Chapter 112 Ajax Cleaning Product Is A Medium-Sized Firm Ope

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

Ajax Cleaning Product is a medium-sized firm operating in an industry dominated by a large competitor, Tile King. Ajax produces a tunnel wall scrubber similar to Tile King's model and chooses to price its product at the same level, $20,000, to avoid a price war. The firm's short-run total cost (TC) function is given by TC = 800,000 - 5,000Q + 100Q². The assignment requires calculating Ajax's marginal cost (MC) curve, deriving its marginal revenue (MR) function based on its pricing strategy, and analyzing the firm's pricing decisions considering the industry context.

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Understanding the dynamics of competitive pricing and cost structures in a duopolistic market is essential for firms like Ajax and Tile King operating within similar product segments. Ajax’s decision to match Tile King’s price illustrates strategic interactions that influence marginal costs, marginal revenues, and ultimately, profitability. This paper delves into the calculation of Ajax's marginal cost, the derivation of its marginal revenue, and the implications of its pricing strategy within the industry context.

Marginal Cost Calculation for Ajax

The total cost (TC) function provided for Ajax is TC = 800,000 - 5,000Q + 100Q². To determine the marginal cost (MC), which is the additional cost of producing one more unit of output, we differentiate the total cost with respect to quantity (Q). The mathematical operation involves taking the derivative of the total cost function:

MC = d(TC)/dQ = d/dQ [800,000 - 5,000Q + 100Q²] = -5,000 + 200Q

Therefore, Ajax's marginal cost curve is MC = -5,000 + 200Q. It indicates that marginal cost increases linearly with output, starting from a negative value at lower quantities (which suggests initial economies of scale before costs rise with increased production).

Deriving the Marginal Revenue Function

Given Ajax’s pricing strategy to set the price at $20,000, equivalent to Tile King’s price, the firm operates in a market where it perceives the demand curve as price-fixed at this level for competitive purposes. To determine the marginal revenue (MR), typically, the demand function must be known. However, in scenarios where perfect competition or a price-taker assumption is made at a fixed price, the MR equals the price. But assuming Ajax faces a downward-sloping demand curve, the MR function can be derived from the demand curve. Considering a linear demand function of the form:

P = a - bQ

and recognizing that the total revenue (TR) is TR = P × Q = (a - bQ)Q = aQ - bQ², the marginal revenue (MR) is the derivative of TR with respect to Q:

MR = d(TR)/dQ = a - 2bQ

Since Ajax's price is fixed at $20,000, and assuming it faces a demand curve with the same intercept and slope as Tile King, the actual derivation of MR would depend on the specific demand parameters. However, within the duopoly, the MR function typically slopes more steeply than the demand curve. Without explicit demand parameters, it suffices to recognize that Ajax’s MR would generally be less than the price at any given quantity, and its precise form depends on the underlying demand curve shape.

Implications and Strategic Considerations

Ajax's choice to price equal to Tile King’s exhibits a strategic move to maintain market share without initiating a price war—an often observed behavior in oligopolistic markets. The linear marginal cost curve suggests rising costs with increased output, which influences the firm's optimal production point. The MR function illustrates how revenue responds to changes in output, which, combined with marginal cost, determines optimal production quantities, where MR = MC. If Ajax aims to maximize profits, it must find an output level where these two curves intersect, considering the industry’s demand elasticity.

Additional Industry Context and Strategic Insights

The establishment of price parity with Tile King means Ajax’s profitability hinges on cost efficiency and output decisions rather than aggressive pricing strategies. The high fixed costs and increasing marginal costs underscore the importance of optimal output levels. Firms in such industries often resort to marginal analysis to determine the profit-maximizing output, especially under oligopolistic conditions with strategic interdependencies. Moreover, maintaining equilibrium requires considering competitors’ responses, potentially modeled via game theory or Cournot equilibrium analysis.

Conclusion

In conclusion, Ajax’s short-run cost structure and strategic pricing decision highlight fundamental concepts in industrial organization. Calculating the marginal cost as MC = -5,000 + 200Q provides insights into the costs associated with production levels. Deriving the marginal revenue, though dependent on demand specifics, emphasizes the importance of aligning MC and MR to determine optimal output. These analyses inform Ajax’s pricing and production strategies, which must balance cost efficiency with competitive positioning in a duopoly dominated by Tile King. The dynamic interplay of costs, revenues, demand elasticity, and strategic pricing ultimately shapes the firm’s profitability and market sustainability.

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