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?
First, derive a marginal revenue curve (like you did in your previous post.) So,
P=50000, Q=1, TR=50000, MR=50000
P=40000, Q=2, TR=80000, MR=30000
P=30000, Q=3, TR=90000, MR=10000
and so on.
b) he makes 3 cars, charges 30,000 each, and makes 10,000 profit.
c) He makes 5 cars, charges the maximum each buyer will pay TR=150,000 ...
fdc
a) To graph the demand, marginal revenue, and marginal cost curves, we need to plot the quantities and prices for buyers A, B, C, D, and E.
Quantity Buyer A Buyer B Buyer C Buyer D Buyer E Marginal Revenue Marginal Cost
0 $0 $0 $0 $0 $0 N/A $50,000
1 $50,000 $40,000 $30,000 $20,000 $10,000 $50,000 $60,000
2 $50,000 $40,000 $30,000 $20,000 N/A $30,000 $60,000
3 $50,000 $40,000 $30,000 N/A N/A $20,000 $60,000
4 $50,000 $40,000 N/A N/A N/A $10,000 $60,000
5 $50,000 N/A N/A N/A N/A $0 $60,000
6 N/A N/A N/A N/A N/A N/A $60,000
The demand curve can be created by connecting the maximum prices for each quantity with a straight line. The marginal revenue curve is a horizontal line at the same level as the demand curve. The marginal cost curve is a horizontal line at $60,000, representing the constant marginal cost.
b) To find the profit-maximizing rate of output and price, we need to find the quantity and price at which marginal revenue equals marginal cost.
From the table, we can see that the quantity at which marginal revenue equals marginal cost is 1. Therefore, the profit-maximizing rate of output is 1 car per period.
To find the price, we can refer to the demand curve at this quantity. At a quantity of 1, the price is $50,000. Therefore, the profit-maximizing price for the monopolist is $50,000.
To calculate the profit, we need to subtract the total cost (fixed costs + variable costs) from the revenue.
Total cost = Fixed costs + (Marginal cost x Quantity)
Total cost = $50,000 + ($10,000 x 1)
Total cost = $60,000
Revenue = Price x Quantity
Revenue = $50,000 x 1
Revenue = $50,000
Profit = Revenue - Total cost
Profit = $50,000 - $60,000
Profit = -$10,000
The monopolist makes a loss of $10,000.
c) If the monopolist can price discriminate, they can sell different quantities to different buyers at different prices. The monopolist can charge each buyer the maximum price they are willing to pay.
From the table, we can see that buyer A is willing to pay $50,000, buyer B is willing to pay $40,000, buyer C is willing to pay $30,000, buyer D is willing to pay $20,000, and buyer E is willing to pay $10,000.
To determine the number of cars the monopolist will sell under price discrimination, we need to check which buyers are willing to buy at each price.
At a price of $50,000, buyer A is willing to buy 1 car.
At a price of $40,000, buyer B is willing to buy 1 car.
At a price of $30,000, buyer C is willing to buy 1 car.
At a price of $20,000, buyer D is willing to buy 1 car.
At a price of $10,000, buyer E is willing to buy 1 car.
Therefore, the monopolist will sell 1 car to each buyer, resulting in a total of 5 cars sold.
d) To calculate the profit under price discrimination, we need to sum up the revenue from each buyer and subtract the total cost.
Revenue from buyer A = Price x Quantity
Revenue from buyer A = $50,000 x 1
Revenue from buyer A = $50,000
Revenue from buyer B = Price x Quantity
Revenue from buyer B = $40,000 x 1
Revenue from buyer B = $40,000
Revenue from buyer C = Price x Quantity
Revenue from buyer C = $30,000 x 1
Revenue from buyer C = $30,000
Revenue from buyer D = Price x Quantity
Revenue from buyer D = $20,000 x 1
Revenue from buyer D = $20,000
Revenue from buyer E = Price x Quantity
Revenue from buyer E = $10,000 x 1
Revenue from buyer E = $10,000
Total revenue = Revenue from each buyer added together
Total revenue = $50,000 + $40,000 + $30,000 + $20,000 + $10,000
Total revenue = $150,000
Total cost = Fixed costs + (Marginal cost x Quantity)
Total cost = $50,000 + ($10,000 x 5)
Total cost = $100,000
Profit = Total revenue - Total cost
Profit = $150,000 - $100,000
Profit = $50,000
Therefore, the monopolist will make a profit of $50,000 under price discrimination.
a) To graph the demand, marginal revenue, and marginal cost curves, we will start by calculating the quantity demanded at different prices based on the information given.
Price Quantity Demanded
$10,000 6
$20,000 5
$30,000 4
$40,000 3
$50,000 2
Now let's plot this information on a graph with quantity on the x-axis and price on the y-axis.
The demand curve will be a downward-sloping line connecting these points: (6, $10,000), (5, $20,000), (4, $30,000), (3, $40,000), and (2, $50,000).
The marginal revenue curve will also be a downward-sloping line, but with twice the slope of the demand curve. This is because for a monopolist, the marginal revenue generated from selling an additional unit is equal to the price at which that unit is sold, plus the marginal revenue generated from all previously sold units.
The marginal cost curve will be a horizontal line at $10,000, as the marginal cost is constant regardless of the quantity produced.
b) To find the profit-maximizing rate of output and price for the monopolist, we need to compare the marginal cost and marginal revenue. The monopolist should produce where marginal cost equals marginal revenue.
In this case, the marginal cost is $10,000 for any quantity produced. From the marginal revenue curve, we can see that when the monopolist produces 2 units, the marginal revenue is $50,000. This means the monopolist should produce 2 units to maximize profit.
The corresponding price at 2 units of output is $50,000. Therefore, the profit-maximizing rate of output is 2 cars and the price is $50,000.
To calculate the profit, we need to subtract the total cost from the total revenue.
Total revenue = Price × Quantity = $50,000 × 2 = $100,000
Total cost = Fixed costs + (Marginal cost × Quantity) = $50,000 + ($10,000 × 2) = $70,000
Profit = Total revenue - Total cost = $100,000 - $70,000 = $30,000
Therefore, the monopolist makes a profit of $30,000.
c) If the monopolist can price-discriminate, it can charge different prices to different buyers based on their willingness to pay. In this case, the monopolist can sell up to the point where the price equals each buyer's maximum willingness to pay.
Based on the given table, the monopolist can sell 2 cars to Buyer A, 2 cars to Buyer B, and 2 cars to Buyer C, totaling 6 cars.
d) To calculate the profit under price discrimination, we need to find the total revenue and subtract the total cost.
Total revenue = (Price from Buyer A × Quantity sold to Buyer A) + (Price from Buyer B × Quantity sold to Buyer B) + (Price from Buyer C × Quantity sold to Buyer C)
Total revenue = ($50,000 × 2) + ($40,000 × 2) + ($30,000 × 2) = $100,000 + $80,000 + $60,000 = $240,000
Total cost remains the same as before, which is $70,000.
Profit = Total revenue - Total cost = $240,000 - $70,000 = $170,000
Therefore, the monopolist makes a profit of $170,000 under price discrimination.