Anyone willing to help with an economics question?

Suppose you own a firm that sells its output in a perfectly competitive market, and you seek to maximize profit. Given a market wage of $450 per week, you choose not to hire a 10th worker when output price is $12, since the marginal revenue product of a 10th worker is only $360. If the output price rose sufficiently, you would be willing to hire a 10th worker. What is the lowest price for your output at which you would be willing to hire a 10th worker?

Answer:
The firm maximizes it profit where its marginal cost equals its marginal revenue. The marginal revenue of the 10th worker equals 360 which is equal to the change in output times price. At price 12 the output change is 30 (Since 360=12*output change, this change is 360/12). We need to equalize the marginal revenue to 450 (marginal cost) and this is possible only by changing the price. We need to find p from the following equation; p*30=450 So p=450/30=15
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