Question

Suppose that a perfectly competitive firm has the following total variable costs \((T V C)\) :$$\begin{array}{|l|l|l|l|l|l|}\hline \text { Quantity: } & \mathbf{0} & \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} \\\\\hline \text {TVC:} & \$ 0 & \$ 6 & \$ 11 & \$ 15 & \$ 18 & \$ 22 & \$ 28 \\\\\hline\end{array}$$,It also has total fixed costs \((T F C)\) of \(\$ 6 .\) If the market price is \(\$ 5\) per unit: a. Find the firm's profit-maximizing quantity using the marginal revenue and marginal cost approach. b. Check your results by re-solving the problem using the total revenue and total cost approach Is the firm earning a positive profit, suffering a loss, or breaking even?

Short answer

Given the market price of $5 per unit, the profit-maximizing quantity was found to be 4 units using both approaches. The firm is currently earning a profit.

Step-by-step solution

Calculating the marginal costs

Marginal cost (MC) is the cost of producing one more unit of a particular good. It can be calculated by the change in the total variable cost (TVC) divided by the change in quantity. Using this formula, calculate the marginal costs for each unit of production.

Applying Marginal Revenue = Marginal Cost Rule (MR = MC)

To find the firm's profit-maximizing quantity using the marginal cost and marginal revenue approach, we need to select the quantity at which marginal revenue (MR) equals marginal cost (MC). Since the firm is operating in a perfectly competitive market, the price is also the marginal revenue (MR), which is $5 in this case.

Calculating total cost (TC)

The total cost (TC) is the sum of total variable costs (TVC) and total fixed costs (TFC). Compute the total cost for each unit of quantity.

Applying Total Revenue = Total Cost Approach

Now, using the total revenue and total cost approach, the total revenue (TR) of a firm can be calculated by multiplying the market price with the quantity. Compare the total revenue with the total cost to check the results of step 2.

Determining the firm's earnings

The difference between Total Revenue (TR) and Total Cost (TC), i.e. (TR-TC), will provide us with the firm's profit or loss. If TR>TC, the firm is earning a profit. If TR<TC, the firm suffers a loss. If TR=TC, the firm breaks even. Using this information, classify the firm's current condition depending on whether it's making a profit, suffering a loss or breaking even.

Key concepts

Perfect Competition

In economics, perfect competition describes a market structure where competition is at its greatest possible level. Key features include having many firms, identical products, and no barriers to entry or exit for businesses. In this scenario, individual firms have no control over the price of their product because there are many businesses offering the same product; hence, the price is determined by the overall market supply and demand. Firms in perfect competition are price takers, as they must sell at the market price if they wish to sell their goods.

Profit Maximization

Profit maximization is the process by which a firm determines the price and output level that returns the greatest profit. The main conditions for profit maximization in perfect competition are when Marginal Revenue (MR) equals Marginal Cost (MC).
When MR is greater than MC, the firm will increase output, while if MR is less than MC, the firm will decrease output. By finding the level of production where MR equals MC, businesses are able to maximize profits because adding any more production would incur more costs than revenue.

Total Variable Cost

Total Variable Cost (TVC) is the overall expense that a firm incurs in direct proportion to the quantity of output it produces. As output increases, TVC increases at a rate based on the variable cost per unit of output. Examples of variable costs include raw materials, hourly wages, and utilities. These costs vary as the firm alters its level of production.

Total Fixed Cost

Total Fixed Cost (TFC) refers to expenses that do not change with the level of production in the short term. These include costs such as rent, salaries, and insurance premiums. No matter how much the firm produces, whether it’s zero or maximum capacity, the total fixed costs stay the same.

Marginal Revenue

Marginal Revenue (MR) represents the additional income earned from selling one more unit of a product. In perfect competition, the MR is constant and equal to the price of the goods, as the price is determined by the market. The firm must accept this price and can only adjust its output levels to control revenues.

Total Revenue

Total Revenue (TR) is the total amount of money a firm receives from selling its products at a given price level. It is calculated by multiplying the price at which goods or services are sold by the total quantity sold, typically noted as TR = Price x Quantity. In perfect competition, since the prices are given, TR increases linearly as the quantity sold increases.

Total Cost

Total Cost (TC) is the sum of all costs a firm incurs to produce certain goods or services. It includes both total variable costs (TVC) and total fixed costs (TFC), expressed as TC = TVC + TFC. Understanding the TC helps firms to determine how much revenue must be earned to cover all costs and to establish the profitability of their products.