Problem 1: Robert’s New Way Vacuum Cleaner Company Is A New

Problem 1: Robert’s New Way Vacuum Cleaner Company is A Newly Started S

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 + 0.02Q^2. 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?

Paper For Above instruction

Problem 1 Roberts New Way Vacuum Cleaner Company is A Newly Started S

Introduction

The determination of optimal pricing and output levels is fundamental to the success of small businesses, especially those operating under monopolistic competition. This paper analyzes Robert’s New Way Vacuum Cleaner Company, applying economic principles to identify profit-maximizing strategies, derive relevant curves, and estimate expected profits. Additionally, it discusses the sustainability of profits over time, considering market dynamics and competitive factors.

Given Data and Market Context

The demand function for the vacuum cleaners is:

Q = 5000 – 25P

where Q is annual units sold and P is the price in dollars. The total cost (TC) function is:

TC = 1500 + 20Q + 0.02Q2

Marginal Cost (MC) can be derived from the total cost as:

MC = d(TC)/dQ = 20 + 0.04Q

Step 1: Expressing Price as a Function of Quantity

Rearranging the demand function:

P = (5000 – Q) / 25 = 200 – 0.04Q

Step 2: Revenue and Marginal Revenue Calculation

Total Revenue (TR) = P × Q = (200 – 0.04Q)Q = 200Q – 0.04Q2

Marginal Revenue (MR) is the derivative of TR with respect to Q:

MR = d(TR)/dQ = 200 – 0.08Q

Step 3: Determine Profit-Maximizing Output and Price

Profit maximization occurs where MR = MC:

200 – 0.08Q = 20 + 0.04Q

Solving for Q:

200 – 20 = 0.08Q + 0.04Q

180 = 0.12Q

Q = 1500 units

Substituting Q into the demand equation to find P:

P = 200 – 0.04(1500) = 200 – 60 = $140

Step 4: Calculating Economic Profit

Total Revenue:

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

Profit = TR – TC = $210,000 – $76,500 = $133,500

Step 5: Graphical Illustration

The curves can be graphically represented with the demand curve decreasing linearly, the MR curve with twice the slope of demand, and the MC curve rising as Q increases. The equilibrium point at Q=1500 and P=$140 reflects profit maximization.

Discussion on Future Profits

Given that Robert’s company operates in a monopolistically competitive market with relatively easy entry, sustained economic profits are unlikely in the long term. New entrants can erode profits by offering similar products, driving prices down until only normal profit remains. Therefore, unless Robert innovates or develops brand loyalty, the economic profit of $133,500 is expected to diminish over time.

Conclusion

By equating MR and MC, the profit-maximizing output and price levels are identified as 1500 units and $140 respectively, yielding an estimated first-year profit of $133,500. The company should consider strategies such as product differentiation or cost leadership to sustain profitability beyond the initial years. Understanding the market structure underscores the importance of innovation and marketing in maintaining competitive advantage and economic profits in a monopolistically competitive environment.

References

  • Mankiw, N. G. (2021). Principles of Microeconomics (9th ed.). Cengage Learning.
  • Sloman, J., & Wride, A. (2019). Economics (11th ed.). Pearson.
  • Frank, R. H., & Bernanke, B. S. (2021). Principles of Economics (7th ed.). McGraw-Hill Education.
  • Varian, H. R. (2014). Intermediate Microeconomics: A Modern Approach (9th ed.). W.W. Norton & Company.
  • Hubbard, R. G., & O'Brien, A. P. (2018). Microeconomics (6th ed.). Pearson.
  • Perloff, J. M. (2019). Microeconomics (8th ed.). Pearson.
  • Pindyck, R. S., & Rubinfeld, D. L. (2017). Microeconomics (8th ed.). Pearson.
  • Samuelson, P. A., & Nordhaus, W. D. (2010). Economics (19th ed.). McGraw-Hill Education.
  • Varian, H. R. (2012). Microeconomic Analysis (3rd ed.). W. W. Norton & Company.

Related Assignments