Question

For a profit-maximizing firm that sells its goods at a price of $40 each and has a profit of $10, what is the production level that maximizes profit when the price is $40, and how can you determine the marginal cost elasticity of demand at this price?

Answer 1

To determine the production level that maximizes profit, set marginal cost equal to marginal revenue. The profit-maximizing level of production is the quantity at which this equality holds true. In this case, the quantity that maximizes profit is 30.

Step-by-step explanation:

To determine the production level that maximizes profit, we can use the concept of marginal cost and marginal revenue. The profit-maximizing level of production is the level at which marginal cost equals marginal revenue. In this case, the profit is $10 and the price is $40. So, we can calculate the quantity that maximizes profit by setting the marginal cost equal to the price:

Marginal Cost = Marginal Revenue

Let's assume the quantity that maximizes profit is represented by x. The marginal cost is the change in total cost divided by the change in quantity, and the marginal revenue is the change in total revenue divided by the change in quantity.

So, the equation becomes:

Change in Total Cost / Change in Quantity = Change in Total Revenue / Change in Quantity

We know that the profit is $10, so the change in total revenue is $10. The change in quantity is also 1, since we are considering a single unit.

Therefore:

Change in Total Cost / 1 = $10 / 1

Change in Total Cost = $10

Since the profit is $10 and the price is $40, the quantity that maximizes profit is calculated by subtracting the profit from the price:

Quantity = Price - Profit

Quantity = $40 - $10

Quantity = 30