7 Modelling the Production Process

Question 1

Inputs and outputs of the production process

Answer 1

Two inputs: capital K, and labour L

A single output: y

Question 2

Define production set

Answer 2

The production set is the set of all technically feasible combinations of inputs and outputs.

Question 3

How can we show the production set for a single input?

Answer 3

Where A is a feasible, but not desirable (able to increase output, or decrease inputs).

B is just feasible and desirable.

Question 4

How can we show the production function?

Answer 4

The boundary of feasible and technically efficient input-output combinations.

Question 5

How can we show the production set for two inputs?

Answer 5

As a 3D version.

Question 6

What is a Cobb-Douglas production function?

Answer 6

y = K^aL^b, where y is the output, K measures capital inputs, and L measures labour inputs.

Question 7

What is meant by no free lunch?

Answer 7

If no inputs are used, no output is created.

Question 8

What is the property of inaction? Diagram?

Answer 8

Doing nothing is always feasible, that is (input, output) = (0,0) is in the property set:

Question 9

Does the property of inaction hold?

Answer 9

Time horizon matters here: it may not hold in the short run due to sunk costs.

Question 10

What are sunk costs? Diagram?

Answer 10

Inputs that must be initially committed before production can start.

Here, bar{x} is the least that must be committed in the short run.

Question 11

When might we consider capital to be fixed? or dynamic?

Answer 11

In the short run, capital is temporarily fixed. In the long run, it is freely variable.

Question 12

How can we illustrate decreasing returns to scale?

Answer 12

This means that output increases by less than inputs increase.

As inputs increase, average product of inputs (given by the dotted line) decreases as its slope decreases.

Scaling up past the production set boundary is infeasible.

Question 13

How can we illustrate increasing returns to scale?

Answer 13

This means that output increases by more than inputs increase.

Scaling down is infeasible.

Question 14

How can we illustrate constant returns to scale?

Answer 14

Output increases by the same degree as inputs increase.

Both scaling up and down are feasible here.

Question 15

How can we determine the type of returns to scale of a Cobb-Douglas production function?

Answer 15

Question 16

How can we show isoquants in a 3D model and 2D model of production?

Answer 16

Question 17

Three characteristics of isoquant lines

Answer 17

1. Further from the origin → the greater the level of associated output.
2. They slope downwards (convexity) - otherwise inconsistent with efficiency
3. They never cross - otherwise inconsistent with efficiency

Question 18

How do we get equations for isoquants? Cobb-Douglas?

Answer 18

Question 19

What does marginal product measure?

Answer 19

Marginal product measures the effect of a small increase in the input on the output.

Question 20

For Cobb-Douglas production function y = K^aL^b what is the marginal product of capital?

Answer 20

Question 21

For Cobb-Douglas production function y = K^aL^b what is the marginal product of capital?

Answer 21

Question 22

What is the slope of the isoquant called?

Answer 22

Marginal Rate of Technical Substitution (MRTS), it gives us the rate at which inputs can be substitutes for the other without disturbing output.

Question 23

How does MRTS change along a Cobb-Douglas production function?

Answer 23

It gets smaller and smaller (convexity).

Question 24

Perfect substitutes: diagram and MRTS equation

Answer 24

MRTS never changes, thus is linear downwards.

Question 25

Perfect complements: diagram and MRTS equation

Answer 25

MRTS is zero.

NOTE: you can illustrate rays going through point A and higher levels of output.

Question 26

MRTS equation involving capital and labour, and MPL and MPK

Answer 26

Question 27

Calculate MRTS for y = K^aL^b using MPL/MPK methods

Answer 27

Question 28

Calculate MRTS for y = K^aL^b using the isoquant method

Answer 28