Using A Spreadsheet Like The Following: Entering Formulas

Using A Spreadsheet Like The Following Entering Formulas For The Tota

Using a spreadsheet like the following, entering formulas for the total revenue and consumer's surplus, for the total revenue and consumers surplus, and given the following demand curve of a consumer for a monopolist's product Q=14-2P (a) find the total revenue of the monopolist when it sells 6 units of the commodity without practicing any form of price discrimination. What is the value of the consumers surplus? (b)/what would be the total revenue of the monopolist if it practiced first-degree price discrimination?How much would the consumers surplus be in this case?(c)What if the monopolist charged P=$5.5o for the first 3 units-what type of price discrimination is this?

Paper For Above instruction

The following analysis explores the calculation of total revenue and consumer surplus for a monopolist under different pricing strategies, using a given demand curve Q = 14 - 2P. We examine scenarios where the monopolist sells a specified quantity without price discrimination, employs first-degree price discrimination, and charges a specific price for limited units, identifying the type of discrimination involved in each case.

Part (a): Total Revenue and Consumer Surplus Without Price Discrimination at 6 Units

The demand curve provided is Q = 14 - 2P, where Q is quantity and P is price. To analyze the scenario where the monopolist sells 6 units without price discrimination, first, we need to determine the market price corresponding to Q=6. Rearranging the demand equation: 6 = 14 - 2P, which simplifies to 2P = 14 - 6, so P = (14 - 6)/2 = 4.

Thus, the monopolist can sell 6 units at a price of P = $4. The total revenue (TR) is calculated as TR = Price × Quantity, which equals TR = 4 × 6 = $24.

Consumer surplus (CS) is the difference between what consumers are willing to pay and what they actually pay for the units purchased. The maximum price consumers are willing to pay for the first unit, derived from the demand curve, occurs at Q=0: P = (14 - Q)/2. At Q=0, P = 14/2 = $7. For 6 units, consumer surplus is represented by the area of a triangle, with height = maximum willingness to pay minus actual price = 7 - 4 = $3, and base = 6 units.

Therefore, consumer surplus = 0.5 × base × height = 0.5 × 6 × 3 = $9.

Part (b): Total Revenue and Consumer Surplus with First-Degree Price Discrimination

First-degree price discrimination involves charging each consumer their maximum willingness to pay for each unit. In a theoretical sense, the monopolist captures all consumer surplus as profit, selling quantities up to the point where the price equals the marginal cost (assuming zero for simplicity). The total revenue under perfect price discrimination is the total area under the demand curve from Q=0 to Q=14.

To find total revenue in this case, determine the maximum quantity where demand is positive. When P=0, Q=14, which indicates the monopolist can sell 14 units if it charges a price of $0. Each unit is sold at its maximum willingness to pay, which decreases linearly from $14 at Q=0 to $0 at Q=14.

Total revenue (TR) is the integral of the demand curve from Q=0 to Q=14. The demand curve P = (14 - Q)/2 can be rewritten as Q = 14 - 2P, or P = (14 - Q)/2. The total revenue is the area under the demand curve: TR = integral of P with respect to Q from 0 to 14.

Calculating directly: TR = ∫₀¹⁴ [(14 - Q)/2] dQ = 0.5 × ∫₀¹⁴ (14 - Q) dQ = 0.5 [14Q - 0.5Q²] evaluated from 0 to 14.

At Q=14: 14×14 - 0.5×14² = 196 - 0.5×196 = 196 - 98 = 98. Multiplying by 0.5 gives TR = 0.5 × 98 = $49.

Consumer surplus is eliminated in perfect price discrimination because the monopolist captures it all as profit, leading to zero consumer surplus.

Part (c): Charging P = $5.50 for the First 3 Units and Its Type of Discrimination

In this scenario, the monopolist charges a fixed price of $5.50 for the first three units. To analyze this, determine how many units the consumers are willing to buy at this price using the demand curve: Q = 14 - 2P.

At P = $5.50, the quantity demanded is Q = 14 - 2(5.50) = 14 - 11 = 3 units. The monopolist charges $5.50 for these units, which corresponds exactly to the quantity demanded at that price point due to the demand curve.

However, since the price is uniform for these units and only applies to the first three units, the monopolist is practicing third-degree price discrimination if different prices are charged to different consumer groups, or block pricing if the same price is charged for a specific quantity. In this specific case, charging the same price for a set quantity doesn't precisely fit classical price discrimination types but can be viewed as a block pricing strategy, which is a subset of third-degree discrimination.

Alternatively, if the price varied across amounts purchased (e.g., lower for additional units), that would be second-degree discrimination. Since the scenario involves a fixed price for a certain quantity segment, it reflects a form of block or segment pricing within third-degree price discrimination.

Conclusion

In summary, the analysis demonstrates how total revenue and consumer surplus vary under different pricing strategies, emphasizing the effects of market power, price discrimination, and consumer welfare. While selling 6 units at a uniform price yields a specific revenue and consumer surplus, perfect price discrimination maximizes total revenue at the cost of consumer surplus. The fixed pricing for the initial units exemplifies segmented pricing strategies, with implications for market efficiency and consumer well-being.

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