Question

Consider the following demand and supply equations for sugar:

Qd = 1,000 -1,000P

Qs = 800 + 1,000P

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 deadweight loss at that point.

Answer 1

Answer: a.

We know that demand function is Qd = 1,000 -1,000P and supply function is Qs = 800 + 1,000P.

We also know that market equilibrium is arrived where demanded and supplied quantities become equal to each other. Knowing this, let us equal both the functions as follows:

1,000 -1,000P = 800 + 1,000P

200 = 2000P
P = $0.10 per pound
Our market equilibrium price = P = $0.10 per pound of sugar

When we put the value of P in any of the two equations, we get the value of Q. Let us do this with demand function:

Q = 1000 - 1000*0.10
Q = 900
Equilibrium quantity demanded and supplied in the market is 900 pounds

Equilibrium price and quantity for sugar = $0.10, 900 pounds respectively (answer)

Calculation of consumer surplus:

Demand function is: Qd = 1,000 -1,000P
At price of $0.10, quantity demanded is 900 pounds (Figure A)

Now count, at what price the quantity demanded will be zero?
If we see, we will find at at price of $1, the quantity becomes zero. (Figure B)

Differential Price = $1 minus $0.10 (Figure B minus Figure A) = $0.90
Differential quantity = 900 - 0 = 900 pounds
Differntial value = Differential Price x Differential Quantity = 0.90 x 900 = $810

Consumer surplus = Differential value / 2 = $810 / 2 = $405

Consumer Surplus = $405 (answer)


Answer: b.

Price floor = $0.20
Demand at $0.20 price = Qd = 1,000 -1,000*0.20 = 800
Supply at $0.20 price = Qs = 800 + 1,000*0.20 = 1000
Differential quantity = 1000 - 800 = 200 pounds
Price floor = $0.20

Government will have to buy 200 pounds at the price floor of $0.20

For clearing the market, government will have to buy at price floor = 200 pounds * $0.20 = $40 (Answer)

Deadweight loss:

Difference between supplied quanity and equilibiurm quantity = 1000 - 900 = 100 (figure C)
Differential price for the purpose of deadweight loss = (Price floor) minus (price at 1000 pounds quantity as per demand function)
Differential price for the purpose of deadweight loss = $0.20 - (1000 = 1,000 -1,000P)
Differential price for the purpose of deadweight loss = $0.20 - 0 = $0.20 (Figure D)

Deadweight loss = Figure C * Figure D / 2
Deadweight loss = (100 * 0.20) /2
Deadweight loss = 10 $ (Answer)