CAE 3 (2017)

Ejercicio Inglés
Universidad Universidad de Barcelona (UB)
Grado Administración y Dirección de Empresas - 1º curso
Asignatura Microeconomía
Año del apunte 2017
Páginas 3
Fecha de subida 11/07/2017
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Group B6 Delfina Andrade Continuos assessment exercise 3  1.      Fill the gaps in the table below according the production concepts in the short run: L Q 0 MPL APL 0 - - 1 150 150 150 2 400 250 200 3 600 200 200 4 760 160 190 5 910 150 182 6 900 -10 150  2.      The production function of a company is given by the expression Q = 3KL2 – 1/3K L3 – 5KL. Knowing that K = 1: a)      Determine the following function: the Average Productivity of Labour (APL) and the Marginal Productivity of Labour (MPL). When does this production function make sense (in terms of number of workers)? APL= (3L2 – 1/3L3 – 5L)/L= 3L-1/3L2-5 MPL= 6L-1L2-5/1= 6L-L2-5 This production make sense when L is a number grater than 0, because therefore we would not have any workers and production would not be possible.
b)      Determine what stage the company produces when L = 3.
Q=3*9-1/3*27-15= 3 APL= 3/3= 1 MPL= 0 c)      Calculate the maximum quantity of production the company can produce.
Q=3L2-1/3L3-5L Q’=6L-L2-5=0 —> L1=1. L2= 5 Q(5)= 3*25-1/3*125-25= 8,33 Then, the maximum quantity of production the company can produce is 8’33.
Group B6 Delfina Andrade 3.      Given the production function of a firm: Q = 4K2L.  Calculate the total cost function in the long term, knowing that the wage is 10 (w = 10) and the interest rate is 20 (r = 20).
TC=(L*W)+(K*r) TC=(10L+20K) TC=30*(Q/4)1/3 Q=4K2L MPL/MPK=w/r 4K2/8KL= 10/20 —> K=L —> Q=4K3—> K=(Q/4)1/3 4.      The total revenue of a company comes from the expression TR = 20q – 4q2 and its total cost function TC = 4q. It asks: a)      Calculate the maximum profit that can get this company.
B=TR-TC B=20q-4q2-4q B=-4q2+16q B’=-8q+16=0—> q=2 —> B(2)= 20*2-4*4-4*2= 16 The maximum profit the company can achieve is 16.
b)      Calculate the maximum total revenue.
dTR/dq=20-8q=0 —> q=2’5 The maximum total revenue is 2’5.
c)      Determine the maximum number of units that the company can sell without incurring losses.
B=0 —> B=TR-TC=0 —> TR=TC 20q-4q2=4q —> -4q2+16q —> q=4  5.      These are Average Total Costs (ATC) or Unitary Costs corresponding to  five different factory sizes that a company can build to produce steel: Group B6 Delfina Andrade It asks: a)      Quantity of production with minimum ATC in the short term for each size Size 1—> Minimum ATC at quantity 4 Size 2—> Minimum ATC at quantity 5 Size 3—> Minimum ATC at quantity 7 Size 4—> Minimum ATC at quantity 9 Size 5—> Minimum ATC at quantity 10 b)      Calculate ATC in the long run for each level of production (1 ≤ Q ≤ 13) Quan tity 1 2 3 4 5 6 7 8 9 10 11 12 13 ATC 15 13 12 10 9,5 8,5 8 8,5 9,5 10 11,5 13 16 c)      Optimal production in the long term (long term breakeven production) The optimal production in the long run is the one that has the minimum unitary cost, in this case is the size 3 with a ATC of 8.
d)     Represents the ATC envelope curve in the long run ATC 16 12 8 4 0 1 2 3 4 5 6 7 8 9 10 11 12 13 ...

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