Question

Consider a market where supply and demand are given by Q_X^S = -16 + P_X and Q_X^d = 74 - 2P_X. Suppose the government imposes a price floor of $34, and agrees to purchase and discard any and all units consumers do not buy at the floor price of $34 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 $34 price floor.

$ __________

Answer 1

Solution:-

At the market equilibrium for good x , Qd =Qs ir, 74—2P=—16+P or, 3P =90 or, P= 30 ( equilibrium price)

Putting equilibrium price in the demand or supply function, Q = —16+30=14 (equilibrium quantity)

• Demand at price floor Pf= 34 , Q =74—2×34   = 74—68=6 , supply at this price ( $34)= —16+34 = 18 , so unsold stock = 18—6 =12 , cost to the government to buy unsold stock = 34×12 = $408 .
• The deadweight loss is the welfare loss to the society, it is the amount which neither goes to consumer or producer. ( let's draw the diagram of market with price floor)
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