Question

Consider the market for wheat where demand is given​ by:

Qd=80-4p

and supply is given by: Qs=50+1p

Now suppose​ that, due to a market failure​ (an artificial shipping​ constraint), a maximum of 46 units of wheat can be supplied by firms in the market.

Calculate the amount of deadweight loss caused by the marker failure. (Round answer to the nearest penny and as a positive number).

Answer 1

Market supply is fixed at 46 units of wheat. This implies that quantity demanded = quantity supplied = 46. At this quantity, consumers are willing to pay (80 - 46)/4 = $8.5

Equilibrium price without quota is found at

80 - 4p = 50 + p

30 = 5p

p = $6 and q = 50 + 6 = 56 units.

Deadweight loss = area between Q = 46 and Q = 56 units bounded by demand curve and supply curve

= 0.5*(8.5 - 6)*(56 - 46) + 0.5*(10 + 4)*6

= 54.50

Hence the deadweight loss is 54.50.