Answer the question on the basis of the following information for a pure monopolist: $\begin{array}{ccc}
\begin{array}{ccc}
\
\text { Output } & & \text { Total Cost } \
\hline
0 & & \$ 250 \
1 & & 260 \
2 & & 290 \
3 & & 350 \
4 & & 480 \
5 & & 700
\end{array}
\begin{array}{l}
\text { Product }\
\begin{array}{c}
\text { Price } \
\hline \$ 500 \
300 \
250 \
200 \
150 \
100
\end{array}
\end{array}
\end{array}$ If the given profit-maximizing monopolist is able to price discriminate,charging each customer the price associated with each given level of output,how much profit will the firm earn?

Question

Quizplus · Accepted Answer

To calculate the profit when the monopolist is able to price discriminate, we need to calculate the profit for each level of output and sum them up. Profit is calculated as (Price - Average Cost) * Quantity. However, in price discrimination, the monopolist charges each unit at the maximum price that each consumer is willing to pay, so we calculate profit for each unit as (Price - Marginal Cost).1. For the first unit: Price = $500, Cost = $260, Profit = $500 - $260 = $2402. For the second unit: Price = $300, Cost to produce 2 units = $290, Cost to produce 1 unit = $260, Marginal Cost for 2nd unit = $290 - $260 = $30, Profit = $300 - $30 = $2703. For the third unit: Price = $250, Cost to produce 3 units = $350, Cost to produce 2 units = $290, Marginal Cost for 3rd unit = $350 - $290 = $60, Profit = $250 - $60 = $1904. For the fourth unit: Price = $200, Cost to produce 4 units = $480, Cost to produce 3 units = $350, Marginal Cost for 4th unit = $480 - $350 = $130, Profit = $200 - $130 = $705. For the fifth unit: Price = $150, Cost to produce 5 units = $700, Cost to produce 4 units = $480, Marginal Cost for 5th unit = $700 - $480 = $220, Profit = $150 - $220 = -$70 (a loss, so this unit wouldn't be sold under price discrimination)Summing up the profits: $240 + $270 + $190 + $70 = $770However, we must also consider the initial total cost at zero output, which is a fixed cost of $250. Since the question asks for the profit beyond the initial total cost, we subtract this fixed cost from the total revenue calculated:Total profit = $770 - $250 = $520It appears there was a mistake in my calculation as none of the provided options match the recalculated total profit. Let's correct the approach by considering the total revenue and total cost directly for each unit sold, as the initial calculation did not accurately follow the price discrimination profit calculation method.1. For the first unit: Revenue = $500, Cost = $260, Profit = $500 - $260 = $2402. For the second unit: Revenue = $300, Additional Cost = $290 - $260 = $30, Additional Profit = $300 - $30 = $2703. For the third unit: Revenue = $250, Additional Cost = $350 - $290 = $60, Additional Profit = $250 - $60 = $1904. For the fourth unit: Revenue = $200, Additional Cost = $480 - $350 = $130, Additional Profit = $200 - $130 = $705. For the fifth unit: Revenue = $150, Additional Cost = $700 - $480 = $220, Additional Profit = $150 - $220 = -$70Correctly summing the profits without the incorrect subtraction of fixed costs and excluding the loss-making fifth unit, we get:Total Profit = $240 + $270 + $190 + $70 = $770Given the mistake in the recalculated total profit and the options provided, it seems there was an error in my explanation regarding the correct option based on the recalculated profit. The correct approach to find the profit when price discriminating is to calculate the total revenue from selling each unit at its respective price and then subtract the total cost from this total revenue. Given the misunderstanding in the calculation process and the options provided (A) $120, (B) $250, (C) $300, (D) $420, it seems there was a mistake in my initial calculation and explanation. Without the correct calculations aligning with the options, the correct answer cannot be determined from the provided explanation. The initial premise to calculate profit based on price discrimination was correct, but the execution and final summation were flawed, leading to confusion.

Answer the Question on the Basis of the Following Information