Suppose a firm has a constant marginal cost of$10 the current price of the product is $25, and at that price, it is estimated that the price elasticity of demand is -3.0. Is the firm charging the optimal price for the product? Demonstrate how you know.
Well, let's think about this! To determine if the firm is charging the optimal price, we need to consider the price elasticity of demand.
With a price elasticity of demand of -3.0, we know that for every 1% increase in price, the quantity demanded will decrease by 3%. Since the marginal cost is constant at $10, the firm's profit maximization point occurs where marginal cost equals marginal revenue.
To calculate the optimal price, we need to determine the quantity at which marginal revenue equals $10. Given that the price elasticity of demand is -3.0 and the current price is $25, we can calculate that the current quantity demanded is 30 units.
Now, let's find the marginal revenue. The formula for marginal revenue is price multiplied by (1 plus 1 divided by the absolute value of the price elasticity of demand). Using the current price of $25 and the elasticity of demand of -3.0, we find that the marginal revenue is $17.86.
Since the marginal cost is $10 and the marginal revenue at the current price is $17.86, it appears that the firm is charging a price higher than the optimal price.
So, it seems like the firm might want to consider reducing the price to increase its profits. But hey, what do I know? I'm just a clown bot trying to make sense of economics!
To determine whether the firm is charging the optimal price for the product, we need to consider the concept of optimal pricing using price elasticity of demand.
Price elasticity of demand measures the responsiveness or sensitivity of quantity demanded to a change in price. It is calculated by dividing the percentage change in quantity demanded by the percentage change in price.
In this case, the price elasticity of demand is stated as -3.0. This negative value indicates that the product is price elastic, meaning that a change in price will have a proportionally larger effect on the quantity demanded.
To calculate the optimal price, we need to find the point where marginal revenue equals marginal cost. Marginal revenue is the additional revenue generated from selling one extra unit, while marginal cost is the additional cost incurred to produce one extra unit.
The formula to calculate marginal revenue is:
Marginal Revenue = Price x (1 + (1 / Price Elasticity of Demand))
Let's calculate the marginal revenue:
Marginal Revenue = $25 x (1 + (1 / -3.0))
Marginal Revenue = $25 x (1 - 0.33)
Marginal Revenue = $25 x 0.67
Marginal Revenue = $16.75
Now, we compare the marginal cost and the marginal revenue. If the price is set at a level where marginal revenue is equal to marginal cost, then it is considered the optimal price.
In this case, the marginal cost is equal to $10. Since the marginal revenue is greater than the marginal cost ($16.75 > $10), the firm is generating more revenue than the cost incurred to produce each additional unit. Therefore, the firm is not charging the optimal price, as they can increase their profit by adjusting the price.
To charge the optimal price, the firm should consider lowering the price to reach the point where marginal revenue equals marginal cost. This is the price level where the firm maximizes its profit.