The following table indicates the prices various buyers are willing to pay for a Miata sports car:

Buyer A Maximum price $50,000
Buyer B Maximum price $40,000
Buyer C Maximum price $30,000
Buyer D Maximum price $20,000
Buyer E Maximum price $10,000

The cost of producing the cars includes $50,000 of fixed costs and a constant marginal cost of $10,000. With a Quantity between 0 and 6 cars per period.

a) graph the demand, marginal revenue, and marginal cost curves.

b) What is the profit-maximizing rate of output and price for the monopolist? How much profit does the monopolist make?

Output____________
Price_____________
Profit____________

c) If the monopolist can price-discriminate, how many cars will he sell?

d) How much profit will he make?

a) To graph the demand, marginal revenue, and marginal cost curves, we need to calculate the quantities demanded by each buyer at different price levels. Using the maximum price each buyer is willing to pay, we can determine the quantity demanded.

Buyer A: Willing to pay $50,000, so quantity demanded = 1 (Maximum price meets or exceeds the cost)
Buyer B: Willing to pay $40,000, so quantity demanded = 2
Buyer C: Willing to pay $30,000, so quantity demanded = 3
Buyer D: Willing to pay $20,000, so quantity demanded = 4
Buyer E: Willing to pay $10,000, so quantity demanded = 5

We can plot these quantities on the demand curve. The demand curve will be a downward-sloping line, indicating that as the price decreases, the quantity demanded increases.

Next, we can calculate the marginal revenue by looking at the change in revenue for each additional unit sold. Since the price remains constant for all units sold, the marginal revenue will also be constant. To calculate marginal revenue, we need to calculate the total revenue at different levels of output.

Total Revenue = Price x Quantity

Output (Q) Price Total Revenue Marginal Revenue
0 - $0 -
1 $50,000 $50,000 $50,000
2 $40,000 $80,000 $30,000
3 $30,000 $90,000 $10,000
4 $20,000 $80,000 -$10,000
5 $10,000 $50,000 -$30,000

We can plot these points on the marginal revenue curve. The marginal revenue curve will be a horizontal line at the constant level of $50,000.

Finally, we can plot the marginal cost curve. Since the marginal cost is constant at $10,000, the marginal cost curve will be a horizontal line parallel to the quantity axis.

b) To find the profit-maximizing rate of output and price for the monopolist, we need to find the quantity at which marginal revenue equals marginal cost. From the table above, we can see that the quantity at which marginal revenue equals $10,000 (marginal cost) is 4 units. Therefore, the profit-maximizing rate of output is 4 cars per period.

To find the price, we can go back to the demand curve and locate the price associated with the quantity of 4 cars. From the table above, we can see that the price for 4 cars is $20,000. Therefore, the profit-maximizing price for the monopolist is $20,000 per car.

To calculate the profit, we subtract the total cost from the total revenue. The total cost includes fixed costs and variable costs:

Total Cost = Fixed Costs + (Variable Cost per unit x Quantity)

Total Cost = $50,000 + ($10,000 x 4) = $50,000 + $40,000 = $90,000

Total Revenue = Price x Quantity = $20,000 x 4 = $80,000

Profit = Total Revenue - Total Cost = $80,000 - $90,000 = -$10,000

Therefore, the monopolist incurs a loss of $10,000.

Output: 4 cars
Price: $20,000
Profit: -$10,000

c) If the monopolist can price discriminate, they can sell different quantities at different prices to different buyers based on their maximum willingness to pay.

To determine the number of cars the monopolist will sell, they will set prices such that each buyer purchases a car up to their maximum willingness to pay. In this case, the maximum willingness to pay for each buyer is given:

Buyer A: $50,000
Buyer B: $40,000
Buyer C: $30,000
Buyer D: $20,000
Buyer E: $10,000

The monopolist will set prices such that each buyer purchases a car. Therefore, the monopolist will sell 5 cars in total, one to each buyer.

d) To calculate the profit the monopolist will make under price discrimination, we need to determine the revenue and costs.

Total Revenue = Buyer A's Price + Buyer B's Price + Buyer C's Price + Buyer D's Price + Buyer E's Price
= $50,000 + $40,000 + $30,000 + $20,000 + $10,000
= $150,000

Total Cost = Fixed Costs + (Variable Cost per unit x Quantity)
= $50,000 + ($10,000 x 5)
= $50,000 + $50,000
= $100,000

Profit = Total Revenue - Total Cost
= $150,000 - $100,000
= $50,000

Therefore, the monopolist will make a profit of $50,000 under price discrimination.

Profit: $50,000