Question

The demand and supply curves for Fuji apples are given by Q^D = 50 – 6P and Q^S = 4P – 2, where P is price per bag and Q is in thousands of bags. What are consumer surplus and producer surplus at the equilibrium price?

Answer Choices:

	CS = $29,422; PS = $44,180
	CS = $15,006; PS = $7,657
	CS = $856,000; PS = $1,126,113
	CS = $450; PS = $375

Answer 1

Ans) Step 1÷ Calculate equilibrium price and quantity.

To calculate equilibrium price, equate Qs and Qd

50-6P = 4P-2

50+2 = 4P+6P

52 = 10P

P = $5.2

To calculate equilibrium quantity, put value of P in either demand or supply equation.

Qd = 50-6P = 50-6×(5.2) = 50 - 31.2 = 18.8 × 1000 = 18,800 (as Q is in thousand)

Or

Qs = 4P-2 = 4(5.2)-2 = 18,800

So, Pe = $5.2 and Qe=18,800

Step 2÷ calculate willingness to pay by putting Qd = 0

Qd = 50 - 6Pwp

0 = 50 -6Pwp

6Pwp = 50

Pwp = $8.3

Step 3÷ calculate willingness to sell by putting Qs=0

Qs = 4Pws - 2

0=4Pws - 2

2=4 Pws

Pws = 0.5

Step 4÷ calculate consumer surplus and producer surplus

Consumer surplus = 1/2× Qe × (Pwp - Pe) = 1/2× 18,800 × (8.3-5.2) = $29,140

Producer surplus = 1/2× Qe × (Pe-Pws) = 1/2×18,800×(5.2 - 0.5) = $44,180

No option is correct. (Option 1 could be correct but consumer surplus is wrong)