Question

Suppose that the total fixed cost for a guitar manufacturer is $90. the marginal cost of the first guitar produced is $80 and decreases by $10 for the next three guitars produced. thereafter, the marginal cost increases by $10 for each successive guitar. refer to the information above to answer this question. if the manufacturer can sell her guitars for $70, how many should she produce in order to maximize her profits?

Answer 1

The guitar manufacturer should produce four guitars to maximize profits as the selling price is $70, and the marginal cost for producing the fourth guitar is $50, which is the highest quantity that can be produced before the marginal cost exceeds the selling price.

Step-by-step explanation:

The question involves calculating the profit-maximizing quantity of output for a guitar manufacturer. The fixed costs are $90, and the marginal costs change as more guitars are produced: the cost decreases for the first few units and then increases for subsequent ones. The selling price per guitar is $70. To determine the optimum production level, we should look for the point where the profit is maximized, which is where total revenue exceeds total costs by the greatest amount, but where additional units would not add to the profit.

The marginal cost of producing the first guitar is $80, which already exceeds the selling price, therefore producing the first guitar will incur a loss. Similarly, the second and third guitars have marginal costs of $70 and $60, respectively, making their production unprofitable as well. However, the fourth guitar has a marginal cost of $50, which means it could be sold for a profit of $20. After the fourth guitar, marginal costs begin to rise again, going back to $60, $70, $80, etc., which means that producing more than four guitars would not be profitable since the selling price is constant at $70.

Therefore, considering both fixed and variable costs, the guitar manufacturer should produce four guitars to maximize profits.