Author are typically paid a royality which is a fixed percentage of revenue; a common figure 10% of sales revenue. Show that the price desired by an author is always less than the price desired by a profit maximising publisher. What is the elasticity of demand at the price desired by the author?
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To show that the price desired by an author is always less than the price desired by a profit maximizing publisher, we need to consider the incentives and objectives of each party involved.
An author desires to maximize their own earnings from book sales, while a profit maximizing publisher aims to maximize their overall profit.
Let's assume that the price desired by the author is P_a, and the price desired by the profit maximizing publisher is P_p. The author's royalty is typically a fixed percentage of the revenue, often around 10% as mentioned in the question. This means that the author's earnings per unit sold are 10% of the selling price.
For an author, the earnings per unit sold can be expressed as:
Earnings_per_unit_sold_a = 0.1 * P_a
On the other hand, for a profit maximizing publisher, the total profit per unit sold can be expressed as the difference between the revenue and the cost per unit. Let's assume that the cost per unit is C. Therefore, the profit per unit sold for the publisher is:
Profit_per_unit_sold_p = (P_p - C)
Since the publisher aims to maximize profit, they will set the price P_p in such a way that the profit per unit sold is maximized, while taking into account the demand and cost factors. However, for simplicity, let's assume that the publisher sets the price such that the demand is fully met.
Now, to show that P_a < P_p, we need to compare the incentives of the author and the profit maximizing publisher. Since the author's earnings are directly tied to the selling price through the royalty percentage, it is in the author's interest to keep the price relatively low to maximize their earnings per unit sold. On the other hand, the publisher aims to maximize overall profit, which means setting a higher price if the demand allows for it.
To find the elasticity of demand at the price desired by the author (P_a), we need more information about the demand function. Elasticity of demand measures the responsiveness of demand to changes in price. It is typically calculated as the percentage change in quantity demanded divided by the percentage change in price:
Elasticity_of_demand = (% change in quantity demanded) / (% change in price)
Without specific information on the demand function, it is not possible to calculate the elasticity of demand at the price desired by the author. The elasticity of demand would vary depending on the specific demand function, market conditions, and other factors.
In summary:
- The price desired by an author (P_a) is typically lower than the price desired by a profit maximizing publisher (P_p) because the author's earnings are directly tied to the selling price through the royalty percentage.
- The elasticity of demand at the price desired by the author cannot be determined without additional information on the demand function.