Answer: Dead-weight loss is $30.
Explanation: Equilibrium in a goods market is given by,
[tex]Q_{d} = Q_{s}
8000 - 2000 P = 1000P - 1000
9000 = 3000P
P= $3[/tex]
Substituting this value of P into the demand equation we can find the equilibrium quantity.
[tex]Q=8000 - 2000P
=8000 - 6000
= 2000[/tex]
P=$3, Q=2000 without the subsidy.
At this quantity, value of government subsidy is
[tex]= 2000 * $0.30
= $600[/tex]
Supply with subsidy is Qs= 1000(P+0.30) - 1000
Equilibrium is given by,
Qd= Qs
8000 - 2000P = 1000P + 300 - 1000
8700 = 3000P
P=$2.9 is price paid by consumers, but the sellers receive P + 0.30 = $3.2 per unit.
Q= 2,200
[tex]Dead-weight loss = \frac{1}{2} * $0.30 * (2200 - 2000)
= \frac{1}{2} * $0.30 * 200
= $30[/tex]
