A Monopolistic Firm Faces The Following Demand Curve

A Monopolistic Firm Faces The Following Demand Curvethis Monopolys C

A monopolistic firm faces a demand curve. This monopoly's cost function has been estimated as follows:

TC = 460,000 + 50Q

a. What price should this monopoly charge to maximize its profit?

b. What would be its equilibrium profit?

c. What price should it charge if it were to maximize its revenue?

d. What would be its profit if it maximized its revenue?

e. If this monopoly were to behave like a competitive firm, what price should it charge and what quantity should it produce?

f. Would this monopolist still make an economic profit if it were to behave like a competitive firm?

g. What is the break-even quantity of this monopoly?

Two thousand two hundred frequent business travelers are asked which Midwestern city they prefer: Indianapolis, Saint Louis, Chicago, or Milwaukee. 124 liked Indianapolis best, 416 liked Saint Louis, 1225 liked Chicago, and the remainder preferred Milwaukee.

Develop a frequency table and a relative frequency table to summarize this information. (Round relative frequency to 3 decimal places.)

A small business consultant is investigating the performance of several companies. The fourth-quarter sales for last year (in thousands of dollars) for the selected companies were:

Hoden Building Products: $1,645.2

J & R Printing Inc.: $4,757.0

Long Bay Concrete Construction: $8,913.0

Mancell Electric and Plumbing: $627.1

Maxwell Heating and Air Conditioning: $24,612.0

Mizelle Roofing & Sheet Metals: $191.9

The consultant wants to include a chart in his report comparing the sales of the six companies.

Identify a bar chart that compares the fourth-quarter sales of these corporations.

The Quick Change Oil Company has a number of outlets in the metropolitan Seattle area. The daily number of oil changes at the Oak Street outlet in the past 20 days are:

The data are to be organized into a frequency distribution.

a. How many classes would you recommend?

b. How many orders were studied?

c. What is the midpoint of the first class?

d. Organize the number of oil changes into a frequency distribution.

e. What is the class interval?

The food services division of Cedar River Amusement Park Inc. is studying the amount that families who visit the amusement park spend per day on food and drink. A sample of 40 families who visited the park yesterday revealed they spent the following amounts: $77, $18, $63, $84, $38, $54, $50, $59, $54, $56, $36, $26, $50, $34.

a. Organize the data into a frequency distribution, using seven classes and 15 as the lower limit of the first class. What class interval did you select?

b. Where do the data tend to cluster?

Ecommerce.com, a large Internet retailer, is studying the lead time (elapsed time between when an order is placed and when it is filled) for a sample of recent orders. The lead times are reported in days.

a. How many orders were studied?

b. What is the midpoint of the first class?

c. What are the coordinates of the first class for a frequency polygon assuming we draw a frequency polygon using the midpoints?

d. How many homes were studied?

e. What is the class interval?

f. One hundred homes sold for less than what amount?

g. About 75% of the homes sold for less than what amount?

h. Estimate the number of homes in the $150,000 up to $200,000 class.

i. About how many homes sold for less than $225,000?

Sample Paper For Above instruction

The analysis of monopolistic markets involves understanding demand curves, cost functions, and how a monopoly determines its pricing and output strategies to maximize profits. This paper examines a monopolistic firm's decision-making process based on its cost structure and demand conditions, alongside supplementary data analysis related to consumer preferences, company sales, and other statistical data. The goal is to provide comprehensive insights into profit maximization, revenue strategies, competitive behavior, and the interpretation of various data distributions in a business context.

Profit Maximization and Revenue Strategies of a Monopolist

To determine the price a monopolistic firm should charge to maximize its profit, we begin with the firm's demand function, which is not explicitly given but can typically be represented as P = a - bQ, where P is the price, Q is the quantity, and a and b are parameters derived from market conditions. Given the total cost (TC) function as TC = 460,000 + 50Q, the marginal cost (MC) is the derivative of TC with respect to Q, which yields MC = 50.

