Profit Maximization Analysis for a Restaurant

How can a restaurant determine its profit-maximizing level of output?

Given the daily demand function of p=32-0.2q, marginal cost function mc=0.4q, and average cost function atc=300+0.2q, how can the firm determine its profit?

Calculating Profit-Maximizing Level

To determine the profit-maximizing level of output, the restaurant needs to find the quantity at which marginal revenue (MR) equals marginal cost (MC). This intersection point will indicate the optimal level of production for maximizing profit.

In the given scenario, the restaurant should produce 40 units to maximize profit. At this quantity, the total revenue is $640, and the total cost is $580, resulting in a profit of $60.

By substituting q=40 into the demand function p=32-0.2q, the price per unit is calculated as $16. The total revenue (TR) is then determined by multiplying the price per unit by the quantity produced.

The total cost (TC) consists of fixed costs and variable costs, which can be calculated using the given average cost function. Subtracting total cost from total revenue gives the firm's profit.

Therefore, to maximize profit, the restaurant should produce 40 units, resulting in a profit of $60.