C6 C7: Costs Flashcards
Conditions Profit max
- Find profit max Q
- Producing in an efficient way
Efficient production
Not being able to produce the current level of output with fewer/cheaper resources
Production Function
q=f(L,K)
L: labour in hours worked
K: Capital
In SR
K is fixed
(para las flashcards lo llamaremos K!)
Average Product of Labour: APL
q/L -> f(L,K)/L
(para K, cambias L por K)
Marginal Product of Labour: MPL
MPL: dq/dL -> df(L,K)/dL
(para K, cambias L por K)
Grafico APL, MPL
Grafico
MPL<APL
Law Diminishing returns
If a firm keeps increasing an input, holding the other constant (as well as tech etc) the corresponding increase in output will eventually become smaller
Law of diminishing returns calculo
dMP/dL < 0
Segunda derivada de la funcion f(L,K)
In LR
All factors can vary
Isoquant
A curve that gives all the different combinations of L and K that can produce a single level of output q! (fixed)
Isoquant for q!
q! = f(L,K)
Properties of Isoquants
- The further from origin the bigger the output
- Do not cross
- Downward slopping
- Cannot be thick
Isoquant graphs and equations
Perfect substitutes: AL+BK
Perfect Compliments: min[AL, BK]
Imperfect subs/comp: el resto
Grafico de cada uno
Slope isoquants
Marginal Rate of Technical Substitution (MRTS)
MRST
dK/dL
-MPL/MPK
Returns to scale
By what proportion the output of a firm changes when we increase all inputs by the same proportion
Constant returns to scale
If output rises by in the same proportion than inputs
Increasing returns to scale
If output rises more than in proportion to inputs
Decreasing returns to scale
If output rises less than in proportin to inputs
Opportunity cost
Value of next best alternative
Explicit Cost
Costs that are priced in the market
Implicit cost
Cost not explicitely priced in the market and not correspond to an explicit expenditure
Sunk cost
Unavoidable costs
SR Costs: Fixed costs FC
Arise from fixed inputs
SR Costs: Variable costs VC
Arise from variable inputs
VC= VC(q)
SR Costs: Total costs
Fixed + Variable
C(q) = FC + VC(q)
SR Costs: Marginal costs MC
dC(q)/dq
SR Costs: Average costs AC
Total costs/q
AFC + AVC
Graficos Costs, Average costs
Graficos
Interseccion de MC en los minimos de AC, AVC
As MC below AC, every unit decreases AC, when above every extra unit increases AC
Como hacer incremento de costes
Incremento en variables
Incremento en fijos
Costs in terms of inputs
C = rK + wL
Costs in terms of inputs: In SR
rK = fixed costs (K -> K!)
wL= VC (se puede hacer una funcion de q rearraging la equacion C= rK + wL)
Shape MC (SR)
MC(q) = w · 1/MPL
(para esto si lo tenemos en terminos de inputs se rearrange para tener en terminos de q)
-> Opposite shape q MPL (me la se)
Shape AVC
w·1/APL
Mismo razonamiento q MC
Shape me lo se
Shape AC
AC = rK/q + w/APL
Igual q AVC pero por encima
Grafico traduccion funcion f(L,K) a MPL, APL a MC, AVC,AC
Me lo se, pero vamos dibujar el grafico
Long run costs: Isocost Lines
A line showing all combinations of L and K that cost the same amount
Grafico
Long run costs: Optimal bundle
Grafico
Interseccion isoquant con isocost
Requerimientos optimal bundle
- Has to be on isoquant
q!= f(L,K) - Slope isoquant = Slope isocost
MRTS = -MPL/MPK tiene q ser igual q -w/r
Encontrar optimal bundle
Con las ecuaciones de los requerimientos
Cost minimizing problem
min C(L,K) = wL + rK
st q!= f(L,K)
Substitution como siempre
Long run cost function def.
Gives us the total costs of a given q as a function of cost minimizing bundles of L and K for producing q
Long run cost function
C(q) = wL(q) + rK(q)
