Question

A computer company produces affordable, easy-touse home computer systems and has fixed costs of \(\$ 250 .\) The marginal cost of producing computers is \(\$ 700\) for the first computer, \(\$ 250\) for the second, \(\$ 300\) for the third, \(\$ 350\) for the fourth, \(\$ 400\) for the fifth, \(\$ 450\) for the sixth, and \(\$ 500\) for the seventh. a. Create a table that shows the company's output, total cost, marginal cost, average cost, variable cost, and average variable cost. b. At what price is the zero-profit point? At what price is the shutdown point? c. If the company sells the computers for \(\$ 500,\) is it making a profit or a loss? How big is the profit or loss? Sketch a graph with AC, MC, and AVC curves to illustrate your answer and show the profit or loss. d. If the firm sells the computers for \(\$ 300,\) is it making a profit or a loss? How big is the profit or loss? Sketch a graph with \(\mathrm{AC}, \mathrm{MC}\) , and AVC curves to illustrate your answer and show the profit or loss.

Short answer

The company's zero-profit point occurs at a price of $450, while the shutdown point is at a price of $400. If they sell the computers for $500, they make a profit of $250, and if they sell for $300, they incur a loss of $750.

Step-by-step solution

Output and Marginal Cost

First, let’s list the output and given marginal costs for each computer: Output (Q) | Marginal Cost (MC) -----------|------------------- 1 | 700 2 | 250 3 | 300 4 | 350 5 | 400 6 | 450 7 | 500 b. Total Cost, Variable Cost, Average Cost, and Average Variable Cost

Calculate Variable Cost (VC)

To calculate the variable cost, we add up the marginal costs for each computer produced: Output (Q) | Marginal Cost (MC) | Variable Cost (VC) -----------|-------------------|------------------- 1 | 700 | 700 2 | 250 | 700 + 250 = 950 3 | 300 | 950 + 300 = 1250 4 | 350 | 1250 + 350 = 1600 5 | 400 | 1600 + 400 = 2000 6 | 450 | 2000 + 450 = 2450 7 | 500 | 2450 + 500 = 2950

Calculate Total Cost (TC)

To calculate the total cost, we add the fixed cost to the variable cost for each output: Output (Q) | Marginal Cost (MC) | Variable Cost (VC) | Total Cost (TC) -----------|-------------------|-------------------|---------------- 1 | 700 | 700 | 250 + 700 = 950 2 | 250 | 950 | 250 + 950 = 1200 3 | 300 | 1250 | 250 + 1250 = 1500 4 | 350 | 1600 | 250 + 1600 = 1850 5 | 400 | 2000 | 250 + 2000 = 2250 6 | 450 | 2450 | 250 + 2450 = 2700 7 | 500 | 2950 | 250 + 2950 = 3200

Calculate Average Cost (AC) and Average Variable Cost (AVC)

Finally, we calculate the average cost and average variable cost by dividing the total cost and variable cost, respectively, by the output: Output (Q) | Marginal Cost (MC) | Variable Cost (VC) | Total Cost (TC) | Average Cost (AC) | Average Variable Cost (AVC) -----------|-------------------|-------------------|----------------|------------------|--------------------- 1 | 700 | 700 | 950 | 950 / 1 = 950 | 700 / 1 = 700 2 | 250 | 950 | 1200 | 1200 / 2 = 600 | 950 / 2 = 475 3 | 300 | 1250 | 1500 | 1500 / 3 = 500 | 1250 / 3 = 417 4 | 350 | 1600 | 1850 | 1850 / 4 = 463 | 1600 / 4 = 400 5 | 400 | 2000 | 2250 | 2250 / 5 = 450 | 2000 / 5 = 400 6 | 450 | 2450 | 2700 | 2700 / 6 = 450 | 2450 / 6 = 408 7 | 500 | 2950 | 3200 | 3200 / 7 = 457 | 2950 / 7 = 421

Zero-profit point and shutdown point

The zero-profit point occurs when the average cost (AC) equals the price (P), and the shutdown point occurs when the average variable cost (AVC) equals the price (P). b. For this exercise, since the AC is lowest at 450 when the output is 5 computers, the zero-profit point price is $450. Similarly, the shutdown point is when AVC = P, which in this case is 400 (when output is 5 computers). c. If the company sells the computers for \(500, their profit would be positive because their average cost is lower than the selling price (450 < 500). The profit per computer would thus be \)50 per computer, with a total profit of \(50 * 5 = \)250. d. If the firm sells the computers for \(300, their profit would be negative because their average cost is higher than the selling price (450 > 300). The loss per computer would be \)150 per computer, with a total loss of \(150 * 5 = \)750.

Key concepts

Marginal Cost Analysis

Understanding the concept of marginal cost is crucial for businesses and students of microeconomics alike. Marginal cost denotes the expense associated with producing one additional unit of a good or service. It's often depicted as the slope of the total cost curve, indicating how the total cost changes with an increase in production.

In the practical exercise provided, the marginal cost for each additional computer produced is seen to increase progressively. This informs us that the more units you produce, the more it's going to cost to produce each extra one - a common scenario due to factors like increased labor or raw materials needed at higher production capacities. By listing the output and corresponding marginal costs, students can see the direct correlation in a tabular format.

To better absorb this notion, it is helpful to visualize these cost changes on a graph and understand that the point where the marginal cost curve intersects the average total cost curve is critical — it represents the minimum point of the average total cost curve, informing price-setting decisions for profit optimization.

Average Cost Calculation

Average cost plays a pivotal role in pricing and economic decisions. It is the total cost of production divided by the number of goods produced, incorporating both fixed and variable costs. As demonstrated in our exercise, calculating average cost involves summing the fixed cost with the variable cost for each number of units and then dividing by the total number of units produced.

This calculation enables a company to determine the cost of producing each unit and at which point it is possible to achieve economies of scale. It's important to note that the average cost tends to decrease as more units are produced, up to a certain point, due to the spreading out of fixed costs. However, once the optimal level of production is exceeded, the average cost may start to increase due to factors such as lower efficiency or higher per-unit variable costs.

Incorporating the average cost into decision-making benefits businesses by allowing them to identify the most cost-effective scale of production for their products. For instance, pinpointing the output level where the average cost is minimized, as shown in the solution to the problem, can be instrumental in maximizing profits.

Profit Maximization

Profit maximization is the process by which a company determines the price and output level that returns the greatest profit. The central tenets of this concept revolve around revenue and cost. To maximize profit, a firm will continue producing units until marginal cost equals marginal revenue — the additional income from selling one more unit.

In our exercise, if the company sells its computers at a price that exceeds the average cost, it realizes a profit. Conversely, selling below the average cost incurs a loss. The zero-profit point is the price at which the company exactly covers all its costs, including both variable and fixed costs, which the textbook solution identifies as a price of $450 for five computers.

By assessing the relationship between cost curves and market price, students can appreciate that the ideal price level for profit maximization in the free market is often not simply the highest price, but rather the price that aligns with cost considerations, demand elasticity, and competitive dynamics. Sketching and analyzing the graphs of average cost (AC), marginal cost (MC), and average variable cost (AVC) is an effective way to visualize and comprehend the profit or loss at different price points.