Question

Consider a market where supply and demand are given by Qx s = -16+Px and Qd=92-2Px suppose the gouvernment imposes a price floor of $40, and agrees to purchase any and all units consumers do not buy at the floor price of $40 per unit. determine the cost to the gouvernment of buying firm's unsold units. Compoute the lost social welfare (deadweight loss) that stems from the $40 price floor

Answer 1

Government cost of unsold units

$Q_S=P_x-16$

$Q_d=92-2P_X$

Initial equilibrium points:

$P_x-16=92-2P_x$

$P_x+2P_x=92+16$

$3P_x=108$

$P_x=36$ $Q_S\to 36-16=20$ $Q_d\to 92-2(36)=20$

Price Floor $(P_f)=\$ 480$

$Q_s=40-16=24$

$Q_d=92-2(40)=12$

Unsold units = $24-12=12$

Cost of unsold units= $12 \times 40=\$ 480$

Cost of unsold units= Government cost = $ 480

Dead-weight loss

=$(Q_d\ at P_x=36)- (Q_d\ at\ P_x =40)$

= $20-10=10$

cost = $10\times 40=\bold{\$400}$