MONOPOLIO

EJERCICIO 1: "Problemas de Microeconomía - Dieguez y Porto – Ejercicio 19

C= 50x + 120 P= -5x + 250

IT= Px= (- 5x + 250) * x Þ - 5 x² + 250x

Img= - 10x + 250

CMg= 50

B’= I’ – C’ Þ I’ = C’

-10x + 250 = 50 Þ -10x + 200 = 0 Þ x = 20

P₂₀ = - 5x + 250= -5 * 52 + 250= 150

IT₂₀ = - 5 x² + 250x= -5 * 20² + 250 * 20= 3.000

CT₂₀ = 50x + 120= 50 * 20 + 120= 1.120

B₂₀ = 3.000 – 1.120= 1.880

B= IT – CT + 30x

= -5x² + 250x – 50x –120 - 30x

= -5 x² + 170x = 120 Þ x = 17

P₁₇ = - 5x + 250= - 5 * 17 + 250= 165

IT17 = - 5 x² + 250x= – 5 * 17² + 250 * 17= 280

CT₁₇ = 50x + 120= 50 * 17 + 120= 1.480

B₁₇ = 280 – 1.480= 1.325

B= (1 – 0,5) I – C

= 0,95 (250X – 5x²) – (120 + 5x)

= 237x – 4,75x² – 120 –50x

= 4,75 x² + 187x –120= 0

Máx. B

B’= - 9,5x + 187= 0 Þ x= 19,6

P_19,6 = - 5x + 250= - 5 * 19,6 + 250= 152

IT_19,6 = - 5 x² + 250x= – 5 * 19,6² + 250 * 19,6= 2.830

CT_19,6 = 50x + 120= 50 * 19,6 + 120= 1.100

B_19,6 = I – C= 2.830 – 1.100= 1.730

B= 0,85 (I – C)

= 0,85 * ((-5 x² + 250x) – (50Xx+ 120))

= 0,85 (- 5 x² – 200x – 120)

= - 4,25 x² + 170x -102

B’= - 8,5x + 170 = 0 Þ x = 20

B"= - 8,5 < 0

P₂₀ = - 5x + 250= - 5 * 20 + 250= 150

IT₂₀ = - (5 * 15%) x² + (250 * 15%)x= – 4,75 * 20² + 237 * 20= 2.840

CT₂₀ = 50x + 120= 50 * 20 + 120= 1.120

B= (2.840 * 15%) - (1.120 * 15%) = 2.470 – 974= 1.496

B= IT – CT – t

IT= Px = - 5 x² + 250x

CT+ t= 50x + 120 + 120

= 50x +240

B= - 5 x² + 250x –50x –240 Þ - 5 x² + 200x –240

Máximo Beneficio

B’= - 10x – 200 Þ x= 20

B"= -10<0

P₂₀ = - 5x + 250= - 5 * 20 + 250= 150

IT₂₀ = - 5 x² + 250x= – 5 * 20² + 250 * 20= 3.000

CT₂₀ = 50x + 120= 50 * 20 + 120= 1.240

B= I – C= 3.000 – 1.240= 1.760