Consider a market where supply and demand are given by QxS 1

Consider a market where supply and demand are given by QxS -10 Px and Qxd- 71 2Px Suppose the government imposes price floor of $33, and agrees to purchase and discard any and all units consumers do not buy at the floor price of $33 per unit. Instructions: Enter your responses rounded to the nearest penny (two decimal places) a Determine the cost to the government of buying firms\' unsold units b. Compute the lost social welfare (deadweight loss) that stems from the $33 price floor

Solution

When PX = $33,

QXd = 71 - (2 x 33) = 71 - 66 = 5

QXs = - 10 + 33 = 23

Surplus = QXs - QXd = 23 - 5 = 18

When QXd = 5,

From demand function: 5 = 71 - 2PX

2PX = 66

PX = $33 (Demand price)

From supply function: 5 = - 10 + PX

PX = $15 (Supply price)

(a) Cost to government = Floor price x Surplus = $33 x 18 = $594

(b) Deadweight loss = (1/2) x QXd x (Demand price - Supply price) = (1/2) x 5 x $(33 - 15) = 2.5 x $18 = $45