CAE 3 (2017)

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 Universidad Universidad de Barcelona (UB) Grado Administración y Dirección de Empresas - 1º curso Asignatura Microeconomía Año del apunte 2017 Páginas 4 Fecha de subida 19/06/2017 Descargas 2 Puntuación media Subido por jbayona75

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CAE 2 1. Fill the gaps according to the production concepts in the short run: L Q MPL APL 0 0 0 0 1 150 150 150 2 400 250 200 3 600 200 200 4 760 160 253,333 5 910 150 182 6 900 -10 150 2. The production function of a company is: (K=1) Q = 3KL2 – 1/3KL3 – 5KL a) APL? MPL? When does this production function make sense (in terms of number of workers)? As K=1 the function is Q = 3L2 – 1/3L3 – 5L APL = Q L MPL = ∂Q ∂L = (3L2 – 1/3L3 – 5L) / L; ; APL= 3L – 1/3L2 – 5 MPL = 6L – L2 – 5 This production function make sense when the number of workers is between 3 and 6, because within this two numbers productivity increases, above 6 or below 3 it will decrease.
b) Determine what stage the company produces when L = 3.
APL (3) = 3·3 – 1/3 · 32 – 5; APL = 1 MPL (3) = 6·3 – 32 – 5; MPL = 4 CAE 2 c) Calculate the maximum quantity of production the company can produce.
Q’ = 0; 6L – L2 – 5 = 0; L2 – 6L + 5 = 0 L1 = 5 L= − ( −6 ) ± √ 6 −4 ·1 ·5 2·1 = 6 ± √ 16 2 6± 4 2 = L2 = 1 As K=1 the function is Q = 3L2 – 1/3L3 – 5L Then we compute the results obtained before: Q(5) = 3·52 – 1/3 · 53 – 5L = 25/3 Q(1) = 3·12 – 1/3 · 13 – 1L = -7/3(As it’s a negative result it can’t be the solution) So we have that the maximum quantity that this company can produce is 25/3 that can be reached when L = 5.
3. Given the production Q = 4K2L. Calculate the total cost function in the long term knowing that wage is 10 and the interest rate 20.
TC = K · r + L · w; TC = 20K + 10L; Q = 4K2L; L = Q / (4K2) TC = CF + CV; TC = 20K + 10Q / (4K2) 4. The total revenue of a company comes from TR= 20Q – 4Q2 and TC = 4Q a) Maximum profit? TR’ = 20 – 2·4Q; TR’ = 20 – 8Q TC’ = 4 TC’ = 4 MaxP = TR’ – TC’; MaxP = 20 – 8Q – 4 MaxP = 16 – 8Q; 16 = 8Q; Profit = TR – TC Profit = 20Q – 4Q2 – 4Q Max profit = 20 · 2 – 4 · 22 – 4 · 2 Max profit = 16 Q= 2 CAE 2 b) Calculate the maximum total revenue TR = 20Q – 4Q2 MaxTR = TR(2) = 20·2 – 4 · 22; MaxTR= 24 c) Determine the maximum number of units that the company can sell without incurring losses.
B = TR – TC; B = 20Q – 4Q2 – 4Q; B = 16Q - 4Q2 Q1 = 0 (not useful) B = Q ( 16 – 4Q) = 0 Q2 = 16/4 = 4 B (4) = 16 · 4 – 4 · 42 = 0 The maximum number of units that the company can sell without losses is 4 units.
CAE 2 5. ATC of five factory sizes that a company can build to produce steel Size 1 Size 2 Size 3 Size 4 Size 5 Q ATC ATC ATC ATC ATC 1 15,50 18,00 - - - 2 13,00 15,50 - - - 3 12,00 12,00 - - - 4 11,75 10,00 - - - 5 13,00 9,50 10,00 - - 6 15,00 11,00 8,50 - - 7 - 14,00 8,00 - - 8 - - 8,50 10,00 - 9 - - 10,00 9,50 12,00 10 - - - 10,00 11,00 11 - - - 12,00 11,50 12 - - - 15,00 13,00 13 - - - - 16,00 .
a) Quantity of production with minimum ATC in the short term for each size.
Bold Red = minimum ATC per size b) Calculate the ATC in the long run for each level of production.
Q Min AT M 1 2 3 4 5 6 7 8 9 10 11 12 13 15,5 0 13,0 0 12,0 0 10,0 0 9,5 0 8,5 0 8,0 0 8,5 0 9,5 0 10,0 0 11,5 0 13,0 0 16,0 0 c) Optimal production in the long term (long term breakeven production) The optimal production in the long term is the one selected in bold Blue and corresponds to the factory of size 3.
d) Represent the ATC envelope curve in the long run.
ATC envelope curve in the long run 18 16 14 12 10 8 6 4 2 0 ATC envelope curve in the long run 0 2 4 6 8 10 12 14 ...

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