Assume that we know that the domestic supply function for peanuts in the US is:
ID: 1218328 • Letter: A
Question
Assume that we know that the domestic supply function for peanuts in the US is:
P = 4 + 0.001Q
where Q is the number of bushels per year and P is the price in dollars per bushel.
Suppose that we know that the domestic demand function for peanuts (holding domestic income and other demand shifting variables constant) is:
P = 30 - 0.004 Q.
a) If there is no international trade, what is the equilibrium price and quantity?
b) Suppose that the world price of peanuts is $5 per bushel and international trade is not restricted. Find the domestic production and consumption of peanuts and US imports at the world price.
c) Suppose that the US government wishes to restrict imports to 1000 (million bushels) per year. What $/bushel tariff would have this effect?
d) How much tariff revenue per year would a $1/bushel tariff on peanuts generate?
Explanation / Answer
a.
P = 4 + 0.001Q-------------(1)(supply function)
P = 30 - 0.004 Q------------(2)(demand function)
At equilibrium,
Supply = demand
Thus,
4+.001*Q = 30 - .004*Q
Q = (30-4)/.005 = 5200
P = 4+.001*5200 = 9.2
Thus,
At equilibrium,
Q = 5200 bushels, P = $9.2 per bushels
b.
when, P = $5
Supply quantity:
5 = 4+.001Qs
Or
Qs = 1/.001 = 1000 bushels
Domestic production=1000 bushels
Demand quantity:
5 = 30 - .004*Qd
Qd= 25/.004 = 6250
Domestic consumption=6250 bushels
Since, demand is higher than the supply. Thus, quantity will be imported.
Imported quantity= 6250 – 1000 = 5250 bushels
c.
If, import is limited to 1000 bushels.
Thus, domestic price = $5 + tariff
Also,
Qd – Qs = 1000
Qd = 1000 + Qs
P = 30 - .004*Qd
5+ tariff = 30 - .004*(1000 + Qs) ------------------------- (3)
5+ tariff = 4+.001*Qs -----------------------------------------(4)
By eq. 3 & 4
4+.001*Qs = 30 - .004*(1000 +Qs)
4+.001*Qs = 30 – 4 - .004*Qs
Qs= 22/.005 = 4400 bushels
5+Tariff = 4+ .001*4400 = 8.4
Tariff = 8.4 – 5 = $3.4 per bushel
d.
If tariff is $1 per bushel.
5+1 = 4+.001*Qs
Qs = 2/.001 = 2000 bushels
Also,
5+1 = 30 -.004*Qd
Qd = 24/.004 = 6000 bushels
Thus,
Import = 6000 – 2000 =4000 bushels
Thus, tariff revenue collected @ $1 per bushel = 1*4000 = $4000