# CAE 4 (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 0 Puntuación media Subido por jbayona75

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CAE 4: PERFECT COMPETITION CAE 4: PERFECT COMPETITION 1. In a perfectly competitive market, where demand function is P = 40 – 0,01QD, involved 200 companies with a short term production function: q = 2 L0,5, fixed costs 25€ and wage per worker 4€.
a) Get all the short term costs functions of the representative company and represents them graphically.
TC = 25 + (4 x Q2) / 4 ; TC = 25 + 4L ; TC = 25 + Q2 40 35 30 25 CT CF 20 15 10 5 0 0 0.5 1 1.5 2 2.5 3 3.5 4 b) Obtain the supply function of each individual company and the market supply.
MC = TC’= P; MC = 2Q = P; Individual supply Q = 0,5 P Market supply Q = 200 x P/2 ; QS =100 P CAE 4: PERFECT COMPETITION c) Find the equilibrium price and quantity in the short term.
QS = 100 P P = 40 – 0,01QD; QD = (40 – P) /0,01 QS = QD 40 – P =100 P x 0,01; P = 40/2 =20 Q(20) = 2000 40 35 30 25 20 15 10 5 0 0 1000 2000 3000 4000 d) What are the benefits of each company in the short term.
TB = TI – TC; TB = (20 x 10) – (25 + 102) = 75 e) In the long term there is a complete freedom of entry of new companies in the market and all of them can operate with a minimum average costs of 10€ for q=10, what will be the equilibrium price and quantity, the number of companies and the benefits for each? Q = 4000 – 100P; Q = 4000 – 100 · 10 = 3000 QS = QD; 3000 = 4000 – 100P; Pe = 10 Qe = 3000 3000/10 = 300 empreses CAE 4: PERFECT COMPETITION 2. In a perfectly competitive market which fixed costs of 20€, hourly wage 5€ and the following table: a) Complete the table with the values of average productivity of labor, marginal productivity of labor, total costs, variable costs, average costs and marginal costs.
L Q APL (Q/L) MPL (∂Q/∆L) TC (CF+CV) AVC (CV/Q) ATC (CT/Q) MC (∂TC/∂Q) 1 10 10 10 25 0,5 2,5 0,5 2 25 12,5 15 30 0,4 1,2 0,33 3 55 18,3 30 35 0,27 0,63 0,17 4 70 17,5 15 40 0,28 0,57 0,33 5 80 16 10 45 0,31 0,56 0,50 6 85 14,2 5 50 0,35 0,59 1 7 88 12,6 3 55 0,40 0,63 1,67 b) If the market price in the short term is 1€, which will be the production of each individual company and the level of benefit? Max B when P = MC; TB = TI – TC; TB = 1 · 85 – 50; P =1; MC = 1; Q =85 TB = 35 c) If the state imposes a price ceiling of 17cents, which will be the production level of each individual company and the level of benefit? P = MC; P = 0,17; MC = 0,17; Q = 55 TB = TI – TC; TB = 0,17 · 55 – 35; TB = -25,65 3 2.5 2 ATC AVC MC 1.5 1 0.5 0 0 10 20 30 40 50 60 70 80 90 100 CAE 4: PERFECT COMPETITION 3. In a perfectly competitive market, the demand is given by Q D = 2000 – 100P, and the long term total costs function of the companies is CT(q) = 2q3 – 4q2 + 20q a) What will be the price of the product in the long term? ATC = (2q3 – 4q2 + 20q) / q; ATC = 2q2 – 4q + 20 ∂ATC / ∂Q; MC = 4q – 4; Q=1 MC = ∂TC = 6q2 – 8q + 20; MC (1) = 18 P = MC; P = 18 b) What will be the market production equilibrium, the production of each company and the number of companies participating in the market? QD = 2000 – 100 · 18; QS = QD; 200 = 2000 – 100P; QD = 200 Pe = 18; Qe = 200 200 / 1 = 200 empreses c) If a technological innovation allows to produce with the following total costs function TC = q2 + 2q; and the state decides to limit the participation in the market giving only 40 licenses to 40 companies, what would be the market equilibrium price and the market equilibrium production and the production of each company? P = MC = ∂TC; P = 2q + 2; Q = (p-2) / 2 Qs = ( (p-2) / 2 ) · 40; Qs = 20p – 40 Qd = Qs; 2000 – 100p = 20P – 40; Pe = 17 Qe = 20 · 17 – 40 Qe = 300 d) What are the business benefits of the first situation (a) and (b) and what are the total profits in the second case with barriers to entry (c)? Benefits a and b: TB = TI – TC; TB = 1·18 – (2·13 – 4·12 + 20·1); TB = 0 Benefits c: Q = (17- 2) / 2; Q = 7,5 TB = TI – TC; TB = 7,5 · 17 – 7,52 + 2 · 7,5 TB = 56,25 ...

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