I am on the chapter for monoplies.
I need to calculate the total cost for the following question. I am not quite clear if I am to use the $2 million that was paid to author to write the book to calculate the total cost, since the question is stating that the marginal cost has been a constant $10 per book?
Question:
A publisher faces the following demand schedule for the next novel of one of its popular authors:
Price Quantity Demanded
$100-----------0
$90---------100,000
$80---------200,000
%70---------300,000
$60---------400,000
$50---------500,000
$40---------600,000
$30---------700,000
$20---------800,000
$10---------900,000
$0--------1,000,000
The author is paid $2 million to wirte the book, and the marginal cost of publishing the book is a constant $10 per book
Compute total revenue, total cost, and profit at each quantity.
The $2M paid to the author, in this example problem, is a fixed cost. Let Q be quantity, P be price. Then:
TR = P*Q
TC = 10.*Q + 2,000,000
Profit = TR-TC
I am puzzled by the use of 'marginal cost' as it is usually defined as the change in total cost that arises when the quantity produced changes by one unit. (It could be here the step change between the bands?) I would have thought that the marginal cost would have been a small value for a book.
I would think you would need to use the money paid to the author as this will be an out going against the project.
The function for marginal cost is usually such that the total cost is a 'U' shape curve so that at low volumes the overall cost decreases as the number of items increases and then increases at much higher volumes.
Post your answer (you will need to use a spread sheet) and we will take a look.
Thank you for your response.
Do you know the best way I could post a spread sheet on Jishka for you to review?
Dr Russ.
The marginal cost for a book in this problem is given at $10 per book. Rather high in today's publishing world, but its a nice round number. You are correct, marginal costs are generally not flat. But in this learning example, they are flat. Which means average variable cost=marginal cost. BTW, the U shape curve you refer is average costs, not total costs.
G:
I know of now easy way of posting a spreadsheet or pasting spreadsheet values on Jishka.
To calculate the total cost, total revenue, and profit at each quantity, you'll need to understand the concepts of marginal cost, total cost, total revenue, and profit.
Total Cost (TC) refers to the sum of all costs incurred in the production of a given quantity of output. In this case, the marginal cost is given as a constant $10 per book. However, it does not explicitly state whether this includes the author's payment. So, we need to clarify whether the $2 million payment should be included as part of the total cost or if it is a separate fixed cost.
Total Revenue (TR) is the total income generated from sales of a given quantity of output. It is calculated by multiplying the quantity sold (Q) by the price (P).
Profit (π) is the difference between total revenue (TR) and total cost (TC), and it represents the financial gain from producing and selling a given quantity of output.
To compute the total cost, total revenue, and profit at each quantity, follow these steps:
1. Determine the quantity demanded (Q) for each price:
- At $100 price, Q = 0
- At $90 price, Q = 100,000
- At $80 price, Q = 200,000
- And so on...
2. Calculate the total revenue by multiplying the quantity demanded (Q) by the corresponding price (P) at each quantity:
- Total Revenue (TR) = Q * P
3. Determine the total cost for each quantity, including any relevant costs:
- The marginal cost is given as $10 per book, but it does not specify whether the author's payment is included in this cost. If it is not included, you need to subtract it separately, as it is a fixed cost.
- If the author's payment of $2 million is included, you can calculate the total cost using the marginal cost, which is $10 per book multiplied by the quantity demanded (Q) at each price point.
4. Compute the profit at each quantity by subtracting the total cost (TC) from the total revenue (TR).
- Profit (π) = TR - TC
By following these steps, you can calculate the total cost, total revenue, and profit at each quantity for this monopolistic case study.