Chapter 112: Ajax Cleaning Product Is A Medium-Sized Firm Op

Chapter 112 Ajax Cleaning Product Is A Medium Sized Firm Operating In

Chapter 112 Ajax Cleaning Product Is A Medium Sized Firm Operating In

Chapter 11 2. Ajax Cleaning product is a medium sized firm operating in an industry dominated by one large firm. Title: King Ajax produces a multithreaded tunnel wall scrubber that is similar to a model produced by Tile King. Ajax decides to charge the same price as Tile King to avoid the possibility of a price war. The price charged by Tile King is $20,000. Ajax has the following short-run cost curve: TC= 800,000-5,000Q + 100Q².

(A) Compute the marginal cost curve for Ajax.

(B) Given Ajax's pricing strategy, what is the marginal revenue function for Ajax?

4. Unique Creations holds a monopoly position in the production and sale of magnometers. The cost function facing Unique is estimated to be TC= 100,000+20Q.

a. What is the marginal cost for Unique?

b. If the price elasticity of demand for Unique is currently -1.5, what price should Unique charge?

c. What is the marginal revenue at the price computed in part (b)?

6. Wyandotte Chemical Company sells various chemicals to the automobile industry. Wyandotte currently sells 30,000 gallons of polyol per year at an average price of $15 per gallon. Fixed costs of manufacturing polyol are $90,000 per year and total variable costs equal $180,000. The operation research department has estimated that a 15 percent increase in output would not affect fixed costs but would reduce average variable costs by 60 cents per gallon. The marketing department has estimated the arc elasticity of demand for polyol to be -2.0.

a. How much would Wyandotte have to reduce the price of polyol to achieve a 15 percent increase in the quantity sold?

b. Evaluate the impact of such a price cut on (i) total revenue, (ii) total costs, and (iii) total profits.

Paper For Above instruction

The analysis of firm behavior in imperfect markets such as monopolies, duopolies, and firms operating under strategic pricing and cost conditions reveals key insights into price-setting, output decisions, and profit maximization. This essay delves into several market scenarios, examining the cost structures, revenue functions, and strategic behaviors that influence business outcomes in various competitive environments.

AJAX Cleaning Product in a Monopolistic Industry

Ajax Cleaning Product operates within an industry dominated by a major player, Tile King. To maintain competitiveness and avoid destructive price wars, Ajax adopts a strategic pricing approach, matching Tile King’s price of $20,000. The firm's short-run total cost (TC) function is given by TC= 800,000 - 5,000Q + 100Q², where Q indicates the quantity produced.

Marginal Cost (MC) Computation: The marginal cost is derived by differentiating the total cost function with respect to output (Q). Thus, MC = d(TC)/dQ = -5,000 + 200Q. This indicates that the marginal cost increases linearly with output after a certain level, which is typical for quadratic cost functions.

Marginal Revenue (MR) Function: Since Ajax sets its price equal to Tile King’s price ($20,000), and assuming the demand is responsive to price changes, the MR function can be derived from the demand curve. If the demand function is inferred from the price and the competitive setting, MR typically has the same intercept as the demand curve but twice the slope. For simplicity, if the demand is elastic around the price point, MR can be described generally as MR = P(1 + 1/ε), where ε is the price elasticity of demand (

Unique Creations Monopolistic Pricing Strategy

As a monopoly, Unique Creations's total cost function is TC= 100,000 + 20Q. The marginal cost (MC) is obtained by differentiating TC with respect to Q, resulting in MC=20. This constant marginal cost informs pricing decisions under monopoly conditions.

If the price elasticity of demand (ε) is -1.5, the profit-maximizing price (P) can be found using the Lerner index formula, which states that (P - MC)/P = -1/ε. Substituting the known values, the optimal P is calculated as P = MC (1 - 1/ε). Hence, P = 20 (1 - 1/(-1.5)) = 20 (1 + 2/3) = 20 (5/3) ≈ $33.33.

The marginal revenue (MR) at this price can be derived as MR = P (1 + 1/ε). With ε = -1.5, MR = 33.33 (1 + 1/(-1.5)) = 33.33 (1 - 2/3) = 33.33 1/3 ≈ $11.11. This indicates the revenue's sensitivity to quantity changes at this price point.

Wyandotte Chemical's Pricing and Demand Response

Wyandotte sells 30,000 gallons of polyol at $15 per gallon. The fixed costs are $90,000, while total variable costs are $180,000, implying an average variable cost of $6 per gallon. An anticipated 15% increase in output, with no change in fixed costs, would involve additional variable costs. The price elasticity of demand is -2.0, suggesting significant responsiveness to price adjustments.

Price Reduction for Increased Sales: To increase sales by 15%, Wyandotte’s current demand estimate is Q = 30,000, and the target quantity becomes Q' = 34,500. The change in quantity (ΔQ) is 4,500 units. Using the elasticity formula, ΔQ/Q = ε ΔP/P, rearranged to ΔP/P = ΔQ/Q divided by ε, yields ΔP/P = 0.15 / -2.0 = -0.075, or a 7.5% reduction in price. Therefore, the new price should be approximately $15 (1 - 0.075) = $13.88.

Impact on Revenue, Costs, and Profits: The reduction from $15 to approximately $13.88 per gallon would increase sales by 15%, from 30,000 to 34,500 gallons. Total revenue initially was $450,000, and after the decrease, it becomes approximately $13.88 * 34,500 ≈ $479,460. \n

Total variable costs with new production are 34,500 * $6.00 = $207,000, a modest increase from the previous $180,000. Fixed costs remain at $90,000. The total costs then are $207,000 + $90,000 = $297,000, compared to initial costs of $180,000 + $90,000 = $270,000. Profits will depend on the difference between total revenue and total costs, which suggests a potential profit increase due to higher sales volume despite lower unit price.

Conclusion

Firm strategies in competitive and monopolistic markets are driven by their cost structures, demand elasticity, and strategic objectives. Ajax's approach reflects competitive pricing in an industry with a dominant firm, requiring careful analysis of cost and revenue functions. Unique Creations’s monopoly setting demonstrates how elasticity informs optimal pricing, while Wyandotte's demand response illustrates the revenue and cost implications of price adjustments. Accurate demand estimation and understanding cost behaviors are essential for effective decision-making in various market conditions.

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