Question

Suppose the world price for shoes is $32 per pair. Domestic demand and domestic supply are determined by the following equations: Domestic Demand: p = 120 ≠ 2q Domestic Supply: p = 20 + 3q where p and q represent price and quantity, respectively.

1. Under free trade, the domestic economy purchases _____________ pairs of shoes.

A) 15 B) 22 C) 44 D) none of the above

2. Under free trade, domestic producers supply ___________ pairs of shoes.

A) 2 B) 4 C) 8 D) none of the above

3. Under free trade, the domestic economy imports _________ pairs of shoes.

A) 10 B) 20 C) 30 D) none of the above

4. Suppose that an import quota is set at 30 pairs of shoes. Then domestic consumers purchase _______ pairs of shoes and domestic producers supply ________ pairs of shoes.

A) 38; 8 B) 36; 6 C) 34; 4 D) none of the above

Answer 1

(1)world price of each pair of shoes is $32.

Domestic demand: p = 120-2q

put p = 32 and solve for q

=> 32 = 120 - 2q

=> 2q = 120 - 32

=> q = 88 / 2

=> q = 44

The domestic economic purchases 44 pairs of shoes under the free trade (i.e., at world price of shoes)

Answer:Option (C)

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(2) Domestic supply: p =20 +3q

Put p =32 and solve for q

=> 32 = 20 + 3q

=> 3q = 32-20

=> q = 12/3

=> q=4

The domestic producers supply 4 pairs of shoes under the free trade (i.e., at world price of shoes)

Answer: Option (B)

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(3) At a world price of $32 per pair of shoes, domestic demand is 44 pairs of shoes and domestic supply is 4 pairs of shoes.

=> Import = Domestic demand - Domestic supply

=> Import = 44 - 4

=> Import = 40

Under free trade, the domestic economy imports 40 pairs of shoes.

Answer: option (D)

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(4)

Domestic demand: p = 120 - 2q

=> q = (120 - p)/2

=> q = 60 - 0.5p

=> qd = 60 - 0.5p --------------- (jnverse domestic demand function)

and

Domestic supply: p = 20 + 3q

=> q = (p -20)/3

=> qs = (p-20)/3 ------------------- (inverse domestic supply function)

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Import quota is set at 30 pairs of shoes.

=> Import = domestic demand - domestic supply

=> 30 = (60 -0.5p) - [(p-20)/3]

=> 30 = [3 (60 - 0.5p) - (p-20)]/3

=> 30 *3 = [180 -1.5p - p + 20]

=> 90 = [200 -2.5p]

=> 2.5p = 200 - 90

=> 2.5p = 110

=> p = (110 / 2.5)

=> p = 44

The world price would be 44 if import quota is 30.

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=> qd = 60 - 0.5p

put p = 44

=> qd = 60 - 0.5(44)

=> qd = 60 -22

=> qd = 38

The domestic demand at p=44 is 38 pairs of shoes.

and

qs = (p -20)/3

put p =44

=> qs = (44-20)/3

=> qs = 24 /3

=>qs = 8

The domestic supply at p=44 is 8 pairs of shoes.

Therefore, at an import quota of 30 pairs of shoes. Then domestic consumers purchase 38 pairs of shoes and domestic producers supply 8 pairs of shoes.

Answer: option (A)