Microeconomics Chapter 7: Costs – Study Notes

Costs in Microeconomics

The Nature of Costs

Understanding the nature of costs is essential for firms aiming to maximize profit. Economists and accountants measure costs differently, with economists considering both explicit and implicit costs, while accountants focus on explicit costs for financial reporting.

• Explicit Costs: Direct, out-of-pocket payments for inputs (e.g., wages, rent, materials).

• Implicit Costs: The value of forgone opportunities (e.g., income from alternative uses of resources).

• Economic (Opportunity) Cost: The value of the best alternative use of a resource, including both explicit and implicit costs.

• Accounting Cost: Only explicit costs, as recorded in financial statements.

Example: If a business owner uses their own building for a store, the implicit cost is the rent they could have earned by leasing it to someone else.

Opportunity Costs

Opportunity cost is a central concept in economics, representing the value of the next best alternative forgone when a choice is made.

• Formula: Opportunity Cost = Value of Next Best Alternative – Cost Incurred

Example (Solved Problem 7.1): Meredith chooses between attending a derivatives class (free with registration) and a Warren Buffett talk (valued at $100, ticket costs $40). Her opportunity cost of attending the derivatives class is $60, the net benefit she would have received from the Buffett talk ($100 – $40).

Costs of Durable Inputs

Durable goods are assets usable for several years (e.g., machinery, buildings). Measuring their cost involves:

• Allocating the initial purchase cost over time (depreciation).

• Adjusting for changes in the value of capital over time.

Sunk Costs

Sunk costs are past expenditures that cannot be recovered. They are not relevant for current production decisions and are not considered opportunity costs.

• Example: Money spent on non-refundable equipment is a sunk cost.

Short-Run Costs

Types of Short-Run Costs

In the short run, some inputs are fixed while others are variable. Key cost concepts include:

• Fixed Cost (F): Costs that do not vary with output (e.g., rent).

• Variable Cost (VC): Costs that change with the level of output (e.g., raw materials).

• Total Cost (C): The sum of fixed and variable costs.

Formula:

• $C = F + VC$

Marginal and Average Costs

• Marginal Cost (MC): The extra cost of producing one more unit of output.

• Formula: $MC = \frac{\Delta VC}{\Delta q}$

• Average Fixed Cost (AFC): $AFC = \frac{F}{q}$

• Average Variable Cost (AVC): $AVC = \frac{VC}{q}$

• Average Cost (AC): $AC = \frac{C}{q}$

Relationship Between Average and Marginal Cost Curves

Marginal cost intersects average cost and average variable cost at their minimum points. When MC is below AC, AC falls; when MC is above AC, AC rises.

Effects of Taxes on Costs

Taxes can shift cost curves:

• Specific Tax: Increases both MC and AC by the tax amount per unit.

• Lump-Sum Tax: Increases fixed cost, shifting AC upward but not affecting MC.

Example (Solved Problem 7.2): A lump-sum franchise tax raises the minimum value of the average cost curve but does not change the output level at which the minimum occurs.

Long-Run Costs

Long-Run Cost Concepts

In the long run, all inputs are variable and fixed costs are avoidable ($F = 0$). The firm can adjust all factors of production to minimize cost for any output level.

• Long-Run Total Cost: $C = wL + rK$ (where w is wage rate, L is labor, r is rental rate of capital, K is capital)

Isocost Lines

An isocost line shows all combinations of labor and capital that cost the same total amount.

• Equation: $C = wL + rK$

• Solved for K: $K = \frac{C}{r} - \frac{w}{r}L$

Example Table: Bundles of Labor and Capital That Cost the Firm $200

Labor (L)	Capital (K)
0	25
5	20
10	15
15	10
20	5
25	0

Cost Minimization

Firms minimize cost by choosing the optimal combination of inputs. Three equivalent rules:

• Lowest-Isocost Rule: Choose the input bundle on the lowest isocost line that touches the isoquant.

• Tangency Rule: Choose the bundle where the isoquant is tangent to the isocost line.

• Last-Dollar Rule: Allocate spending so the last dollar spent on each input yields the same marginal product.

Mathematical Condition (Tangency Rule):

• $\frac{MP_L}{w} = \frac{MP_K}{r}$

• Where $MP_L$ and $MP_K$ are marginal products of labor and capital, respectively.

Example (Solved Problem 7.3): For a Cobb-Douglas production function $q = A L^a K^b$, cost is minimized when $\frac{a}{b} = \frac{wL}{rK}$.

Expansion Path and Long-Run Cost Function

The expansion path traces the cost-minimizing combinations of inputs as output increases. The long-run cost function shows the minimum cost for each output level.

• Fixed-Proportions Example: If one unit of labor and one unit of capital are needed per unit of output, then $C = (w + r)q$.

Economies and Diseconomies of Scale

• Economies of Scale: Average cost decreases as output increases.

• Diseconomies of Scale: Average cost increases as output increases.

Returns to Scale: Related to how output responds to proportional increases in all inputs.

Returns to Scale	Effect on Long-Run Average Cost
Increasing	Decreases
Constant	Constant
Decreasing	Increases

Long-Run Average Cost as Envelope of Short-Run Average Cost Curves

The long-run average cost (LRAC) curve is the lower envelope of all possible short-run average cost (SRAC) curves, each corresponding to a different plant size.

The Learning Curve

Learning by doing leads to lower average costs as cumulative output increases. The learning curve shows this relationship.

• Example: As a firm produces more CPUs, workers become more efficient, reducing average cost per unit.

Cost of Producing Multiple Goods

Economies of Scope

Economies of scope occur when it is less costly to produce multiple goods together than separately.

• Production Possibility Frontier (PPF): Shows the maximum output combinations possible with given resources.

Example: A dairy producing both milk and cheese may share inputs, reducing total cost compared to producing each separately.

Technology Choice at Home Versus Abroad

Firms may alter their input mix in response to differences in input prices across countries, affecting cost minimization strategies.

Additional info: Where the original content referenced figures or tables not fully shown, standard textbook explanations and logical examples were provided to ensure completeness.