Market Structures: Please Respond To The Following

Market Structuresplease Respond To The Following From The Scena

1. "Market Structures" Please respond to the following: From the scenario, assuming Katrina’s Candies is operating in the monopolistically competitive market structure and faces the following weekly demand and short-run cost functions: VC = 20Q+0.006665 Q2 with MC=20 + 0.01333Q and FC = $5,000 P = 50-0.01Q and MR = 50-0.02Q Where price is in $ and Q is in kilograms. All answers should be rounded to the nearest whole number. Algebraically, determine what price Katrina’s Candies should charge in order for the company to maximize profit in the short run. Determine the quantity that would be produced at this price and the maximum profit possible.

2. "Maximizing Revenue" Please respond to the following: From the scenario, assuming Katrina’s Candies is operating in the monopolistically competitive market structure and faces the following weekly demand and short-run cost functions: VC = 20Q+0.006665 Q2 with MC=20 + 0.01333Q and FC = $5,000 P = 50-0.01Q and MR = 50-0.02Q Where price is in $ and Q is in kilograms. All answers should be rounded to the nearest whole number. Algebraically, determine what price Katrina’s Candies should charge if the company wants to maximize revenue in the short run. Determine the quantity that would be produced at this price and the maximum revenue possible.

Paper For Above instruction

Katrina’s Candies operates within a monopolistically competitive market structure, characterized by many producers offering differentiated products, free entry and exit in the long run, and some degree of market power that allows firms to set prices above marginal cost. To maximize her company's profit and revenue in the short run, mathematical and economic analysis based on the provided demand and cost functions is essential. The approach involves leveraging fundamental microeconomic principles, including profit maximization where marginal revenue equals marginal cost, and revenue maximization where marginal revenue equals zero. This analysis elucidates the optimal pricing and output decisions for Katrina’s Candies under the stipulated market conditions.

Profit Maximization in the Short Run

In the short run, profit maximization occurs where marginal revenue (MR) equals marginal cost (MC). Given the functions:

  • Marginal Revenue: MR = 50 - 0.02Q
  • Marginal Cost: MC = 20 + 0.01333Q

Setting MR equal to MC:

50 - 0.02Q = 20 + 0.01333Q

Solving for Q:

50 - 20 = 0.02Q + 0.01333Q

30 = 0.03333Q

Q = 30 / 0.03333 ≈ 900

Thus, Katrina’s Candies should produce approximately 900 kg to maximize profits.

Next, to find the optimal price, substitute Q into the demand function:

P = 50 - 0.01Q = 50 - 0.01 × 900 = 50 - 9 = 41

Therefore, the profit-maximizing price is approximately $41 per kilogram.

To estimate the maximum profit, calculate total revenue (TR) and total cost (TC) at Q = 900:

  • TR = P × Q = 41 × 900 = $36,900
  • Variable Cost: VC = 20Q + 0.006665Q² = 20(900) + 0.006665(900²) = 18,000 + 0.006665(810,000) ≈ 18,000 + 5,399 ≈ 23,399
  • Total Cost: TC = FC + VC = 5,000 + 23,399 = $28,399

Maximum profit = TR - TC = $36,900 - $28,399 ≈ $8,501.

Revenue Maximization in the Short Run

Revenue maximization occurs where marginal revenue (MR) equals zero. From the MR function:

MR = 50 - 0.02Q

Set MR to zero:

0 = 50 - 0.02Q

0.02Q = 50

Q = 50 / 0.02 = 2,500

At Q = 2,500, the corresponding price is:

P = 50 - 0.01Q = 50 - 0.01 × 2,500 = 50 - 25 = $25

Total revenue at Q = 2,500:

TR = P × Q = 25 × 2,500 = $62,500

Cost calculations:

  • VC = 20(2,500) + 0.006665(2,500²) = 50,000 + 0.006665(6,250,000) ≈ 50,000 + 41,656 ≈ 91,656
  • TC = 5,000 + 91,656 = $96,656

Profit at this quantity would be:

Profit = TR - TC = $62,500 - $96,656 ≈ -$34,156

This indicates revenue maximization leads to a high output level but with a significant loss due to high costs. Nonetheless, for revenue maximization, the optimal price is roughly $25, and the output level approximately 2,500 kg.

Conclusion

In summary, Katrina’s Candies in a monopolistically competitive market should produce around 900 kg and charge approximately $41 per kilogram to maximize short-term profit, resulting in an estimated profit of about $8,501. For revenue maximization, a higher output of approximately 2,500 kg at a lower price of $25 leads to the highest possible revenue, although with a notable loss due to costs. These calculations exemplify the crucial trade-offs between profit and revenue maximization in different strategic scenarios within perfect competition and monopolistic competition frameworks.

References

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