Answer to Question #177699 in Microeconomics for SPENCER GYABENG

Question

Given two commodity system where both commodities are perishable and income Y is a exogenous D1= -2000+7Y-200P1+300P2

S1=-200+500P1-100P2

D2=-1000+4Y+200P1-100P2

S2=-800-100P1+300P2

And that for flow equilibrium , D1=S1 and D2=S2

a. find the reduced form

b. hence find the flow equilibrium values of the endogenous variables when consumers' income (Y) is $9.00

c. find the change in the flow equilibrium values that result from a unit change in Y .

Answer 1

Solution

a. find the reduced form

$D_1=S_1\\ \implies -2000+7Y-200P_1+300P_2=-200+500P_1-100P_2\\ 7Y-700P_1+400P_2=1800------------(1)$

$D_2=S_2\\ \implies -1000+4Y+200P_1-100P_2=-800-100P_1+300P_2\\ 4Y+300P_1-400P_2=200------------(2)$

Subtracting $(2)$ from $(1)$ we get:

$11Y-400P_1=2000$

Hence the reduced form

b. hence find the flow equilibrium values of the endogenous variables when consumers' income (Y) is $9.00

Soln

Substitute Y for $9.00

We get;

$11(9)-400P_1=2000\\ P_1=-4.7525$

c. find the change in the flow equilibrium values that result from a unit change in Y .

Soln

Unit change for y we will get

$12Y-400P_1=2000\\ \implies 12(9)-400P_1=2000\\ P_1=-4.73$