# Consider a market where supply and demand are given by QXS = -14 + PX and QXd = 82 – 2PX. Suppose the government imposes a price floor of \$37, and agrees to purchase any and all units consumers do not buy at the floor price of \$37 per unit. Determine the cost to the government of buying firms’ unsold units. Compute the lost social welfare (deadweight loss) that stems from the \$37 price floor.

A price floor is a government-mandated minimum price for a particular good or service. In this case, the government has imposed a price floor of \$37 on the market where supply and demand are given by QXS = -14 + PX and QXd = 82 – 2PX.

a. To determine the cost to the government of buying firms’ unsold units, we must first calculate the equilibrium quantity and price without the intervention of a price floor. This can be done by setting the quantity supplied equal to the quantity demanded:
QXs = QXd
-14 + Px = 82 – 2Px
2Px = 96
Px = 48
Qx = 34 (where q represents quantity).
The equilibrium point with no intervention from a price floor occurs at (48,34). Now that we know equilibrium without any policy interference from a price floor, we can calculate how much it will cost the government to purchase all unsold units at \$37 per unit:
Cost to Government= 37 * (82-34) = 2786

## Consider a market where supply and demand are given by QXS = -14 + PX and QXd = 82 – 2PX. Suppose the government imposes a price floor of \$37, and agrees to purchase any and all units consumers do not buy at the floor price of \$37 per unit. Determine the cost to the government of buying firms’ unsold units. Compute the lost social welfare (deadweight loss) that stems from the \$37 price floor.

b. We can calculate lost social welfare (deadweight loss) that stems from the \$37 price floor by calculating consumer surplus and producer surplus in both cases and taking their difference:

Equilibrium without Price Floor: Consumer Surplus CS1= ½(81 – 48)*(96–48) = 1152 Producer Surplus PS1= ½*(48– 14)*(34–14) = 300 Total Social Welfare SW1=(CS1+PS1)= 1452

Equilibrium with Price Floor: Consumer Surplus CS2= ½*(81 – 37)*(82–37) = 907 Producer Surplus PS2= ½*(\$37 – 14)(82–\$37)= 408 Total Social Welfare SW2=(CS2+PS2)= 1315

Deadweight Loss DWL=\$Abs{SW1-SW2}\$ = 137

This means that due to imposition of Price Floor (\$37), there is deadweight loss of 137 which is nothing but foregone social welfare due to inefficient allocation of resources in economy due to Price Floor as consumers were willing to pay more than producers were willing accept resulting into mismatch between buyers willingness & sellers willingness thus creating an underutilization of available resources & hence causing deadweight loss.

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