CHAPTER 6 (test 1) Flashcards
Define Production
Production describes the process by which a person, company, government, or non-profit agency uses inputs to create a good or service for which others are willing to pay (selling the good in a market)
What are final goods and intermediate goods?
final - a good that is bought by a consumer
intermediate - a good that is used to produce another good to sell in a market (ex. wheat to produce bread)
What is a production function and how is it different from the utility function?
It is a mathematical relationship that describes how much output can be made from different combinations of inputs
> similar to a utility function for consumers, but it is more tangible and concrete
> sum of utility exponents is almost always 1, but this is not necessarily the case for the production function’s exponents
> also, the producer model is a bit more complicated and we have more assumptions because we have to consider the short run and long run time frames
What are the 9 simplifying assumptions about firms’ production behaviour?
- the firm produces a single good
- the firm has already chosen which product to produce
- firms minimize costs associated with every level of production (this is necessary for profit maximization)
- only two inputs are used in production: capital and labour
> capital = buildings, equipment, etc.
> labour = all human resources - in the short run, firms can choose the amount of labour employed, but capital is assumed to be fixed in total supply
- The more inputs the firm uses, the more output it makes
- Inputs are characterized by diminishing returns > when the other input is held fixed
- The firm can employ unlimited capital and labour at fixed prices > input prices don’t change
- Capital markets are well functioning (the firm is not budget-constrained)
Define the short run and long run
What are fixed inputs and variable inputs?
Short run = period of time in which one or more inputs used in production cannot be changed
Long run = the amount of time necessary for all inputs into production to be fully adjustable
fixed inputs = inputs the cannot be changed in the short run
variable inputs = inputs that can be changed in the short run
Explain the idea of diminishing returns in production
If the amount of capital is held constant, each additional worker eventually produces less incremental output than the last, and vice versa
what does a production function look like and what is the Cobb-Douglas production function?
Q = f(K,L)
Q = quantity of output
K = quantity of capital used
L = quantity of labour used
Cobb-Douglas production function is a common functional form where the quantity of each input is raised to a pwr and then multiplied together
What is the equation for average product of labour in the short-run? Why is the average product focused around labour?
APL = Q / L
focused around labour because capital is fixed and we’re just changing labour
What does the marginal product refer to?
What is the equation for the marginal product of labour?
Refers to the additional output that a firm can produce using an additional unit of an input (holding use of the other input constant)
- it is generally assumed to fall as more of an input is used (diminishing marginal product)
MPL = change in Q / change in L
(again, it’s about LABOUR in the short run because capital is fixed in the short run)
With the production function: Q = K^0.5 L^0.5, AND you know that capital is fixed at 4 units, what should you do with the function?
You should plug 4 into the function so that you can find output as a function for labour (because we’re really just deciding how much labour we need to put in)
so it would be: Q = 2L^0.5
What does cost minimization refer to? What two concepts does the cost minimization model require?
Refers to the firm’s goal of producing a specific quantity of output at minimum cost
> example of a constrained optimization problem
> firms will minimize costs subject to a specific amount of output that must be produced
Requires isoquants and isocost lines
What is an isoquant curve?
An isoquant is a curve representing combinations of inputs that allow a firm to make a particular quantity of output
What is the slope of an isoquant? (what it means and what is the equation)
The slope of an isoquant will describe how inputs may be substituted to produce a fixed level of output
This relationships is referred to as the Marginal Rate of Technical Substitution > the rate at which the firm can trade input X for input Y, holding output constant (MRTSxy)
MRTSlk = - (change in K / change in L)
OR = MPL / MPK
As you move down an isoquant, what happens to the slope and what does this mean?
Moving down an isoquant means capital is declining and therefore the slope is getting SMALLER (disregarding the fact that it’s negative), which means the firm has less capital and each unit is relatively more productive
If the MPL < APL, then APL will ______
decrease
(and vice versa)
Why is the Short-run production function curve not straight? Describe the graph
Because of diminishing marginal returns
y axis = total output
x axis = labour
curve is upward sloping with the slope getting smaller and smaller (diminishing marginal returns to labour) > as you use more and more labour, you will get less and less output from an additional unit of labour
___ is a function of ___ in the short-run
Q
L
L^-0.5 is the same as what?
