Producer theory, technology & profit Flashcards
What are the three types of inputs?
Labour, land and capital.
What is the production function?
It measures the maximum possible output that a representative firm can produce from a given input.
What’s an isoquant?
Shows all the combinations of inputs (capital and labour) that produce the same output.
What are the three technology assumptions?
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.
What is marginal productivity?
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
What rate does marginal productivity increase at with the changes in input?
Diminishing rate. When input increases after a while the additional product derived from this increase reduces.
What is TRS?
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.
How can you link marginal rate of substitution with technical rate of substitution?
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
What is returns to scale?
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)
How can you tell if a production function has diminishing returns to scale ?
If the new quantity is smaller than K(x1,x2… xn)
How can you tell if a production function has increasing returns to scale?
If the new quantity is larger than K(x1,x2… xn)
Name three types of methods of productions?
- Fixed proportions
- Perfect substitutes
- Cobb douglas function
What is the fixed proportion method of production?
- Much like perfect compliments
- L shaped graph
- Depicts unsubstitutable relationship between capital and labour.
- f(x,z)=min(ax,bz)
What is the perfect substitutes methods of production?
- diagonal graph
- f(x,z)= ax + bz
What is the cobb douglas method of production?
-f(x,z)= A(t)x^az^b Where A(t) is representative of how technology changes over time.
What can you infer from the cobb douglas function?
if a+b=1 the production function has constant returns to scale.
a+b>1 increasing returns to scale
a+b
What is the only goal firms can pursue and why?
-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.
How is profit maximised?
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.
How can you tell profit is maximised?
dπ/dq=dr(q)/dq-dc(q)/dq=0
and secondly
d^2π/dq^2=dmR(q*)/d^2-dmC/dq^2
