# Understanding the elasticity of demand for a monopoly

Question: Your are working for a firm that is a monopoly. It is producing using technology that exhibits obvious decreasing returns to scale. After working with them for a while, a co-worker makes a mistake and accidentally increases the price per unit from \$10 to$11 for a week. You notice that the quantity sold drops by 5%. Management asks you to think about whether any strategic implications can be drawn from this episode. What do you write in your memo in response?

Answer: Quantity decreases by 5% while price increased by 10%, so total revenue increases. Since there are no economies of scale, cost decreases as you sell less and does total profit rises. Management should then raise the price.

I would like to clarify certain things about this answer. Intuitively I understand that if the percent increase in price is greater than the percent decrease in quantity then the firm is making profit. This, however, is not parallel with my understanding of elasticity. We know that a monopolist operates on the elastic portion of demand curve i.e. $|e|>1$ since this is where revenue is positive. Using this methodology for the question above, we should observe an $|e| > 1$. However this is not what we see, rather it is $|e|=|\frac{.05}{.10}|=|0.5|<1$. How come these two explanations are not parallel?

From the sounds of the question, the firm isn't operating at optimal efficiency. As you note, this firm is not on the elastic portion of the demand curve because $|e|=|\frac{.05}{.10}|=|0.5|<1$.