Question

In: Economics

Consider the market for wheat where demand is given​ by: Qd=120-4p and supply is given​ by:...

Consider the market for wheat where demand is given​ by: Qd=120-4p

and supply is given​ by: Qs=50 + 2p.

Now suppose​ that, due to a market failure​ (an artificial shipping​ constraint), a maximum of 63.32 units of wheat can be supplied by firms in the market.

​The amount of the deadweight loss caused by the market failure is ​$__________________.

Solutions

Expert Solution

As per the question the market demand for wheat is Qd = 120 – 4P

The market supply for wheat is Qs = 50 + 2P

At the market equilibrium point the market demand is equal with market supply

Qd = Qs

120 – 4P = 50 + 2P

120 – 50 = 2P + 4P

70 = 6P

P = 70/6 = $11.67 (equilibrium price)

At this price the equilibrium quantity demanded = 120 -4P

= 120 – 4(11.67) = 73.32

The market equilibrium price P=$11.67 and quantity is 73.32

Due to market failure the quantity of wheat supplied by the market is 63.32

At this quantity the price received by supplier Qs = 50 +2P

63.32 = 50 + 2P

2P = 13.32

P = $6.66

At this quantity the price pay by buyer Qd = 120 – 4P

63.32 = 120 – 4P

4P = 56.68

P = $14.17

So P1 = $14.17   and     P2 = $6.66

Q1 = 73.32        and    Q2=63.32

Deadweight loss is the loss of economic welfare caused due to market failure.

The deadweight loss = 0.5x(P1-P2)x(Q1-Q2)

The deadweight loss = 0.5x(14.17 – 6.66)x(73.32-63.32)

The deadweight loss = 0.5x(7.51)x(10) =37.55

The amount of deadweight loss caused due to market failure is 37.55

Rahul Sunny answered 1 year ago
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