Week 6 Discussion: Market Structures Please Respond To The F

Week 6 Discussionmarket Structuresplease Respond To The Followingfro

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.

Paper For Above instruction

The scenario presents a monopolistically competitive market where Katrina’s Candies operates, facing specific demand and cost functions. To determine the optimal pricing, quantity, and maximum profit, we need to analyze the profit maximization condition, which occurs when marginal revenue (MR) equals marginal cost (MC).

Given functions are:

  • Variable Cost (VC): 20Q + 0.006665Q²
  • Fixed Costs (FC): $5,000
  • Price (P): 50 - 0.01Q
  • Marginal Revenue (MR): 50 - 0.02Q
  • Marginal Cost (MC): 20 + 0.01333Q

The profit maximization occurs where MR = MC. Setting MR equal to MC gives:

50 - 0.02Q = 20 + 0.01333Q

Simplifying this equation to solve for Q:

50 - 20 = 0.02Q + 0.01333Q

30 = 0.03333Q

Q = 30 / 0.03333 ≈ 900 kilograms

Now, substituting Q = 900 into the demand function P = 50 - 0.01Q to find the optimal price:

P = 50 - 0.01 * 900 = 50 - 9 = $41

Next, to calculate maximum profit, we first determine total revenue (TR) and total cost (TC).

TR = P Q = $41 900 = $36,900

Variable cost at Q = 900:

VC = 20 900 + 0.006665 900² = 18,000 + 0.006665 * 810,000 = 18,000 + 5,399.85 ≈ $23,399.85

Total fixed costs are $5,000, so total costs are:

TC = VC + FC = $23,399.85 + $5,000 ≈ $28,399.85

Finally, the profit is:

Profit = TR - TC = $36,900 - $28,399.85 ≈ $8,500.15

Rounding to the nearest whole number, Katrina’s Candies should charge approximately $41 per kilogram for optimal profit, produce about 900 kilograms, and realize a maximum profit of roughly $8,500 in the short run.

References

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