Answer to Question #216228 in Economics for NURSYAHIRA BINTI M

Question

Brazil is the world’s largest coffee producer. Suppose the functions of domestic supply of and the domestic demand for coffee in that country are given as 𝑆 𝑑 = 80 + 20𝑃 and 𝐷 𝑑 = 200 − 20P respectively, while the function of the world supply of coffee is 𝑆 𝑑+𝑤 = 50 + 100𝑃. The supply of and the demand for coffee are measured in million 60 kg bags, while the price is measured in USD.

a)In autarky, what would be the equilibrium price of coffee, the quantity of coffee produced and the quantity of coffee consumed in Brazil?

b)When Brazil opens trade, what would be the equilibrium price of coffee, the quantity of coffee produced and the quantity of coffee consumed?

c)If the country imposes a 72 percent ad valorem tariff on the imported coffee, what is the new function of the world supply of coffee? Next, calculate the equilibrium price, the quantity of coffee produced by domestic firms, the quantity of coffee consumed by the domestic consumers and the quantity of coffee imported?

Answer 1

a) In autarky, the equilibrium price of coffee, the quantity of coffee produced and the quantity of coffee consumed in Brazil are:

80 + 20P = 200 − 20P,

40P = 120,

P = 3,

Q = 80 + 20×3 = 140 units are produced and consumed.

b) When Brazil opens trade, the equilibrium price of coffee, the quantity of coffee produced and the quantity of coffee consumed are:

50 + 100P = 200 - 20P,

120P = 150,

P = 1.25,

Q = 50 + 100×1.25 = 175 units are consumed.

The amount produced is:

80 + 20×1.25 = 105 units.

So, 175 - 105 = 70 units will be imported.

c) If the country imposes a 72 percent ad valorem tariff on the imported coffee, then the new function of the world supply of coffee is:

𝑆 𝑑+𝑤 = 50 + 100P(1 - 0.72) = 50 + 28P,

The new equilibrium price is:

50 + 28P = 200 - 20P,

48P = 150,

P = 3.125.

The quantity of coffee produced by domestic firms is:

Qs = 80 + 20×3.125 = 142.5 units.

The quantity of coffee consumed by the domestic consumers is:

Qd = 200 - 20×3.125 = 137.5 units.

The quantity of coffee imported is zero.