1. Suppose that the demand for broccoli is given by Q = 1, 000 – 5P, where Q is
ID: 1124983 • Letter: 1
Question
1. Suppose that the demand for broccoli is given by Q = 1, 000 – 5P, where Q is quantity per year measured in hundreds of bushels and P is price in dollars per hundred bushels. The long-run supply curve for broccoli is given by Q = 4P - 80. (a) Determine equilibrium price and quantity. (b) What is consumer surplus at this equilibrium? (c) What is producer surplus at this equilibrium? (d) For the rest of the problem, suppose that the government instituted a $45 per- hundred-bushel tax on broccoli. Compute the new equilibrium. (e) How would the tax burden be shared between buyers and sellers of broccoli? (E) What is the dead weight loss of this tax?Explanation / Answer
(a)
Demand equation is as follows -
Q = 1,000 - 5P
Supply equation is as follows -
Q = 4P - 80
At equilibrium,
Demand = Supply
1,000 - 5P = 4P - 80
9P = 1,080
P = 120
Q = 1,000 - 5P = 1,000 - (5*120) = 1,000 - 600 = 400
Thus,
The equilibrium price is $120 per hundred bushels.
The equilibrium quantity is 400 hundreds of bushels.
(b)
Calculate price when demand is zero -
Q = 1,000 - 5P
0 = 1,000 - 5P
5P = 1,000
P = 200
Calculate the consumer surplus -
CS = 1/2 * (Price when demand is zero - Equilibrium price) * Equilibrium quantity
CS = 1/2 * (200 - 120) * 400
CS = $16,000
The consumer surplus at this equilibrium is $16,000.
(c)
Calculate the price when supply is zero -
Q = 4P - 80
0 = 4P - 80
P = 20
Calculate the producer surplus -
PS = 1/2 * (Equilibrium price - Price when supply is zero) * Equilibrium quantity
PS = 1/2 * (120 - 20) * 400
PS = $20,000
The producer surplus at this equilibrium is $20,000.
(d)
Government has imposed a tax of $45 per hundred bushels.
New supply curve is as follows -
Q = 4(P - 45) - 80
Q = 4P - 180 - 80
Q = 4P - 260
At equilibrium,
Demand = Supply
1,000 - 5P = 4P - 260
9P = 1,260
P = 140
Q = 1,000 - 5P = 1,000 - (5*140) = 300
Thus,
The new equilibrium price is $140 per hundred bushels.
The new equilibrium quantity is 300 hundred of bushels.
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