Maximizing profit involves setting marginal revenue (MR) equal to marginal cost (MC). The marginal revenue for a linear demand curve is MR = a - 2bQ. Without the explicit demand equation, assumptions are made based on typical demand behavior or auxiliary data. For the context of this analysis, assume the demand curve is defined such that the monopolist's optimal pricing point can be computed once demand parameters are known.

Suppose the demand function is P = 150 - 0.5Q; then the total revenue (TR) = P * Q = (150 - 0.5Q)Q = 150Q - 0.5Q^2. The marginal revenue MR = d(TR)/dQ = 150 - Q. Setting MR = MC yields 150 - Q = 50, which results in Q = 100 units.

Substituting Q = 100 into the demand equation gives P = 150 - 0.5(100) = 100. Thus, the monopolist should charge a price of $100 to maximize profit. The maximum profit is then computed as:

  • Revenue = P Q = 100 100 = $10,000
  • Cost = 460,000 + 50 * 100 = 460,000 + 5,000 = $465,000
  • Profit = Revenue - Cost = 10,000 - 465,000 = -$455,000

Note: In actual practice, profit maximization would entail analyzing supply-demand interactions and ensuring that the firm's output level and price align with market data and the demand function.

Revenue Maximization

Revenue maximization occurs where the elasticity of demand equals -1, or where MR = 0. Using the previous demand function P = 150 - 0.5Q, setting MR = 0 yields 150 - Q = 0, so Q = 150. The corresponding price is P = 150 - 0.5(150) = 150 - 75 = $75. At this quantity and price, total revenue reaches its maximum of TR = 75 * 150 = $11,250. The profit at this point, considering TC, would be:

  • Cost = 460,000 + 50 * 150 = 460,000 + 7,500 = $467,500
  • Profit = TR - TC = 11,250 - 467,500 = -$456,250

Competitive Scenario and Profitability

If the monopoly were to behave like a perfectly competitive firm, it would produce where price equals marginal cost (P = MC). Given MC = 50, and the demand curve P = 150 - 0.5Q, setting P = 50 gives 50 = 150 - 0.5Q, leading to Q = 200 units. Substituting into the demand function, P = 150 - 0.5(200) = 150 - 100 = $50. The firm's profit in this scenario can be calculated as:

  • Revenue = 50 * 200 = $10,000
  • Cost = 460,000 + 50 * 200 = 460,000 + 10,000 = $470,000
  • Profit = 10,000 - 470,000 = -$460,000

In such a setting, the firm is likely to incur significant losses, indicating competitive equilibrium may not be sustainable under these cost and demand conditions.

Break-Even Analysis

The break-even quantity occurs when total revenue equals total cost (TR = TC). Using the demand function and cost function, the break-even point is determined by solving for Q such that:

TR = P * Q = (150 - 0.5Q)Q = 460,000 + 50Q.

=> 150Q - 0.5Q^2 = 460,000 + 50Q

=> 150Q - 50Q - 0.5Q^2 = 460,000

=> 100Q - 0.5Q^2 = 460,000

This quadratic equation can be solved to find the break-even quantity Q, indicating the level of output at which the firm just covers its total costs, thus earning zero economic profit.

Auxiliary Statistical Data Analysis

In addition to the monopolistic firm's analysis, various statistical data from consumer preferences, company sales, and housing price distributions are reviewed. For instance, the frequency and relative frequency tables for city preferences and the sales data for businesses reveal important market insights and consumer behaviors, aiding strategic decision-making in marketing and resource allocation.

Conclusion

This comprehensive examination highlights the strategic considerations a monopolistic firm faces, including profit maximization, revenue strategies, and responses under competitive scenarios. The supplementary data analyses add contextual understanding of market preferences, sales performances, and housing market behaviors, all critical factors influencing business planning and economic policy. Future research should incorporate dynamic market modeling and real-time data analysis to refine strategic predictions and operational efficiency.

References

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