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: 


Ans) Step 1÷ Calculate equilibrium price and quantity.
To calculate equilibrium price, equate Qs and Qd
506P = 4P2
50+2 = 4P+6P
52 = 10P
P = $5.2
To calculate equilibrium quantity, put value of P in either demand or supply equation.
Qd = 506P = 506×(5.2) = 50  31.2 = 18.8 × 1000 = 18,800 (as Q is in thousand)
Or
Qs = 4P2 = 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 × (8.35.2) = $29,140
Producer surplus = 1/2× Qe × (PePws) = 1/2×18,800×(5.2  0.5) = $44,180
No option is correct. (Option 1 could be correct but consumer surplus is wrong)
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