Midterm 2

Question 1

Production Function:

Answer 1

Q=f(K, L)
K= Capital - machines, tools, etc.
L= Labor
Q = output
Q is interchangeable for TP
TP = Total Product

Question 2

Linear Production Function

Answer 2

Q = K+L

Question 3

Cobb-Douglas Production Function

Answer 3

Q = K^.5L^.5

Question 4

Fixed Proportion Production Function

Answer 4

K and L are used together in a fixed proportion (similarly to perfect complements).

Question 5

Technological Change

Answer 5

A change in L and/or K that represents a change in output.
Ex:
Q=K+L → Q=2K+L
Q=K^.5L^.5 → Q=10K^.5L^.6

Question 6

Average Product (AP):

Answer 6

Measures how many units of product a worker can produce on average.
AP(L) = Q/L
AP(K) = Q/K

Question 7

Marginal Product (MP):

Answer 7

When the firm hires one more worker/purchases another unit of capital, its output increases. Measures the increase in output of the last worker/capital.
MP(L) = derivative Q/derivative L
MP(K) = derivative Q/derivative K
(Essentially the partial derivative of K or L)
ex:
MP(L) Q=K+L → MP(L) = 0+1 →
MP(L) =1

Question 8

Marginal Product of Fixed Proportion Product Functions:

Answer 8

MP always = 0 for Fixed Proportions.

Question 9

What is the name of the curve for a production function?

Answer 9

Isoquant.

Question 10

What is an isoquant?

Answer 10

Isoquant - The curve that shows the various combinations of inputs that will produce the same output.
x-axis is always labeled at L
y-axis is always labeled as K
K-intercept is = Q/MPK
L-intercept is = Q/MPL

Question 11

What is the slope of an isoquant called?

Answer 11

Slope of an isoquant → (-) Rate of Technical Substitution (RTS)
- Shows the amount of input that must be substituted for another to maintain constant output

Question 12

How do you find the RTS?

Answer 12

RTS = MPL/MPK
Slope = (-)MPL/MPK

Question 13

What are Returns to Scale?

Answer 13

Measures the change rate in output in response to proportional changes in all inputs
i.e. change all inputs by the same amount and see how it affects output.

Question 14

What is the equation for an isocost and what are the characteristics of it?

Answer 14

Equation: TC = WL + VK
w = wage (price of labor)
v = price of capital
TC = Total Cost
Curve is always linear, infinite isocost for varying levels of cost
- if w↑, isocost steeper, if w↓, isocost flatter
- if v↑, isocost flatter, if v↓, isocost steeper

Question 14

Three types of Returns to Scale:

Answer 14

• Constant: When all inputs are doubled, the output is doubled
• Increasing: When all inputs are doubled, the output is more than double
• Decreasing: When all inputs are doubled, the output is less than double.

Question 14

How do returns to scale affect Linear and Fixed Proportion production functions?

Answer 14

The returns to scale for Linear and Fixed Proportions are always constant returns to scale.

Question 15

Cobb-Douglas Returns to Scale:

Answer 15

If sum of exponents:
>1, increasing returns to scale
<1, decreasing returns to scale
=1, constant returns to scale

Question 16

What is the cost curve for the production function called?

Answer 16

Isocost.

Question 17

How do you find the slope of an isocost?

Answer 17

w/v.

Question 17

Isoquant + Isocost:

Answer 17

At the optimal combination of outputs, isocost is tangent to the isoquant, slope of isoquant = slope of isocost.
RTS = w/v
MPL/MPK = w/v
MPL/w = MPK/v

Question 18

What is Marginal product per dollar spent on K or L?

Answer 18

MPL/w = MPK/v. Whichever is greater tells us which input the firm should use more of, because it is relatively cheaper.

Question 19

What is the Expansion Path?

Answer 19

The curve that passes through the tangency points between isocosts and isoquants.
Tangency points are the points that are cost minimizing combinations of inputs for each level of output.

