Question

Suppose that a perfectly competitive firm has the following total variable costs \((T V C):\) Quantity: \(\quad 0 \quad 1 \quad 2 \quad 3 \quad 4 \quad 5 \quad 6\) TVC:\(\$ 0 \quad \$ 6 \quad \$ 11 \quad \$ 15 \quad \$ 18 \quad \$ 22 \quad \$ 28\) 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

The profit-maximizing quantity for the firm is 3 units. However, the firm is making a loss of \$6 at this quantity.

Step-by-step solution

- Calculating the Marginal Costs

The Marginal Cost (MC) can be found by calculating the change in Total Variable Costs (TVC) divided by the change in quantity. As Quantity changes from 0 to 6, the MC would be: MC = TVC/ Quantity.\nThe MC at different quantities would be: \[MC = {0, 6, 5, 4, 3, 4, 6}\] respectively for each quantity from 1 to 6.

- Profit Maximizing Quantity

As per the rule of profit maximization in perfect competition, the firm should expand its output upto the point where the Marginal Revenue (MR) is equal to Marginal Cost (MC). In a perfect competitive market, the MR is equal to market price, in this case 5$, so The MR=MC point is where the cost is also 5$, which is at quantity 2 and 3. We choose the larger quantity because the MC is increasing and revenue will be higher.

- Calculate Total Revenue and Total Cost

To substantiate the initial result, follow the total revenue and total cost approach. Total Revenue (TR) is determined by multiplying the price per unit by the number of units sold. Here, it's 5$ per unit. Total Cost (TC) is the sum of Total Variable Cost (TVC) and Total Fixed Cost (TFC). Here, TFC is 6$ Whilst TVC is given for each quantity.

- Compare Total Revenue and Total Cost

Calculate the profit or loss by subtracting Total Cost from Total Revenue. TR = P*Q and TC = TFC + TVC. For quantity = 3, TR = 3*5 = 15$, TC = 6 + 15 = 21$. Subtract TC from TR to get profit or loss. Therefore, profit = TR - TC = 15$ - 21$ = -6$. Therefore, the firm is making a loss of 6$.

- Final observation

The firm's profit-maximizing quantity was found to be 3 using the MR = MC approach in perfect competition. From total revenue and total cost approach, it was confirmed the firm is operating at a loss at this production quantity.

Key concepts

Marginal Cost

When studying economics, it's essential to understand the concept of marginal cost (MC). Marginal cost represents the change in total variable costs when one additional unit of a product is produced. It is a critical factor in determining the profit-maximizing quantity for a firm.

Let’s make it simple: imagine you're baking cookies and the cost of making one more cookie after you've already baked a bunch is the marginal cost. If it costs you more to bake each additional cookie than what you can sell it for, you wouldn’t make any dough (pun intended) by baking more cookies.

In the exercise provided, we calculate MC by looking at how much the total variable cost (TVC) goes up as the quantity of goods produced increases. The difference in TVC divided by the change in quantity gives us MC for each additional unit. Having the MC, we can map out the cost of producing one more item at each level of production, which tells us if it’s worth it to increase production or not.

Marginal Revenue

Another fundamental concept is marginal revenue (MR). Marginal revenue is the additional income earned by selling one more unit of a good or service. It’s like when you’ve already sold several lemonades on a hot day, and you want to know how much you’ll make if you sell just one more glass.

In a perfect competition, the marginal revenue is equal to the price at which goods are sold because firms are price takers; they cannot set their prices above the market level. In our exercise, the market price is \(5 per unit, so MR is constant at \)5 for each unit sold. By understanding MR, businesses can make informed decisions about how many goods to produce and sell to maximize their profits. If producing another unit costs more than $5, the firm knows not to make it since it won’t add to their profit.

Perfect Competition

The environment of perfect competition is a theoretical market structure that provides an ideal baseline for economic analysis. In this hypothetical world, numerous small firms compete against each other, and none of them has the power to influence market prices—think of a farmers' market where many vendors sell similar strawberries.

In perfect competition, the price is determined by the intersection of demand and supply in the market. Every firm accepts this price and is known as a 'price taker.' The products are considered identical, and there are no barriers to entry or exit for businesses. With many buyers and sellers, the actions of one company do not impact the overall market. This level of competition means that firms continue producing output until their marginal cost (MC) equals their marginal revenue (MR). It’s a delicate balance, like finding the perfect spot for setting up your lemonade stand in a park full of thirsty people.

Total Revenue and Total Cost Approach

The total revenue and total cost approach is another way for firms to calculate their profit-maximizing output. Total revenue (TR) is the entire amount of money a company makes from selling its goods. It’s basically how much cash the register holds after a day’s sales, calculated by multiplying the number of goods sold by the price. Total cost (TC) includes all costs a business incurs to produce those goods, both fixed costs (like rent) and variable costs (like ingredients).

In the textbook example, to assess the firm's performance, we multiply the quantity of goods sold by the set market price to find TR. Next, we tally up the total variable costs (TVC) and add the total fixed costs (TFC) to determine TC. The difference between TR and TC indicates whether the firm is turning a profit, recording a loss, or just breaking even. This method complements the marginal cost and revenue approach by confirming the results and providing a clearer picture of the firm's overall financial health.