Economics of Cost Minimization Chapter 1

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Questions and Answers

At which output level does the firm minimize its costs given fixed capital?

At any level below q0

At q1, where MRTS equals the ratio of input prices (correct)

At q2, where STC2 is minimized

At q0, where STC0 is applied

How does an increase in input prices affect the firm's cost curves?

Cost curves will remain unchanged

Cost curves will shift sideways

Cost curves will shift downwards

Cost curves will shift upwards (correct)

Which factor would NOT affect the shape and position of a firm's cost curves?

Changes in input prices

Availability of skilled labor

Technological innovation

Fixed capital levels (correct)

What is the implication of technological innovation on cost curves?

Cost curves will shift downwards indicating reduced costs Signup and view all the answers

Which statement about the marginal rate of technical substitution (MRTS) is true regarding cost minimization?

MRTS must equal the ratio of input prices for cost minimization Signup and view all the answers

What is the definition of accounting cost?

The actual cost paid for inputs. Signup and view all the answers

Which of the following best describes economic profit?

Total Revenues minus total costs, including implicit costs. Signup and view all the answers

In a perfectly competitive market, how is the economic profit of a firm primarily affected?

By the amount of labor and capital hired. Signup and view all the answers

What does the term 'sunk cost' refer to in economic terms?

Expenditures that cannot be recovered once made. Signup and view all the answers

When a firm is producing at the lowest possible cost, which of the following conditions must be met?

The marginal rate of technical substitution (MRTS) must equal the input price ratio. Signup and view all the answers

If a firm uses 10 units of capital and 10 units of labor to produce q units of output with an MRTS of 2, what can be inferred about the firm’s input choices?

The firm is overusing labor compared to capital. Signup and view all the answers

Which of the following statements about implicit costs is true?

Implicit costs encompass the lost income from the firm’s resources in their next best alternative use. Signup and view all the answers

What happens to total cost when there are decreasing returns to scale?

Total cost expands more rapidly than output. Signup and view all the answers

In what scenario does the average cost decrease?

When marginal cost is below average cost. Signup and view all the answers

What occurs when marginal cost equals average cost?

Average cost remains unchanged. Signup and view all the answers

If you have three students with heights of 165cm, 170cm, and 175cm, what happens when a new student with a height of 169cm enters?

The average height remains the same. Signup and view all the answers

What is the optimal scale in production?

Both increasing and decreasing returns to scale occur over different output levels. Signup and view all the answers

How is marginal cost defined?

As the cost of increasing output by one unit. Signup and view all the answers

What is the relationship between average cost and marginal cost when average cost is falling?

Marginal cost is below average cost. Signup and view all the answers

What occurs when total cost expands more slowly than output?

Increasing Returns to Scale. Signup and view all the answers

What happens in a situation where a new student's height exactly matches the average height?

The average height remains unchanged. Signup and view all the answers

What is indicated when marginal cost is consistently rising?

Average cost must also be rising. Signup and view all the answers

When the MRTS is greater than the wage-to-rent ratio (w/r), what should the firm do to minimize costs?

Hire more labor and less capital Signup and view all the answers

What does the term 'Expansion Path' refer to in a firm's production?

A set of input combinations used for different output levels Signup and view all the answers

If a firm operates under constant returns to scale, what happens to total costs when output increases?

Total costs increase proportionally Signup and view all the answers

To achieve cost minimization in input choice, what must be true regarding the marginal products and factor prices?

MPL/w must equal MPK/r Signup and view all the answers

Which of the following scenarios indicates a firm is not minimizing its costs?

MPL/w > MPK/r Signup and view all the answers

What is the implication of a firm's MRTS being different from its w/r value?

The firm can substitute inputs to reduce costs Signup and view all the answers

In cost minimization, how does the firm adjust its input usage as output expands?

It hires more capital and labor to use cost-minimizing combinations Signup and view all the answers

What relationship does the condition MPL/w = MPK/r illustrate in production?

Marginal product per dollar spent is equal for both inputs Signup and view all the answers

Which type of returns to scale results in an increase in total costs at a lesser rate than the increase in output?

Increasing returns to scale Signup and view all the answers

When can the marginal cost equal the average cost?

When the average cost is neither rising nor falling Signup and view all the answers

What happens to the average cost and marginal cost when output expands under decreasing returns?

Both average cost and marginal cost increase Signup and view all the answers

In the short run, why might a firm not be able to use the cost minimizing combination of inputs?

Some inputs are fixed and cannot be adjusted Signup and view all the answers

Which is true regarding average and marginal products in the context of costs?

Their behaviors are similar to those of average and marginal costs Signup and view all the answers

What characterizes the long run in terms of input costs?

All inputs are variable Signup and view all the answers

Under increasing returns, how do average costs and marginal costs behave as output expands?

Both costs decrease Signup and view all the answers

What are fixed costs associated with in the short run?

Inputs that are fixed Signup and view all the answers

What is the term for the point where marginal cost intersects with average cost at its minimum?

Optimal scale Signup and view all the answers

As output expands in the context of constant returns, what happens to average cost and marginal cost?

Both average cost and marginal cost remain the same Signup and view all the answers

Which statement best describes the relationship of marginal cost to average cost at the minimum point?

