Question

Sus: P =	2	+	35	*Q
Dus: P =	54000	-	70	*D
Sc: P =	0	+	10	*Q
Dc: P =	18000	-	20	*D

Answers:

Pw =	$8,666.96
Dm=Qx=	$400.04

Just need help on figuring out how these answers were found, thanks.

Answer 1

Consider the given problem here there are two “US” and “C” their respective demand and supply schedule are given in the question. The demand and supply of US are given below.

=> P = 2 + 35*Qd, => Qs = P/35 – 2/35, => Qs = P/35 – 0.057, the supply schedule of US.

=> P = 54,000 – 70*Qd, => Qd = 54,000/70 – P/70, => Qd = 771.43 – P/70, the demand schedule of US.

So, at the autarky the demand must be equal to supply.

=> Qd = Qs, => 771.43 – P/70 = P/35 – 0.057, => 771.43 + 0.057 = P/35 + P/70 = 3*P/70.

=> 3*P/70 = 771.487, => P = 771.487*70/3 = 18,001.36, => P_US = 18,001.36.

Now, let’s assume that demand and supply of “C” are given below.

=> P = 10*Qs, => Qs = P/10, the supply schedule of “C”.

=> P = 18,000 – 20*Qd, => Qd = 18,000/20 – P/20, => Qd = 900 – P/20, the demand schedule of “C”.

At the equilibrium the demand must be equal to supply.

=> Qd = Qs, => 900 – P/20 = P/10, => 3*P/20 = 900, => P = 900*20/3 = 6,000, => P_C = 6,000.

So, here the autarky price of country “C” is less than the US, => US is importer and C is exporter of the good.

=> the import demand schedule of US is given below.

=> Md = Qd – Qs = (771.43 – P/70) – (P/35 – 0.057) = 771.43 – P/70 – P/35 + 0.057 = 771.487 – 3P/70.

=> Md = 771.487 – 3P/70, the import demand schedule.

The export supply of country-C is given by.

=> Xs = Qs – Qd = P/10 – (900 – P/20) = P/10 – 900 + P/20 = 3P/20 – 900,

=> Xs = 3P/20 – 900, be the export supply schedule of “country-c”.

So, at the equilibrium the import demand must be equal to the export supply.

=> Md = Xs, => 771.487 – 3P/70 = 3P/20 – 900, => 3P/20 + 3P/70 = 900 + 771.487.

=> 3P/20 + 3P/70 = 900 + 771.487 = 1,671.487, => 3P/10(9/14) = 1,671.487.

=> 27*P/140 = 1,671.487, => P = 1,671.487*140*27 = 8,666.96, => P = 8,666.96.

The equilibrium export and import are “Xs = 3P/20 – 900 = Md = 400.04”.