Suppose that the demand curve for apples is given by Qd = 140 - 5P, where Qd is the number of pounds demanded per year and p is the price per pound. The supply of apples can be described by Qs = 40 + 3P, where Qs is the number of pounds provided.
A What is the equilibrium price? (Hint: At the equilibrium, quantity demanded and quantity supplied are equal, Qd = Qs.)
equate demand to supply
140-5P=40+3P
100=8P
P= 12.5
B What is the equilibrium quantity supplied and demanded?
Put the value of P in demand, supply equation In supply equation we get Q= 77.5 = 40+3*12.5 = quantity demanded = quantity supplied as this is an equilibrium point
C Calculate the consumer surplus at the equilibrium price.
We need price when Qd= 0
Put Qd= 0 in demand equation to get P= 140/5 =28
Consumer surplus = ½*(28-12.5) *77.5 = 600.625
D Calculate the producer surplus at the equilibrium price.
We need price when Qs= 0
Put Qs= 0 in supply equation to get P= -40/3
Producer surplus = ½*(12.5-(-40/3) *77.5 = 1000.9125
E Calculate the total surplus at the equilibrium price.
Total surplus = 600.625+1000.6125 = 1601.0375
F Now suppose that the government imposes a tax of $8 per each pound sold, paid by
the consumers,. In this case, what are the price and the consumer surplus?
Now supply curve becomes Qs= 40+3(p-8) = 16+3p
For equilibrium:
16+3p = 140-5p
8p = 124
P = 15.5 and Q= 140-5*15.5=62.5
Consumer surplus = ½*(28-15.5)*62.5 = 390.625