Question

Assume that the market for good x is defined as follows: qd = 64 - 16p and qs = 16p - 8. if the government restricts output in this market to 16 units, what is the loss associated with this policy?

Answer 1

I guess the answer is $9.

At equilibrium, Qd=Qs

Therefore, 64-16P=16P-8  

Or, 32P=72 or, P=72/32=$2.25

At equilibrium, Qd=Qs=28.

If government restricts quantity to 16 units then it will create deadweight loss to the market.

If quantity=16,

Qd=16=64-16P or, Pdemand= 3

Demand price is $3 at this fixed quantity=16  Similarly, Qs=16=16P-8 or, Psupply= $1.5

At this quantity, supply price is $1.5

So, deadweight loss= loss in consumer surplus+ loss in producers surplus

={(1/2)*(28-16)*(3-2.25)} + {(1/2)*(28-16)*(2.25-1.5)}

= (4.5+4.5)=9

Therefore, loss equals $9.