3- Diffrentiation Flashcards
Quotient rule
y= u/v
dy/dx= (v(du) - u(dv)) / v^2
Derivative of e^x
e^x
Derivative of lnx
1/x
Derivative of ln2x
1/x
Derivative of total revenue
marginal revenue
Change in revenue approximation equation
Change in revenue = marginal revenue x change in demand
From the tangent on TR curve
How to work out total revenue?
P x Q
How to work out average revenue?
TR/ Q
Demand curve is the AR curve
Demand function for perfect competition
P= b
- Price an AR are constant
Total revenue for perfect competition
bQ
Marginal revenue of perfect competition
b
derivative of TR
Change in total cost approximation equation
change in total cost = marginal cost x change in output
What is marginal product of labour?
The derivative of output with respect to labour.
What is output assumed to be a function of?
L and K
L(labour)
K (capital)
Relationship between marginal product of labour and labour
As labour increases, MPL decreases- shows law of diminishing marginal productivity.
Law of diminishing marginal productivity
States an increase in labour will eventually decline marginal output. Once the size of the workforce has reached a certain threshold, the marginal product of labour will get smaller.
Elasticity equation
dQ/dP x P/Q
S.R production function- how to work out the max workforce to optimise output.
- Find second derivative of function and find max point value.
Where is the maximum point for APL (average product of labour)?
Where APL = MPL- due to law of diminishing returns.
Or find max point value using diffrentiation
How to find profit max quantity of monopoly firm?
Profit (pi) = TR (PQ) - TC (CQ)
Diffrentiate and find max point
Where does a monopolist profit maximise?
MC=MR
Second derivative when curve is concave upwards?
Positive
Second derivative when curve is concave downwards?
Negative
