Economics Chapter 9: Theory of the Firm 2

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Questions and Answers

What condition indicates that a production function exhibits decreasing returns to scale?

α + β < 0

α + β > 1

α + β < 1 (correct)

α + β = 1

When is a production function characterized by constant returns to scale?

If α + β = 0

If α + β < 1

If α + β = 1 (correct)

If α + β > 1

In the context of Cobb-Douglas production functions, what does it mean when α + β > 1?

The production function is undefined.

There are constant returns to scale.

There are decreasing returns to scale.

There are increasing returns to scale. (correct)

What is the formula for the marginal product MP1 in a Cobb-Douglas production function?

MP1 = αx1α−1 x2 Signup and view all the answers

If the parameters are set to α = 1 and β = 1, what type of returns to scale does the production function exhibit?

Constant returns to scale Signup and view all the answers

What is the condition that defines increasing returns to scale for a Cobb-Douglas production function?

α + β > 1 Signup and view all the answers

To determine the technical rate of substitution (TRS), which of the following must be calculated?

The marginal products MP1 and MP2 Signup and view all the answers

What happens to the Cobb-Douglas production function if t is increased and α + β < 1?

Output increases less than proportionately Signup and view all the answers

Why is it reasonable to assume that isoquants are convex?

Firms can combine different production techniques effectively. Signup and view all the answers

What does the technical rate of substitution indicate in production?

The amount of one input required to replace another while maintaining output. Signup and view all the answers

What happens if isoquants are not convex?

Firms will resort to using extreme input bundles. Signup and view all the answers

If isoquants pass above the midpoint between two input techniques, what would this imply?

The isoquant is not strictly convex. Signup and view all the answers

What does the marginal rate of substitution (MRS) reflect?

The ratio of marginal utilities of two goods. Signup and view all the answers

What is a likely outcome if a firm has access to multiple production techniques?

The firm can use various techniques simultaneously without conflict. Signup and view all the answers

Which of the following best defines an isoquant?

A curve that represents different combinations of inputs producing the same output. Signup and view all the answers

What is implied about production techniques when isoquants are convex?

Different levels of inputs can produce similar outputs effectively. Signup and view all the answers

What does Chapter 11 bankruptcy primarily allow a firm to do?

Shield itself from its creditors Signup and view all the answers

In the context of the production function, what is a production technique?

A combination of inputs that yields the same output level Signup and view all the answers

What is the relationship between cost minimization and profit maximization for a firm?

Cost minimization is necessary for profit maximization. Signup and view all the answers

What defines an isocost line?

A set of input combinations with the same cost. Signup and view all the answers

What is implied by a production technique being technologically inefficient?

It uses more resources than necessary without increasing output Signup and view all the answers

What was a significant reason for General Motors and Chrysler to file for Chapter 11 bankruptcy in 2009?

To escape burdens of debt and union contracts Signup and view all the answers

Which equation represents the isocost line for a given cost level C0?

$w1 x1 + w2 x2 = C0$ Signup and view all the answers

How does the concept of the 'long run' differ from immediate solutions like bankruptcy in economics?

The long run is a time frame where all costs can be adjusted Signup and view all the answers

In the production function $y = f(x1, x2)$, what does the isoquant represent?

All combinations of inputs that yield the same output. Signup and view all the answers

What is the implication of using two inputs instead of one for production?

There are multiple combinations of inputs available for the same output level. Signup and view all the answers

Which of the following best describes technological efficiency in production?

Producing maximum output with least resource consumption Signup and view all the answers

What does it mean when a firm is said to have alternative production techniques?

It can achieve the same output with different combinations of inputs Signup and view all the answers

Which of the following is true about the firm's profit equation?

Profit equals total revenue minus total cost. Signup and view all the answers

Which example illustrates a technologically inefficient production technique?

Using 3 workers and 3 units of raw materials to produce 1 unit Signup and view all the answers

For a given output level $y_0$, how are production costs impacted?

Costs may vary depending on the methods used. Signup and view all the answers

What can be inferred if costs $C(y)$ are not at the minimum for a given output?

A cheaper production method can lead to higher profits. Signup and view all the answers

What condition must be satisfied for a firm to minimize production costs?

The isoquant is tangent to the isocost line at the optimal input combination. Signup and view all the answers

What relationship exists between marginal cost and average cost when there are increasing returns to scale?