1 / L^0.5
(let’s say in the production function, L^0.5) that means that we can say the slope = L^-0.5)
because it’s the MPL, we can also say it’s the change in Q / change in L
What does the curvature (straight or curved) of Isoquants say about the inputs (capital and labour)
(+ what does this say about the MRTSlk)
STRAIGHTER = inputs are relatively SUBSTITUTABLE > MRTSlk does not vary much along the curve
CURVIER = inputs are relatively complementary > MRTSlk varies greatly along the curve
Describe what perfect substitutes and perfect complements in production will look like on an Isoquant
Perfect substitutes: can be traded off in a constant ratio in a production process > MRTS is constant (straight line)
Perfect complements: must be used in a fixed ratio as part of a production process (ex. cabs and cab drivers)
What is an isocost line? What is the equation?
What is the rearranged version to show capital as a function of the rental rate, wage rate, and labour?
An isocost line shows all of the input combinations that yield the same cost
C = RK + WL
C = total cost
R = rental rate of capital
W = wage rate of labour
Rearranged:
K = (C/R) -(W/R)L
Where/how do we find the minimum cost point for a production function? (+ what’s the rearranged version of the equation)
The minimum cost will be the tangent point between the isoquant line and the isocost line > this occurs where the slopes of each line are equal
- W/R = - MPL / MPK
OR –> MPK / R = MPL / W
(this rearranged version shows the costs are minimized when the marginal product per dollar spend is equalized across inputs)
IF
MPK / R > MPL / W, what does this imply?
MPK / R < MPL / W, what does this imply?
- the marginal product per dollar spend on capital is higher than the marginal product per dollar spend on labour (or capital is more productive) –> this means more capital and less labour should be used in production
- the marginal product per dollar spend on capital is less than the marginal product per dollar spent on labour (or labour is more productive) –> this means more labour and less capital should be used in production
What does returns to scale refer to?
Refers to the change in output when all inputs are increased in the same proportion
- if the sum of the exponents in the Cobb-Douglas production equal 1 then they have constant returns to scale (doubling inputs equals a doubled output)
What do increasing and decreasing returns to scale mean? what is important to note about decreasing returns to scale
Increasing: changing all inputs by the same proportion changes output more than proportionally - doubled inputs = more than doubled outputs (sum of exponents > 1)
Decreasing: changing all inputs by the same proportion changes output less than proportionally - doubled inputs = less than doubled outputs (sum of exponents < 1)
*firms should NOT experience decreasing returns to scale (often is a result of just data input errors)
Why might a firm experience increasing returns to scale?
because of fixed costs > they do not vary with output (meaning they will get spread out across the increasing units of output and therefore our marginal cost is decreasing)
learning by doing > a firm develops more efficient processes as it expands or produces more output
What does total factor productivity growth refer to? What is the equation?
Total factor productivity growth is an improvement in technology that changes the firm’s production function such that more output is obtained from the same amount of inputs
Often it’s assumed to enter multiplicatively with production, for the following equation:
Q = Af(K,L)
A = level of total factor productivity
What is the production function expansion path? How does this relate to the total cost curve?
Expansion path = a curve that illustrates how the optimal mix of inputs varies with total output > connects different cost minimizing points that pertain to different quantities
(vertical axis = K and horizontal axis = L)
**it allows us to construct the total cost curve, which shows a firm’s cost of producing particular quantities
(vertical axis = total cost and horizontal axis = total quantity produced)
How do diminishing marginal returns and returns to scale differ?
Diminishing marginal returns refer to short-run changes, while returns to scale are a long-run phenomenon because we are changing all inputs simultaneously > therefore we should not have diminishing returns to scale because we can change both inputs
Can technological changes change isocost lines? What about isoquant lines?
Won’t change isocost lines > because the prices of inputs are fixed
Will affect the isoquants > An increase in A means that the same number of inputs will produce more output - also implying that the same output can be made with fewer inputs - can shift the isoquant towards the origins (good!)
