# Assume a startup healthcare company faces the following weekly demand and short-run cost...

## Question:

Assume a startup healthcare company faces the following weekly demand and short-run cost functions.

{eq}VC = 20Q + 0.015Q^2\\ MC = 20 + 0.03Q\\ FC = $12,000\\ P = 75 - 0.04Q\\ MR = 75 - 0.08Q {/eq}

where price is in $ and {eq}Q {/eq} is the number of patients per week.

Algebraically, determine the price the company should charge in order for the company to maximize profit in the short run. Determine the quantity that would be produced at this price and the maximum profit possible.

## Profit Maximization:

To maximize profits, any individual firm increases its sales up to the point where the marginal revenue of the last unit produced is equal to the cost of producing it. Thus, at the maximum profit, {eq}MR=MC. {/eq}

## Answer and Explanation: 1

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To maximize profits, the firm will set {eq}MR=MC {/eq}.

The marginal revenue for the firm is:

$$\begin{align} MR=75-0.08Q \end{align} $$

And...

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