Producer theory, technology & profit

Question 1

What are the three types of inputs?

Answer 1

Labour, land and capital.

Question 2

What is the production function?

Answer 2

It measures the maximum possible output that a representative firm can produce from a given input.

Question 3

What’s an isoquant?

Answer 3

Shows all the combinations of inputs (capital and labour) that produce the same output.

Question 4

What are the three technology assumptions?

Answer 4

Free disposal- A firm can have as many inputs as they want as there is no cost to get rid of them.
Convex- If there are two ways of producing the same amount of output., their weighted average will produce atleast the same output.
Long run and short run- In the short run some input variables may be fixed however in the long run all factors of production may vary.

Question 5

What is marginal productivity?

Answer 5

The additional output derived from implementing one additional unit of labour. e.g dq/dk=MPK marginal productivity of capital is the marginal product from an extra unit of capital. dq/dl is the marginal productivity of labour where the change in output (q) is measured from the result of an additional unit of labour

Question 6

What rate does marginal productivity increase at with the changes in input?

Answer 6

Diminishing rate. When input increases after a while the additional product derived from this increase reduces.

Question 7

What is TRS?

Answer 7

It is the slope of the isoquant curve. (example) dk/dl this shows how much of capital the firm is willing to give up for one additional unit of labour.

Question 8

How can you link marginal rate of substitution with technical rate of substitution?

Answer 8

1.Take the total differentiation of isoquant:
dq=dq/dl.dl+dq/dk.dk
which is:
dq= MPL.dl+MPK.dK
remember that for isoquants dq=0 so
-MPL.dL=MPK.dK
-MPL/MPK=dK/dL
-MPL/MPK=TRS

Question 9

What is returns to scale?

Answer 9

It is when all inputs of production are increased by the same factor in any direction causes a proportional change in output. e.g f(kx1, kx2…kxn)=kf(x1,x2…xn)

Question 10

How can you tell if a production function has diminishing returns to scale ?

Answer 10

If the new quantity is smaller than K(x1,x2… xn)

Question 11

How can you tell if a production function has increasing returns to scale?

Answer 11

If the new quantity is larger than K(x1,x2… xn)

Question 12

Name three types of methods of productions?

Answer 12

• Fixed proportions
• Perfect substitutes
• Cobb douglas function

Question 13

What is the fixed proportion method of production?

Answer 13

• Much like perfect compliments
• L shaped graph
• Depicts unsubstitutable relationship between capital and labour.
• f(x,z)=min(ax,bz)

Question 14

What is the perfect substitutes methods of production?

Answer 14

• diagonal graph

- f(x,z)= ax + bz

Question 15

What is the cobb douglas method of production?

Answer 15

-f(x,z)= A(t)x^az^b
Where A(t) is representative of how technology changes over time.

Question 16

What can you infer from the cobb douglas function?

Answer 16

if a+b=1 the production function has constant returns to scale.
a+b>1 increasing returns to scale
a+b

Question 17

What is the only goal firms can pursue and why?

Answer 17

-Profit maximisation
This because of two reasons: In the long run investors will not invest and without profits firms cannot survive to pursue other goals.

Question 18

How is profit maximised?

Answer 18

Graphically this is the point where the revenue curve is furtherest apart from the cost curve. At this point the slope of the revenue is equal to the slope of the cost. This means marginal revenue equals to marginal cost as they are slopes of the revenue curve and cost curve, respectively.

Question 19

How can you tell profit is maximised?

Answer 19

dπ/dq=dr(q)/dq-dc(q)/dq=0
and secondly
d^2π/dq^2=dmR(q*)/d^2-dmC/dq^2