MC(y) < AC(y) Signup and view all the answers

How is the slope of the isocost line determined?

It equals the ratio of the prices of inputs used in production. Signup and view all the answers

When a firm experiences decreasing returns to scale, what is true about the total cost curve?

The total cost curve is convex. Signup and view all the answers

What happens to both marginal cost and average cost as output increases under decreasing returns to scale?

They both increase. Signup and view all the answers

What role does the isoquant play in production theory?

It represents the combinations of inputs that yield the same level of output. Signup and view all the answers

If a firm wants to produce y units of output and has a cost of producing 1 unit as C(1), what is the relationship between total cost and output?

C(y) > yC(1) Signup and view all the answers

What does a lower isocost line indicate about a firm's cost level?

It reflects a lower total expenditure on inputs. Signup and view all the answers

In the context of decreasing returns to scale, what can be said about the slope of the marginal cost line compared to the average cost line?

It is greater than the average cost slope. Signup and view all the answers

What occurs when a production function initially satisfies increasing returns to scale and then transitions to decreasing returns to scale?

Marginal costs may increase as output increases. Signup and view all the answers

Which of the following correctly defines the Tangency Condition in production?

The equality of the slopes of the isoquant and the isocost line. Signup and view all the answers

What do the variables $w1$ and $w2$ represent in the context of isocost lines?

They represent the input prices for different production factors. Signup and view all the answers

What is true about the average cost when operating under increasing returns to scale?

It decreases until production is maximized. Signup and view all the answers

How does the production function behave when it experiences constant returns to scale?

Output increases by the same proportion as input increases. Signup and view all the answers

What must be true about the isoquants for the cost minimization condition to hold?

Isoquants must be smooth and convex to represent diminishing returns. Signup and view all the answers

Study Notes

Chapter 9: Theory of the Firm 2: The Long-Run, Multiple-Input Model

Firms produce goods and services using multiple inputs.
The multiple-input model analyses how firms combine inputs to produce a given output at the lowest cost.
The model considers how firms decide on output levels and input usage to minimize costs and maximize profits.
The single-input model is unrealistic as most goods use a variety of inputs.
Production function with two or more inputs is expressed as: y = f(x1, x2, x3,...)
The long run is a period of time where all inputs are variable.
The short run is a period where one or more inputs are fixed.
The production function (f(x1, x2)) represents the technological constraints on the firm.
The output price (p) and input prices (w1, w2 ) represent market constraints for the firm.

9.1 Introduction

The last chapter modeled firms with one input and one output, which is unrealistic.
Firms combine different inputs to produce goods/services.
Examples of this include land, labor, machinery, fertilizer.
Firms need to determine the least costly combination of various inputs to reach the desired output level.

9.2 The Production Function in the Long Run

The production function (y = f(x1, x2)) shows the relationship between inputs and outputs.
Isoquants are curves showing different combinations of inputs producing the same quantity of output.
Efficient production techniques use the least amount of inputs to produce a certain output.
Marginal products (MP1, MP2) measure the extra output from an extra unit of a given input, holding other inputs constant.
Technical rate of substitution (TRS) measures how much of one input can be substituted for another input to produce the same output.
TRS = - (Δx2/Δx1) = (MP1/MP2).
Technical rate of substitution is analogous to marginal rate of substitution in consumer theory.

9.3 Cost Minimization in the Long Run

For a given output level, the firm seeks the least costly combination of inputs.
Isocost lines represent combinations of inputs that have the same cost.
The firm minimizes cost when the isoquant is tangent to the isocost line.
The tangency condition is: TRS = w1/w2.

9.4 Profit Maximization in the Long Run

Profit maximization occurs when price (p) equals marginal cost (MC).
The firm's profits are maximized along the relevant portion of the marginal cost curve (MC).
Returns to scale (increasing, decreasing, or constant) affect the relationship between output and cost.
With constant returns to scale, marginal cost matches average cost.
With increasing returns to scale, marginal cost is below average cost.
With decreasing returns to scale, marginal cost is above average cost.
Supply curve is a part of the firm's marginal cost curve above the average cost curve.

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Description

This quiz covers the long-run multiple-input model of firms, exploring how they combine various inputs to minimize costs and maximize profits. Students will learn about production functions with multiple inputs, the significance of variable vs. fixed inputs, and the constraints firms face in the market. A solid understanding of these concepts is crucial for analyzing firm behavior in a competitive environment.