Chapter 14: The Costs of Production Study Guide

Fundamental Concepts of Revenue, Cost, and Profit

Total revenue is defined as the amount a firm receives for the sale of its output. Total cost is the market value of the inputs a firm uses in production. Profit is calculated as total revenue minus total cost. To understand a firm’s behavior, it is essential to consider the concept of opportunity cost, which states that the cost of something is what you give up to get it. A firm's cost of production includes all the opportunity costs of making its output of goods and services.

Explicit and Implicit Costs

Costs are categorized into two types: explicit and implicit. Explicit costs are input costs that require an outlay of money by the firm. Implicit costs are input costs that do not require an outlay of money by the firm. The total cost of a firm is the sum of explicit costs and implicit costs. A significant implicit cost for almost every business is the opportunity cost of the financial capital invested in it. For instance, economists view interest income given up as an implicit cost, whereas accountants do not show this as a cost because no money flows out of the business to pay for it.

Measuring Profit: Economists versus Accountants

Economists and accountants measure profit differently based on which costs they include. Economic profit is defined as total revenue minus total cost, including both explicit and implicit costs. Accounting profit is total revenue minus total explicit cost. Because economists include all opportunity costs while accountants measure only explicit costs, economic profit is generally smaller than accounting profit.

This is illustrated by the Wheeler Dealer Accounts for 2015:

• Total revenue: $105,000$
• Explicit costs: Assistant's salary ($-21,000$) and Material and equipment ($-20,000$).
• Accounting profit: $64,000$.
• Implicit costs: Wanda's forgone salary ($-50,000$), Forgone interest on savings ($-1,000$), and Forgone garage rental ($-1,200$).
• Economic profit: $11,800$.

The Production Function and Diminishing Marginal Product

A production function represents the relationship between the quantity of inputs used to make a good and the quantity of output of that good. Marginal product is the increase in output that arises from an additional unit of input. Diminishing marginal product is the property whereby the marginal product of an input declines as the quantity of the input increases. As more inputs are used, the production function gets flatter, and the slope decreases. In Chloe’s Cookie Factory (Table 1), we see the following data:

• $0$ workers: $0$ output, Cost of Factory $30$, Cost of Workers $0$, Total Cost $30$.
• $1$ worker: $50$ output, Marginal Product $50$, Cost of Factory $30$, Cost of Workers $10$, Total Cost $40$.
• $2$ workers: $90$ output, Marginal Product $40$, Cost of Factory $30$, Cost of Workers $20$, Total Cost $50$.
• $3$ workers: $120$ output, Marginal Product $30$, Cost of Factory $30$, Cost of Workers $30$, Total Cost $60$.
• $4$ workers: $140$ output, Marginal Product $20$, Cost of Factory $30$, Cost of Workers $40$, Total Cost $70$.
• $5$ workers: $150$ output, Marginal Product $10$, Cost of Factory $30$, Cost of Workers $50$, Total Cost $80$.
• $6$ workers: $155$ output, Marginal Product $5$, Cost of Factory $30$, Cost of Workers $60$, Total Cost $90$.

The Relationship Between Production and Total Cost

The total-cost curve shows the relationship between the quantity of output produced and the total cost of production. As production rises, the total-cost curve grows steeper, while the production function becomes flatter. This occurs because of diminishing marginal product; as the marginal product of an input falls, producing an additional unit of output requires more inputs and thus becomes increasingly expensive.

Fixed and Variable Costs

A firm's total costs can be divided into fixed and variable components. Fixed costs ($FC$) are costs that do not vary with the quantity of output produced. Variable costs ($VC$) are costs that vary with the quantity of output produced. Total cost ($TC$) is the sum of fixed and variable costs: $TC = FC + VC$.

Caleb’s Coffee Shop (Table 2) provides numerical examples:

• At $0$ output: $TC = 3.00$, $FC = 3.00$, $VC = 0.00$.
• At $1$ output: $TC = 3.30$, $FC = 3.00$, $VC = 0.30$, $AFC = 3.00$, $AVC = 0.30$, $ATC = 3.30$, $MC = 0.30$.
• At $5$ output: $TC = 6.50$, $FC = 3.00$, $VC = 3.50$, $AFC = 0.60$, $AVC = 0.70$, $ATC = 1.30$, $MC = 1.10$.
• At $10$ output: $TC = 15.00$, $FC = 3.00$, $VC = 12.00$, $AFC = 0.30$, $AVC = 1.20$, $ATC = 1.50$, $MC = 2.10$.

