Question

Consider the following demand and supply equations for sugar:

Qd = 1,000 -1,000P

P = 0.000Qs - 0.8 

where P is the price of sugar per pound and Q is thousands of pounds of

sugar.

a. What are the equilibrium price and quantity for sugar? At the same equilibrium price, compute the consumer surplus.

b. Suppose that the government wishes to subsidize sugar production by placing a floor on sugar prices of $0.20 per pound. How much will the government need to spend to ensure that the market clears? Compute the deadwight loss at that 

Answer 1

a) the equilibrium price:

$Qs=Qd$

$P=0.001*(1000-1000P)-0.8=1-P-0.8$

$P=0.1$

the equilibrium quantity:

$Q=1000-1000*0.1=900$

the consumer surplus:

Pmax gives Qd=0

$0=1000-1000P$

$P=1$

$the consumer surplus=1/2*900*(1-0.1)=405$

b) $P=0.2$

$Qd=800$

$Qs=1000$

the deadwight: $Qs-Qd=1000-800=200$

the government need to spend: $200*0.2=40$