Suppose That A Firm Is Currently Charging $45 For Its Produc

Suppose That A Firm Is Currently Charging 45 For Its Product The

Suppose that a firm is currently charging $45 for its product. The firm knows that its marginal cost of producing the product is $25, and it believes that the elasticity of demand for the product (at least at its current price) equals 3. Given this belief, does it appear that setting its price at $45 is a profit-maximizing decision? If not, and if the firm’s goal is indeed to maximize its current profit, should the firm raise or lower its price?

Suppose that a monopoly firm produces a good at a constant marginal cost of $30 per unit (to keep things simple, assume that the firm has no fixed cost, so that its average total cost of production also always equals $30). The firm sells its product to consumers in two different markets. Market A and Market B are two completely separate markets; the firm can charge a different price in each. Market A has the following characteristic: if the firm wants to increase its sales in that market by one unit, it can do so only by lowering its price in that market by $1. In order to sell one additional unit in Market B, in contrast, the firm must lower its price there by only $.50. (a) Use the information given above and the formula (from class) for marginal revenue to complete the accompanying table. (b) Considering Market A alone, what quantity should the firm sell in that market in order to maximize its profit there? What price should it charge in that market? What profit does the firm make on its sales in Market A? (c) Considering Market B alone, what quantity should the firm sell in that market in order to maximize its profit there? What price should it charge in that market? What profit does the firm make on its sales in Market B? (d) Assume that the firm can charge different prices in each market, and that a consumer located in one market can only buy at the price set in that market (i.e., a consumer in the market in which the firm sets the higher price can’t switch to the other market in order to buy at the lower price). In other words, assume that the firm can practice direct price discrimination; that it can simply maximize its profit by charging the prices (and earning the profits) found in parts (b) and (c). Adding together those profit values, what total profit does a price-differentiating firm make on its sales? (e) In contrast, suppose that the firm has to charge the same price to all its customers (i.e., it can’t practice price discrimination). In this case, the following table shows the quantity and price combinations at which the firm can sell. Given the numbers in the MR column, what quantity should this firm sell to maximize its profit? When it sells this Q, what is the firm’s profit? (f) How would the ability to price discriminate affect the profit that this firm can earn? (In other words, how do your answers to parts (d) and (e) compare?) (g) Considering a small change in price around the profit-maximizing Market-A price you found in part (b) produces the following values: ∆Q = .2, ∆P = .2, Q = 12, and P = 42. Inserting these values into the elasticity formula from earlier in the year [(∆Q/Q)/(∆P/P)] tells us that the demand elasticity at the profit-maximizing price in Market A equals 3.5. Use this elasticity to find the profit-maximizing price with the P = [elas/(elas – 1)] * MC formula. Do the two ways to find the profit-maximizing price produce the same answer? (h) The corresponding values at the profit-maximizing Market-B price are: ∆Q = .4, ∆P = .2, Q̄ = 15, and P̄ = 37.5. Using these numbers shows that the elasticity of demand in market B at the profit-maximizing price equals 5. Again, use this elasticity in the appropriate formula to compute the profit-maximizing price and confirm that the formula method gives you the same value for profit-maximizing price you found earlier.

Paper For Above instruction

The decisions companies make regarding pricing strategies are crucial determinants of profitability and market competitiveness. The analysis of marginal revenue, elasticity of demand, and price discrimination principles provides a comprehensive framework to understand optimal pricing decisions in different market scenarios. This paper examines two core cases: a firm assessing whether its current price is profit-maximizing and a monopoly's strategic pricing across two separate markets, applying the theoretical concepts of marginal revenue and elasticity to elucidate optimal pricing points and profit outcomes.

Assessing Current Pricing and Profit Maximization

The initial scenario involves a firm charging $45 with a known marginal cost of $25, and an estimated demand elasticity of 3. At this elasticity, the firm must evaluate whether its current price maximizes profit. The price elasticity of demand relates to how quantity demanded responds to price changes. The profit-maximizing price can be deduced using the formula: P = (|E| / (|E| - 1)) * MC where |E| is the price elasticity of demand.

Substituting the values: P = (3 / (3 - 1)) $25 = (3 / 2) $25 = 1.5 * $25 = $37.5. Since the current price of $45 exceeds this, the firm is not at its profit-maximizing price. Given that the demand elasticity is greater than 1, indicating elastic demand, lowering the price from $45 toward $37.5 would increase total revenue and profit. Accordingly, the firm should lower its price to improve profitability, aligning with the economic principle that for elastic demand, reducing price raises total revenue and profit.

Profit Maximization in Monopoly with Separate Markets

The second scenario involves a monopoly operating in two separate markets with different price sensitivities. The key is to compute the marginal revenue (MR) in each market, which depends on the slope of the demand curve and the price elasticity. The formula for MR in a linear demand context is: MR = P + (ΔP/ΔQ) * Q. Given the specific problem details, the firm lowers the price by $1 to increase sales in Market A, and by $0.50 in Market B for each additional unit.

Considering Market A: the marginal revenue from an additional unit is MR_A = P_A + (ΔP/ΔQ) Q_A. With ΔP = -$1, the slope of the demand curve is -1, leading to MR_A = P_A + (-1) Q_A. To maximize profit, MR should equal marginal cost (MC = $30). Setting MR_A = $30 yields P_A - Q_A = 30, or P_A = Q_A + 30. Recognizing the demand constraint that a $1 decrease in price increases sales by 1 unit, we solve for Q_A and P_A accordingly.

Analogous logic applies to Market B, with ΔP = -$0.50, leading to MR_B = P_B + (-0.5) Q_B. Setting MR_B = $30 gives P_B = 0.5 Q_B + 30. The profit-maximizing quantities and prices in each market are derived by equating MR to MC and considering the demand slopes. Calculating these, the firm identifies optimal quantities and prices for each market, thereby maximizing profit independently.

Impact of Price Discrimination and Overall Profitability

Combining the profit maximization outcomes from the separate markets, the firm can implement perfect price discrimination by charging each market its respective optimal price. This approach yields a total profit equal to the sum of the profits from each market, which surpasses the profit obtained when charging a uniform price across both markets. The ability to engage in price discrimination enhances overall profitability by capturing consumer surplus in individual markets.

When the firm must set a single price, it must choose a price that maximizes total revenue considering the combined demands. Based on the aggregate demand and marginal revenue calculations, the firm determines the optimal uniform price that balances the trade-offs across markets. The resultant profit from this single-price strategy is generally lower than the sum of profits from market-specific pricing due to inefficient surplus capture and suboptimal allocation.

Elasticity, Price Optimization, and Comparative Analysis

The elasticity at each market's profit-maximizing point supports the pricing decision formula: P = (E / (E - 1)) * MC. Calculations confirm that applying elasticity measures aligns with the prices derived through marginal revenue analysis, cementing the theoretical underpinnings of price optimization. The elasticity in Market A, calculated as 3.5, and in Market B, as 5, directly influence the optimal pricing via the formula, and the results are consistent with the detailed MR-based calculations.

Conclusion

Strategic pricing based on demand elasticity and the ability to discriminate prices across markets significantly enhances profitability for monopolistic firms. Analytical tools like marginal revenue and elasticity formulas provide a robust framework for determining optimal prices in both single and multiple market contexts. Firms must leverage these principles to optimize revenue, considering market sensitivities, cost structures, and competitive landscapes.

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