Question

.Suppose Ethiopian Electric Light and Power Corporation (EELPC) is a multi plantmonopolist having two plants, Tekeze plant (plant1) and Fincha plant (Plant2). Theoperating costs of the two plants are given as follows:Tekeze Plant: TC1 = 10 Q12and where Q1-Amount of electric power produced inTekezeFincha plant: TC2 = 20 Q22Q2–amount of electric power produced in FinchaEELPC estimates the demand for electric power by the following functionP= 700–5Q where P-is price (total in million birr) per Giga watt andQ–is the total amount of Giga watt sold and Q = Q1 + Q2

Answer 1

$TC_1 = 10Q_1^{2 }$

$P_1 = 700-5Q _1$

$TR _1= P_1×Q_1 = (700-5Q_1)Q _1$

$TR_1 = 700Q_1 -5Q_1^{2 }$

Equilibrium point $MC = MR$

$MC_1 = 20Q_1$

$MR_1 = 700 - 10Q _1$

$20Q_1 = 700 - 10Q_1$

$30Q _1= 700$

$Q _1=23$

$P_1 = 700 - 5(Q_1)$

$P _1= 700 - 115$

$P_1=585$

$TC_1=10×23^{2}=5290$

$MC_1=20×23=460$

Therefore the equilibrium price is P₁=585 and equilibrium quantity Q₁ = 23

$TC_2 = 20Q_2^{2 }$

$P_2 = 700-5Q _2$

$TR _2= P_2×Q_2 = (700-5Q_2)Q _2$

$TR_2= 700Q_2 -5Q_2^{2 }$

Equilibrium point $MC = MR$

$MC_2= 40Q_2$

$MR_2= 700 - 10Q _2$

$40Q_2= 700 - 10Q_2$

$50Q _2= 700$

$Q _2=14$

$P_2 = 700 - 5(Q_2)$

$P _2= 700 - 70$

$P_2=630$

$TC_2=20×14^{2}=3920$

$MC_2=40×14=560$

Therefore the equilibrium price is P₂=630 and equilibrium quantity Q ₂= 14

total amount of Giga watt sold and

Q = Q1 + Q2

$Q=23+14=37$