# Consider a market where supply and demand are given by QXS = -12 + PX and QXd = 90 – 2PX. Suppose the government imposes a price floor of \$38, and agrees to purchase any and all units consumers do not buy at the floor price of \$38 per unit. Assume that the government simply removes product from the market through its purchase. a. Determine the cost to the government of buying firms’ unsold units. \$______ b. Compute the lost social welfare (deadweight loss) that stems from the \$38 price floor. \$______

Consider a market where supply and demand are given by QXS = -12 + PX and QXd = 90 – 2PX. Suppose the government imposes a price floor of \$38, and agrees to purchase any and all units consumers do not buy at the floor price of \$38 per unit. Assume that the government simply removes product from the market through its purchase.

a. Determine the cost to the government of buying firms’ unsold units.
\$______
b. Compute the lost social welfare (deadweight loss) that stems from the \$38 price floor.
\$______

Solution:-

Number of units supplied at price floor of \$ 38 = -12 + 38 = 26 Units.

Number of units demanded at price floor of \$ 38 = 90 – 2 * 38 = 90 – 76 = 14 Units.

Unsold units of firm = 26 – 14 = 12 units.

Cost to government of buying unsold units of firm = 38 * 12 = \$ 456.

b). Solution:- At equilibrium, Demand = Supply.

90 – 2PX = -12 + PX

90 + 12 = PX + 2PX

102 = 3PX

PX = \$ 34 (Equilibrium Price of Good X = \$ 34.)

Q = -12 + 34 = 22 Units.

Lost social welfare (Deadweight loss) = 0.5 * (38 – 34) * (22 – 14)

= 0.5 * 4 * 8

= \$ 16.

Conclusion:-

 a). Cost to government of buying unsold units of firm \$ 456 b). Lost social welfare (Deadweight loss) \$ 16
Asked on February 14, 2018 in