T4: PRODUCTION AND COSTS Flashcards
What does the production function show?
The maximum quantities of a product that can be obtained from the production factors F (K,L).
K= Capital L= Labor
Returns to scale
- Y2 = Y1 : Constant
- Y2 > Y1 : Increasing
- Y2 < Y1 : Decreasing
Average Productivity (AP)
It equals the units of output produced per unit of a factor of production.
The higher the average product, the more productive a factor of production is.
AP= Q/L
Marginal Productivity
It is the change in output that results from one additional unit of a factor of production.
MP = TP’
Makes sense to hire an employee if:
MP(L) > Wage (W)
On a table how do you calculate APL and MPL
APL = Q/L
MPL = Q2 - Q1
Technical Maximum
The highest level of production possible with the available resources and technology.
Punto más alto en el prodcuction function.
To calculate: Maximize Total Production (MP=0)
Technical Optimum
The point of greatest efficiency in resource usage to achieve a given level of production.
Point in Marginal Productivity curve, where it intersects with the Average Productivity.
To calculate: Maximize Average Productivity
Total Cost Function
TC = w * L + r * K
w + L = Variable Costs
r + K = Fixed Costs
Como Encontrar el Cost Function
- Poner en el TC Function los datos que tenemos.
- Aislar la variable que nos falte en la función TC, de la función de producción.
- Sustituir resultado en función TC.
Average Total Costs
Represents the cost per unit produced
ATC = TC / Q = AVC + AFC
Average Fixed Costs
The proportion of fixed costs attributed to each unit produced
FC / Q = R*K/2
Average Variable Costs
The proportion of average costs attributed to each unit produced.
- The more productive I am (AP is high), the lower the AVC
- At the technical optimum, AVC is minimised, as it is where AP is maximised
AVC = VC/Q = WL/Q = W1/AP
Marginal Cost
The cost of producing one additional unit: The variation in total cost when Q, increases by one unit.
MC = TC’
Cost Function in Perfect Competition
- Línea Large (Símbolo Nike): Coste Marginal
- Línea más abajo (Exponencial de arriba-abajo): Average Fixed Cost
- Siguiente Línea (Sonrisa): Average Variable Cost
- Línea por encima (Distancia entre ambas en lado izquierdo es más amplia, luego se van juntando): Average Total Cost
Datos de Cost Function in Perfect Competition
- Distancia entre ATC y AVC es el Average Fixed Cost.
- Desde la Intersección entre el ATC y el MC (Break-even point), hacia arriba. La empresa genera beneficios.
- Intersección ATC y MC = Breakeven Point. Profit = 0.
- Intersección AVC y MC = Shut Down Point. Desde ese punto hacia abajo, la empresa cierra.
- Entre las curvas de ATC y AVC, la empresa esta generando perdidas recuperables. Aún no cierra.
- Perdidas Recuperables quiere decir que cubro mis Costes Variables, pero no los Fijos.
- Shut down point. Más abajo no puedo cubrir VC.
What rule do all companies operate under?
Price = Marginal Cost
It is the condition of maximum profit.
Situation of Profits Graphically
Area desde el precio (Por encima de ATC) hasta el ATC. Todo el rectángulo.
Situation of Recoverable Losses Graphically
Desde el precio (Entre AVC y ATC) hasta ATC. Todo el rectángulo.
Individual Supply Function + Its Equation
It is the quantity a firm will produce based on the following factors: Market Price, Price of inputs and its Technology.
General Equation:
0 si P < Pmin SDP
P = MC si P >= Pmin SDP
Como calcular encontrar Indivual Supply
Primero: Calcular SDP
- AVC = MC or AVC’ = 0 :
AVC = VC / Q - Sé que VC es todo lo que en la función de TC tenga una Q.
- Cojo de la Función todo lo que tenga Q y lo divido por Q.
Ejemplo:
TC (Q) = 2Q^3 - 8Q^2 + 10Q +10
2Q^3-8Q^2+10Q / Q = Q^2 - 8Q + 10
- El resultado lo derivo, lo igualo a 0 y encuentro Q
4Q - 8 = 0
Q = 2
- Sustituyo en MC o AVC, para encontrar el precio de SDP
Segundo: Forma de Oferta
- Seguir Condición de P = MC
- Derivas función de TC. P = TC’
- Rearrange so it equals 0 (Move P into the equation).
- Lo pones en la función e resolver cuadráticas y lo pones en Q=
Alternatively, or
Q= c *(K/a+L/b)
And, with, combining
Q= cmin(K/a,L/b)
0 if L doesn’t increase proportionally.
Marginal if L increases proportionally
Long term Perfect Competitive Firms
In the long run, because in perfect competitive markets there are no entry barriers, many businesses will enter the market (if profit generating). This will lead to an increase in supply and a reduction in Price. As a result, profits will keep shrinking until the businesses reach zero economic profits. So, in the long term production will always start at a zero economic profits point, thus never having losses.
Why is the AVC curve U shaped?
We look at the marginal productivity graph. 1. Increasing Returns: Every employee contributes more than the last one. 2. Decreasing Return: Every new employee contributes less, but MP is still above AP. 3. Negative Returns: New employee makes AP decrease. I have used and exploited all my resources optimally. I have surpassed efficiency point. Efficiency decreases.
The inverse of this curve is the AVC curve. The highest point in te AP curve is the lowest in the AVC because: AVC = W*L/Q. When my output is at its highest (highest efficiency), my AVC are at its lowest.
