CPT- Core Producer Theory Flashcards
In CPT, what are we looking to break down the price effect into?
- Output effect
* Substitution effect
What are we looking for in CPT?
We are looking to break down the effects of a change in price of an input- in the case of long-run perfect competition, into output and substitution effects.
Under CPT, what do we label our axes?
- Capital (K) on the y-axis
* Labour (L) on the x-axis
What happens to the slope of the isocost line when wages fall?
The slope of the line becomes flatter as the cost of labour has fallen
What happens to the production function if wages fall?
We get a new production function, which is a new isoquant further away from the origin.
What do points a, b, and c represent?
- Point a represents the point at the inital wage, which is the best the firm can do guven that they face a given wage and a given rental rate
- Point b represents the new production point on the new isoquant after wages have fallen
- Point c represents where the firm would be if under new prices they produced the same level of output.
How do we find where the firm would be if under new prices they produced the same level of output?
By shifting back the new isocost line tangential to the original isoquant.
How do we work out points a and b, and therefore what is a little tip we can use here?
a and b are both calculated using profit maximisation, so instead of inputting the initial wage, jus input w so then we can work out both points with the same bit of maths!
How is point c found?
Via cost minimisation
As L is on the horizontal axis and K is on the vertical axis, we are said to be working in what space, and what is the significance of this?
- We are said to be working in the (L,K) space, therefore at the tangencies the Marginal Rate of Technical Substitution in the (L,K) space is equal to the wage-rental ratio.
- ie MRTSlk = w/r
How do we work out how to maximise profit in a firm?
- Differentiating the profit function with respect to L and setting to 0- ie πL = ∂π/∂L = 0
- Differentiating the profit function with respect to K and setting to 0- ie πK = ∂π/∂K = 0
- Solve simultaneously to find K
- Plug this back into an equation
- Solve for L
Under profit maximisation, what do the solutions for L* and K* give us?
The firms factor demand functions
How do we work out how to minimise cost in a firm?
We minimise cost at the new wage subject to achieving this output, hence we minimise the Lagrangean:
• ℒ=wL+rK+λ(Q1- Q(L,K))
• Find the first order conditions for L, K and λ
• Solve simultaneously to find our co-ordinate for point C
Under cost minimisation, what do the solutions for L’ and K’ give us?
The solution (L’,K’) yields the firm’s conditional factor demand functions (conditional on achieving the target level of output)
