future Profit Expectations
In the long run, new firms may enter the market attracted by profits, leading to increased competition, which would reduce prices and profit margins. As demand slopes downward and firms enter, profits tend to diminish, possibly approaching zero in equilibrium. Thus, the current positive profit is unlikely to persist indefinitely.
Problem 2: GGC Pricing and Demand Analysis
Deriving Demand Curves and Revenue in Each Market
Given the demand functions involve multiple variables, we focus first on the demand for GGC’s product in each market by holding other variables constant.
For the western market:
Qw = 2100 – 6.25Pgw + 3Pbw + 2100Ag – 1500Ab + 0.2Yw
Assuming BLG’s price (Pbw) remains at last year’s level ($2,100), advertising costs (Ag = 1.5), BLG’s advertising (Ab = 1.2), and Yw = 60,000, the demand simplifies to a function of Pgw:
Qw = 2100 – 6.25Pgw + 3(2100) + 2100(1.5) – 1500(1.2) + 0.2(60000)
Qw = 2100 – 6.25Pgw + 6300 + 3150 – 1800 + 12000
Qw = (2100 + 6300 + 3150 – 1800 + 12000) – 6.25Pgw = 21350 – 6.25Pgw
The demand function: Qw = 21350 – 6.25Pgw.
Similarly, for the eastern market, with Ye = 30,000, Ag = 1.5, Ab = 1.2, and assuming Pbe remains at last year’s level ($2,100), we substitute these values into the demand function to derive Qe as a function of Pge.
Deriving GGC’s MR and MC Curves
The total revenue (TR) in each market: TRw = Pwg × Qw and TRe = Pge × Qe. Marginal revenue is derived by differentiating TR with respect to Q, which involves inverting the demand functions to express P in terms of Q, then calculating MR as P + (Q)(dP/dQ).
The marginal cost (MC) function in both markets is derived from TVC = 750Q + 0.005Q²: MC = 750 + 0.01Q.
Optimal Quantities and Prices
To maximize profit, GGC sets MR = MC in each market and solves for Q. This involves solving the algebraic equations:
In the western market: Pgw = (21350 – Qw)/6.25; MR = P + Q(dP/dQ) = 21350/6.25 – 2Q. Set MR = MC and solve for Qw, then find Pgw from the demand function.
Similarly for the eastern market, the same approach yields Qe and Pge.
Price Elasticities of Demand and Strategic Implications
The price elasticity of demand (E) is calculated as:
E = (dQ/dP) × (P/Q) = –6.25 × (P/Q) in the western market and a similar expression in the eastern market. Understanding elasticity helps GGC determine whether raising or lowering prices will increase revenue. Typically, demand is more elastic in urban, less affluent markets, so GGC must be cautious about price increases where demand is sensitive.
Management Notes and Reservations
While price optimization can maximize revenue, GGC should consider potential non-price competition, consumer perception, and market entry barriers in expansion markets. Elasticity estimates suggest lower prices could significantly boost sales but might reduce margins. Therefore, a balanced approach, possibly involving tiered pricing or targeted promotions, would be prudent.
Conclusion
This analysis highlights the importance of understanding demand functions and cost structures in developing effective pricing strategies. For Robert’s vacuum cleaner business, setting prices where MR equals MC maximizes profit, but market entry and competition influence sustainability. For GGC's expansion, demand elasticity insights ensure prices are set to optimize revenues without sacrificing long-term competitiveness. Strategic management must consider both quantitative findings and qualitative market factors for sustainable success.