Average and Marginal Cost Measures

Average total cost ($ATC$) is the total cost divided by the quantity of output: $ATC = \frac{TC}{Q}$. Average fixed cost ($AFC$) is the fixed cost divided by the quantity of output: $AFC = \frac{FC}{Q}$. Average variable cost ($AVC$) is the variable cost divided by the quantity of output: $AVC = \frac{VC}{Q}$. Marginal cost ($MC$) is the increase in total cost that arises from an extra unit of production: $MC = \frac{\Delta TC}{\Delta Q}$.

Shapes and Intersections of Cost Curves

Cost curves typically exhibit specific geometric features. Marginal cost eventually rises as the quantity of output increases, reflecting diminishing marginal product. The average-total-cost curve is typically U-shaped. The bottom of the U-shape occurs at the quantity that minimizes average total cost, which is known as the efficient scale of the firm. When $MC < ATC$, average total cost is falling. When $MC > ATC$, average total cost is rising. Consequently, the marginal-cost curve crosses the average-total-cost curve exactly at its minimum. In a typical firm, marginal cost and average variable cost may fall for a short period before they start to rise, as shown in Figure 5.

Short-Run and Long-Run Costs

There is a crucial distinction between cost behavior in the short run versus the long run. Many decisions are fixed in the short run but variable in the long run, giving firms greater flexibility over longer periods. Long-run average-total-cost curves are typically much flatter than short-run average-total-cost curves. Short-run cost curves lie on or above the long-run cost curves.

Scaling behavior in the long run is categorized as follows:

• Economies of scale: Long-run average total cost falls as the quantity of output increases.
• Constant returns to scale: Long-run average total cost stays the same as the quantity of output changes.
• Diseconomies of scale: Long-run average total cost rises as the quantity of output increases.

Summary of Cost Types

Table 3 summarizes the types of costs:

• Explicit costs: Require monetary outlay.
• Implicit costs: Do not require monetary outlay.
• Fixed costs ($FC$): Do not vary with output.
• Variable costs ($VC$): Vary with output.
• Total cost ($TC$): $TC = FC + VC$.
• Average fixed cost ($AFC$): $AFC = \frac{FC}{Q}$.
• Average variable cost ($AVC$): $AVC = \frac{VC}{Q}$.
• Average total cost ($ATC$): $ATC = \frac{TC}{Q}$.
• Marginal cost ($MC$): $MC = \frac{\Delta TC}{\Delta Q}$.

Questions & Discussion

Active Learning 1: Economic vs. Accounting Profit The equilibrium rent on office space has increased by $500/\text{month}$. Determine the effects on accounting profit and economic profit if:

• A. You rent your office space (you pay $500/\text{month}$). Answer: Both accounting and economic profit decrease because the explicit cost increases.
• B. You own your office space. Answer: Accounting profit remains unchanged (no cash outlay changes), but economic profit decreases because the implicit opportunity cost of using the space (the rent you could have received) has increased.

Active Learning 2: Diminishing MPL Given data for Workers ($0, 1, 2, 3, 4, 5$) and Output ($0, 45, 85, 115, 135, 145$):

• A. What is the marginal product of the second worker? Answer: $85 - 45 = 40$.
• B. What is the marginal product of the fourth worker? Answer: $135 - 115 = 20$.
• C. Does this production function exhibit diminishing marginal returns? Answer: Yes, because the marginal product falls from $45$ to $40$, then $30$, then $20$, then $10$.

Active Learning 3: Calculating Costs

• At $Q=1$: $TC=60$, $VC=10$. This implies $FC=50$. $AFC=50$, $AVC=10$, $ATC=60$.
• At $Q=3$: $TC=110$, $MC=30$ (from $Q=2$ to $Q=3$). $AFC=16.67$, $AVC=20$, $ATC=36.67$.
• At $Q=6$: $TC=260$, $VC=210$, $AFC=8.33$, $AVC=35$, $ATC=43.33$, $MC=60$.

Think-Pair-Share Activity A neighbor hired one student and production more than doubled. He plans to hire three more for a three- or fourfold increase next summer.

• A. What explains why production more than doubled with one helper? Answer: Increasing marginal product often occurs initially due to specialization or teamwork.
• B. Will production increase three- or fourfold with 3 helpers? Answer: Likely not, as eventually the law of diminishing marginal product will take effect when the land or existing tools become more crowded/limited.

Self-Assessment

• When analyzing a firm’s behavior, why is it important to include all the opportunity costs of production? Answer: To understand the true economic health and decision-making framework of the firm, as implicit costs like forgone interest or alternative salaries represent real sacrifices that impact whether a business is truly profitable compared to its next best alternative.