The marginal cost of producing a particular item is $2.50. Suppose a consumer is
ID: 1093541 • Letter: T
Question
The marginal cost of producing a particular item is $2.50. Suppose a consumer is willing to purchase one item at $10, a second unit of that item at $9, a third unit of that item at $8, and so on. This means that the consumers demand schedule looks like:
Price Quanity
$10 1
9 2
8 3
7 4
6 5
5 6
4 7
3 8
2 9
1 10
1. If the firm must set a single price and sell all of its units, what price will it select to maximize profits? What will the profit be?
2. Suppose the firm can apply a volume discount, pricing the first good at $10, pricing the second unit at $9, and pricing the third unit at $8, and so on. What is the smallest per-unit price the firm will want to offer? Assuming the volume discount ends at (or before) that price, what will the firms profit be?
Explanation / Answer
1. First we need to calculate revenue at each price which is: Revenue = Price x Quantity.
We also need to calculate Total Cost at each price. Given that MC is constant at $2.50, Average Cost is constant at $2.50 at each level of quantity. Hence: Total Cost = $2.50 x Quantity
Next we calculate Profits which is: Profits = Revenue - Total Costs. Then, select the level of quantity at which profits are maximized. This is shown in the table below.
As shown above, profits are maximized at Price = $7 and the profits at this price is $18.
2. Now, lets calculate Marginal Revenue at each quantity. Then,
MR from selling the 1st unit = $10
MR from selling the 2nd unit = $9 and so on.
Then we can add MR at each level to find Revenue. Then as before calculate Total Costs and Profit to see where profits are maximized. This is shown in the table below.
As the profits are maximized at the minimum price of $3, this is the minimum price the firm will offer to sell. The profits are equal to $32.
Price Quantity Revenue Total Costs Profits 10 1 10 2.50 7.50 9 2 18 5.00 13.00 8 3 24 7.50 16.50 7 4 28 10.00 18.00 6 5 30 12.50 17.50 5 6 30 15.00 15.00 4 7 28 17.50 10.50 3 8 24 20.00 4.00 2 9 18 22.50 -4.50 1 10 10 25.00 -15.00Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.