Question

Country A and country B are two neighboring countries. The inverse supply and demand functions for electricity (TWh) in these two countries are given by:

Sa = 7,5+0.15Xa
Da = 21 -0.075Xa
Sb = 15+0.15Xb
Db = 24 -0.0375Xb

where Sa, is supply price in country A, Da is demand price in country A and Xa, is the corresponding volume in country A. Similar notation for country B. These functions are only valid in the ranges where both prices and quantities are non- negative. Outside these ranges prices and quantities are defined as zero.

b) What is the equilibrium price and corresponding total production when there is one common market and no constraint on transmission?

Answer 1

Date SI PONO Demand In market A, Da = 21-0.075 X a 0.075 X a 21 - Da Xa = 21 - Da 0.075 0.075 = Xa= 280 - Da 0.075 = Xa= 280 - 1000 Da 75 Demand in market B, Du= 24-0.0375X X = 24 - I Do 0.0375 0.0375 Xb = 640 - Db 1 0.0375 - X , 6 40 - 6000 Đ 375 2640 - 2000 D 75 In equilibrium, total market Xat X = Xin and equal in both markets u Da Do = Dm. demand is prices are - XatX₂ = x m = 280 +640 - 1000 Dm - 200000 75 75 3000 X = 920 - Dm 75

Data PO NO x = 920-b8oDm. Similarly for supply side... Sido Market A. 0.15 Xa = 100 sa - 500 is Market X6 = B 1 0.15 Sh - 15 0.15 Xb = 100 So - 100. 15 ISO Total market Supply = XatXo, Supply price - Sm + X + Y : x - lớp S + Jo Su - Cao You 200 sm are som - sto, 150 Is IS 150

Date/ ം 29 No In equilibrium, X = X , Dm a sm 920 - 40 Dm = 200 Sim 150 IS 1070 = 800 sm 15 Sm = 20.0625 Xm = 200 x 20.0625 - 150 117.5.