Answer to Question #178991 in Macroeconomics for RICHARD OSEI

Question

Given the following two-commodity system where both commodities are perishable and income (Y), is 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 of the system

 b. Hence find the flow equilibrium values of the endogenous variables when the 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

(a)D₁=S₁

$-2000+7Y-200P_{1}+300P_{2}=-200+500P_{1}-100P_{2}$

$7Y=-200=2000=500P_{1}=200p_{1}-100p_{2}-300p_{2}$

$7y=1800+700p_{1}-400p_{2}$

$y=257\frac{1}{7}+100p_{1}-57\frac{1}{7}p_{2}$

D₂=S₂

$-100+4y+200p_{1}-100p_{2}=-800-100p_{1}+300p_{2}$

$4y=-800+1000-100p_{1}-200p_{1}+300p_{2}+100p_{2}$

$4y=200-300p_{1}+400p_{2}$

$y=50-75p_{1}+100p_{2}$

(b)

$(9=257.142+100p_{1}-57.142p_{2})75$

$(9=50-75p_{1}+100p_{2})100$

$675=19285.714+7500p_{1}-4285.714p_{2}$

$900=5000-7500p_{1}+714.286p_{2}$

$1575=24285.714+5714.286p_{2}$

$p_{2}=-3.97$

$9=50-75p_{1}+100(-3.97)$

$9=50-75p_{1}-397$

$75p_{1}=9+397-50$

$75p_{1}=356$

$p_{1}=-4.75$

(c)

$y=257\frac{1}{7}+100(-4.75)-57\frac{1}{7}(-3.97)=8.75$

$y=50-75(-4.75)+100(-3.97)=9.25$

$\frac{8.75}{9.25}=0.946$

$=1$