From The Scenario Assuming Katrina's Candies Is Operating In

From The Scenario Assuming Katrinas Candies Is Operating In The Mono

Assuming Katrina’s Candies operates in a monopolistically competitive market, it faces a weekly demand function P = 50 - 0.01Q, a variable cost function VC = 20Q + 0.006665Q², a fixed cost of FC = $5,000, and the marginal cost (MC) derived as MC = 20 + 0.01333Q. To determine the profit-maximizing price, quantity, and profit in the short run, we need to analyze the profit-maximization condition where marginal revenue (MR) equals marginal cost (MC). The given functions are:

  • Demand: P = 50 - 0.01Q
  • Total Variable Cost: VC = 20Q + 0.006665Q²
  • Marginal Cost: MC = 20 + 0.01333Q
  • Marginal Revenue: MR = 50 - 0.02Q

Step 1: Find the Quantity (Q) where MR = MC

To maximize profit, set MR equal to MC:

50 - 0.02Q = 20 + 0.01333Q

Rearranging:

50 - 20 = 0.02Q + 0.01333Q

30 = 0.03333Q

Q = 30 / 0.03333 ≈ 900 units

Step 2: Determine the Corresponding Price

Using the demand function, substitute Q = 900:

P = 50 - 0.01(900) = 50 - 9 = $41

Step 3: Calculate Total Revenue (TR), Total Variable Cost (TVC), Total Cost (TC), and Profit

Total Revenue:

TR = P × Q = $41 × 900 = $36,900

Total Variable Cost:

TVC = 20(900) + 0.006665(900)²

= 18,000 + 0.006665 × 810,000

≈ 18,000 + 5,400 = $23,400

Total Cost:

TC = FC + TVC = 5,000 + 23,400 = $28,400

Profit:

Profit = TR - TC = $36,900 - $28,400 = $8,500

Conclusion

In the short run, Katrina’s Candies should produce approximately 900 kilograms and sell it at a price of $41 per kilogram to maximize profit. The maximum profit achievable with these conditions is approximately $8,500. These findings align with monopolistic competition theory, where firms produce where marginal revenue equals marginal cost and price exceeds average total cost in the short run.

References

  • Perloff, J. M. (2017). Microeconomics (8th ed.). Pearson.
  • Pindyck, R. S., & Rubinfeld, D. L. (2018). Microeconomics (9th ed.). Pearson.
  • Varian, H. R. (2014). Intermediate Microeconomics: A Modern Approach (9th ed.). W. W. Norton & Company.
  • Mankiw, N. G. (2020). Principles of Microeconomics (9th ed.). Cengage Learning.
  • Krugman, P., & Wells, R. (2018). Microeconomics (5th ed.). Worth Publishers.
  • Case, K. E., Fair, R. C., & Oster, S. M. (2017). Principles of Economics (12th ed.). Pearson.
  • Samuelson, P. A., & Nordhaus, W. D. (2010). Economics (19th ed.). McGraw-Hill Education.
  • Frank, R. H., & Bernanke, B. S. (2018). Principles of Economics (7th ed.). McGraw-Hill Education.
  • Hubbard, R. G., & O'Brien, A. P. (2020). Microeconomics (7th ed.). Pearson.
  • Sullivan, A., & Sheffrin, S. M. (2018). Microeconomics: Principles, Applications, and Tools (8th ed.). Pearson.

Related Assignments