Marginal cost is equal to average cost Signup and view all the answers

Study Notes

Costs

Firms aim to produce a given output at the lowest possible cost.
Production costs change as firms adjust the number and mix of inputs.

Chapter Preview

The chapter focuses on how firms choose inputs to minimize production costs for a given output level.
It also examines how production costs change when a firm adjusts the inputs used.

Overview

Basic cost concepts are covered.
Economic profits and cost minimization are discussed.
Firm's expansion path is examined.
Cost curves are explained.
Short-run and long-run considerations are addressed.

Basic Cost Concepts

Accounting cost: Reflects the actual expenses incurred for inputs (out-of-pocket, depreciation, and other bookkeeping entries).
Economic cost: Represents the total amount required to keep an input in its present use, considering its value in its next best alternative use.
Labor costs: Economists and accountants treat labor similarly, with wage payments being explicit current expenses.
Capital costs: Accountants use historical costs and depreciation rules, while economists view capital costs as sunk costs that cannot be recovered. The implicit cost of capital equals its rental rate.

Economic Profits and Cost Minimization

Two primary inputs considered: labor (L) and capital (K).
Both inputs are hired in a perfectly competitive market.
Total costs (TC) are calculated as wL + rK (w = wage rate, r = rental rate).
Economic profit (π) is calculated as total revenue minus total costs (π = Total Revenue – Total Costs).
Firm's economic profit depends on labor and capital hired.

Cost Minimizing Input Choice

Firms aim to produce at the lowest possible cost.
This is examined in three ways:
- MRTS = w/r (Marginal Rate of Technical Substitution equals the input price ratio).
- Graphical approach: the isoquant tangent to the total cost line.
- MP₁/w = MPK/r (Marginal Product of labor per dollar equals the Marginal Product of capital per dollar).

Cost Minimizing Input Choice: MRTS = w/r

Assume a certain output level (q) requires 10 units of capital (K) and 10 units of labor (L).
Suppose MRTS = 2, w = $1, and r = $1.
The calculation would indicate that if the MRTS isn't equal to w/r, the firm can lower cost by adjusting inputs.

Cost Minimizing Input Choice: Graphical Approach

Graphically, the cost-minimizing input combination is where an isoquant is tangent to an isocost line.

Cost Minimizing Input Choice: MP₁/w = MPK/r

Marginal products (MPL, MPK) divided by their respective prices (w, r) should be equal to minimize costs.
If MPL/w is greater than MPK/r, the firm can increase profits by substituting labor for capital.

Firm's Expansion Path

To expand output, firms hire more capital and labor.
Each output increase requires a cost-minimizing input combination.

Cost Curves

The link between output and total costs depends on the production characteristics (constant, decreasing, or increasing returns to scale).

Constant Returns to Scale

As output rises, costs increase proportionally.

Decreasing Returns to Scale

Costs increase more rapidly than output increases.

Increasing Returns to Scale

Costs increase less rapidly than output increases.

Optimal Scale

Initial stages of increasing returns are followed by decreasing returns as output expands.

Average and Marginal Costs

Average cost (AC) is total cost divided by output (AC = TC/q).
Marginal cost (MC) is the extra cost of producing one more unit (MC = ΔTC/Δq).
The relationship between AC and MC is important: MC lies below AC when AC is falling and above AC when AC is rising. MC equals AC at the minimum point of the AC curve.

Average and Marginal Costs: Illustrative Example

The height of students in a classroom illustrates the relationship between average and marginal phenomena.

Average and Marginal Cost Curves: Constant Returns

Both marginal and average costs remain constant as output increases.

Average and Marginal Cost Curves: Decreasing Returns

Both marginal and average costs increase as output increases.

Average and Marginal Cost Curves: Increasing Returns

Both marginal and average costs decrease as output increases.

Average and Marginal Cost Curves: Optimal Scale

Cost curves initially fall as output increases, and then start rising.

Also True for Average and Marginal Products

Illustration of the similar relationship between marginal and average product.

The Short Run and the Long Run

Short run: A period in which some inputs are fixed.
Long run: A period in which all inputs can be varied.
Fixed costs: Costs associated with fixed inputs in the short run.
Variable costs: Costs associated with inputs that can be varied in the short run.

Input Inflexibility and Cost Minimization

Firms may not always be able to use the cost-minimizing combination of inputs in the short run due to fixed inputs.

Shifts in Cost Curves

Input price changes, technological advancement, and economies of scope can affect costs, shifting curve positions.

A Numerical Example

Example calculation of costs for different output levels with specific fixed and variable inputs (labor and capital)

Recap (Summary Points)

Cost minimization in the long run involves adjusting long-run input quantities.
A firm with limited input substitution options would see minimal input changes with small price changes.
Short-run decisions are constrained by fixed inputs.
The graphical explanation of cost curves and how their shapes depend on the production process.

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Description

This quiz explores the principles of cost minimization for firms regarding their production inputs. It covers basic cost concepts, accounting vs economic costs, and the implications of short-run and long-run choices. Test your understanding of how firms can operate at the lowest possible costs while aiming for maximum efficiency.