This question examines the pure monopoly market for silly sprockets. You will use a market demand curve to identify the maximum willingness to pay by consumers for different quantities of silly sprockets, the total revenue associated with selling a particular quantity, and the marginal revenue earned from each unit. Additionally, you will use the marginal cost of producing a silly sprocket to determine how many silly sprockets a monopolist should produce and sell.
Silly Sprockets are produced and sold by a single firm, Sally's Silly Sprockets. The monopolist faces a market demand characterized by the function:
P = 4 - ½Q
where Q is the number of silly sprockets that the monopolist produces and sells, and P represents consumers' maximum willingness to pay for a particular quantity. The table below will help you identify and organize different relationships between quantity, price, total revenue, and marginal revenue.
Quantity
(widgets)
Price
(dollars)Total Revenue
(dollars)Marginal Revenue
(dollars)
0-----
1$3.50
2
3$7.50
4$2.00
5-$0.50
6
Task 1: In the table above, identify consumers' maximum willingness to pay for each quantity of sprockets and fill in the blank cells in the "Price" column. You can find these values by plugging different quantities into the demand function above.
Task 2: In the table above, identify the total revenue and marginal revenue that Sally's Silly Sprockets earns when it produces and sells each quantity of sprockets and fill in the blank cells in the "Total Revenue" and "Marginal Revenue" columns.
Task 3: What quantity of sprockets maximizes Sally's total revenue?
Task 4: Suppose that the marginal cost of producing and selling a sprocket is $2.50. What quantity of sprockets maximizes Sally's profits? What price should Sally charge to maximize her profits?