Question

Hipsterville economy has 4sectors: Kale(K), mason jars (M),vintage goods(V), and bicycle repair (B). The economyis in equilibrium. Suppose the following:Sector Kalesells 10% of its output to M , 25% to V, and retains the rest Sector Mason jars sells 30% of its output to K, 35% to V, 25% to B, and retains the rest Sector Vintage sells 30% of its output to K, 15% to M, 40% to B, and retains the rest Sector Bike repair sells 20% of its output to K, 10% to M, 30% to V, and retains the rest

a) Construct the exchange table(table ofinputs/outputs) for this economy. You can give your answer in table form or in matrix form, but be sure that the meaning of rows and columns is clear.

b)Find a set of equilibrium prices for the economy.

Answer 1

a)

	K	M	V	B
K	0.65 (output)	0.1(input)	0.25 (input)	---
M	0.3(input)	0.1 (output)	0.35 (input)	0.25(input)
V	0.30 (input)	0.15(input)	0.15 (output)	0.40 (input)
B	0.20 (input)	0.1 (input)	0.3 (input)	0.40 (output)

in the above table .. a sector looks across the row to see where its output goes and looks down the column to see what are its inputs..

first column of the table tells that sector K receives and pays for 30% of M , 30% of V and 20% of B

second column depicts that sector M receives and pays for 10 % of K , 15 % of V and 10% of B

third column tells that sector V receives and pays for 25 % of K , 35% of M and 30% of B

fourth column tells that sector B receives and pays for 25% of M and 40% of V

b) let the prices (dollar values) of total annual outputs of the K,M,V,B sectors by P_k,P_m,P_v,P_B

since respective values of the total outputs are P_m ,P_v ,P_B --

sector K must spend 0.3P_m dollars for its share of M output

0.3P_v for its share of V's output

0.2 P_B for its share of b"s output.

to make K's income equal to its expenses

P_k =0.3P_M+0.3P_V+0.2P_B ---1

similarly,

P_m=0.1P_K+0.15P_v+0.1P_B ------2

P_v=0.25P_k+0.35P_m+0.3P_B------3

P_B=0.25P_m+0.40P_v------4

to solve the system of equations 1, 2, 3, 4

Pk-0.3Pm-0.3Pv-0.2Pb =0

-0.1Pk+Pm-0.15Pv-0.1Pb=0

-0.25Pk-0.35Pm+Pv-0.3Pb=0

0Pk-0.25Pm-0.40Pv+Pb=0