Question 20

How do short run and long run curves differ in relation to inputs?

Answer 20

Short run has at least some fixed input, while the long run has no fixed inputs.

Question 20

What does the Expansion Path look like for Linear Production Functions?

Answer 20

It is a straight line that follows one of the axis (either L or K axis), depending on which one is relatively cheaper.
If K and L relatively cost the same, the expansion path is a diagonal line with the slope of 1/1 starting from the origin, signifying that L = K.

Question 21

What is the Cost Function?

Answer 21

TC = f(Q) TC = WL + VK

Question 22

Cost Function for Linear Production Function:

Answer 22

We are given a Linear production function, e.g. Q = 3L +2K, w = 30, v = 40, and we want to find the Cost function, TC = WL + VK for this equation. - First find MPL/w and MPK/v, and whichever value is greater is relatively cheaper, which is what we will consume. - Whichever is relatively more expensive will be set to 0, because we will never consume it for Linear Production Functions. - In this case, L is relatively cheaper, so K is 0. Now solve for L in terms of Q, and you get L = Q/3. Now plug all your values into your Cost Function, and get : TC = WL +VK TC= 30 * Q/3 + 0 TC = 10Q → This is our Cost Function

Question 23

Cost Function for Cobb-Douglas Short Run:

Answer 23

We begin with a Cobb-Douglas production function, e.g. Q = K^.5L^.5 , we are given w = 2, v =1, and one fixed input, e.g. K=400. - Substitute K into our production function, and solve for L in terms of Q and get: L = Q^2 / 400. - We have our cost function TC = WL + VK , substitute all values in: TC = 2(Q^2 / 400) + 1*400 →TC = Q^2 / 200 +400 -- This is our cost function.

Question 23

Cost Function for Fixed Proportion Production Functions:

Answer 23

We start with fixed proportions set to a level of output, e.g. 1 worker and 2 clippers produce Q = 100, w= 10, v =2. To find the cost function, TC = WL + VK, we do: w * # of L + v * # of K = TC for a specific level of Q. Finally, divide TC by Q to find cost of producing one unit, TC/Q. - In this case: 10 * 1 + 2 * 2 = 14 ; 14/100 is the cost in dollars of producing one unit. So our TC equation would be TC = .14Q

Question 24

Average Cost (AC or ATC) and Marginal Cost (MC):

Answer 24

Marginal Cost = Derivative TC/ Derivative Q (basically take the derivative of TC equation) Average Cost or Average Total Cost = TC/Q. - ATC curve is bowl shaped MC = AC at the turning point (minimum) of AC curve. If MC < AC, then AC ↓ If MC > AC, then AC ↑

Question 25

Average Variable Cost (AVC) and Average Fixed Cost (AFC):

Answer 25

Average Variable Cost is a cost that changes, bowl shaped, less than ATC curve. Average Fixed cost is a fixed cost than lessens over time, decreasing curve. AFC + AVC = ATC MC = AVC at the turning point (minimum) of AVC curve.

Question 26

Profit Maximization:

Answer 26

Profit (π) = Total Revenue (TR) - Total Cost (TC) π = TR - TC Marginal Revenue (MR) = derivative of TR Marginal Cost (MC) = derivative of TC When MR = MC, we have profit maximization. If MR > MC, Q ↑ If MR < MC, Q ↓

Question 26

Profit Maximization for Perfectly Competitive Markets:

Answer 26

- Firms are Price Takers - Marginal Revenue = Price (MR =P) - We know MR = MC at profit maximization - Therefore, MC = P at profit maximization.

Question 27

Marginal Cost and its relation to Price for Perfectly Competitive Markets:

Answer 27

- Marginal Cost (MC) above the AVC curve is equal to the supply curve. - MC shows the relationship between Price and Supply - When Price <= MC @ the AVC curve, the firm will shut down because it does not make enough to cover its fixed costs. - When Price >= MC @ the AVC curve, the firm stays open, even if MC is less than ATC curve.