Perfect Competition and costs of production question The table below shows the marginal cost of production for a firm that is in an industry that is perfect competition. The market price of the product is $300. Use this information to answer the questions below.
$$quantity \quad marginal \ cost$$
$$1 \quad 270$$
$$2 \quad 210$$
$$3 \quad 180$$
$$4 \quad 240$$
$$5 \quad 285$$
$$6 \quad 315$$
$$7 \quad 345$$
$$8 \quad 375$$

Suppose the firm’s total fixed costs are $200.
a. What quantity does the firm produce in the short run to maximize profits?
b. What are the firm’s profits in the short run?
c. Does the firm stay in business in the long run? Why?
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Remember that a firm's profit is revenue minus costs, where costs can be fixed (200) or variable (manipulation of the marginal costs).

$$\Pi(q) = pq - c_f - c(q)$$

where $p$ is price, $c_f$ is fixed costs, and $c(q)$ is the cost with respect to $q$. We don't necessarily need to expression the variable costs as a function in this case.

So using the information we have, we know that for producing one unit of the good, our profits are:

$$\Pi(1) = 300 \cdot 1 - 200 - 270 = -170$$

For two goods, we have

$$\Pi(2) = 300 \cdot 2 - 200 - (270+210) = -80$$

And so on...

So you do this calculation for all the quantities and you see which one maximizes profits. That will also allow you to answer part b. As for part c, you have to see if there is a way for profits to be above 0 for some quantity produced.