Question

Question 1

1. Consider the table below showing amounts of good x and y that nation 1 and 2 can produce with one hour of labor time

	N1	N2
X/labor hour	8	4
Y/ labor hour	2	6

1. Which nation has absolute advantage in cloth and which one has absolute advantage in wheat? (explain your answer)
2. How much will nation 1 and nation 2 gain from trade if each nation specialized in the production of the commodity of its absolute advantage and exported some of its output for the commodity of its absolute disadvantage, at the exchange of 8X for 8Y. (Gains to be measured in terms of both units of Y and labor time saved)

2. Consider the table below showing amounts of good x and y that nation 1 and 2 can produce with one hour of labor time

	N1	N2
X/labor hour	1	10
Y/ labor hour	2	8

1. Define comparative advantage by referring to the table above
2. determine which nation has comparative advantage in which commodity
3. Compute the range for mutually advantageous trade.

3. The production function for a shoe producing company is Q= KL², with the price of capital and labor fixed at $10 and $15 respectively. What combination of capital and labor minimizes the cost of producing 100 shoes

Answer 1

First and importantly, you didn't make it clear which of the X and Y goods represent cloth and wheat.

But assuming that X represents cloth and Y represents wheat, let me answer your questions.

FIRST PART-

(a) (i) nation 1 produces 8 units of cloth and 2 units of wheat per unit labor hour, and nation 2 produces 4 units of cloth and 6 units of wheat per unit labor hour. Thus, nation 1 can produce more units of cloth for every labour hour employed than nation 2, and at the same time, nation 2 can produce more units of wheat than nation 1. Thus nation 1 has absolute advantage over nation 2 in the production of cloth, whereas nation 2 has absolute advantage in the production of wheat.

(ii) now of both the nation's specialise in the production of the commodity of its absolute advantage, nation 1 produces cloth and nation 2 produces wheat. Thus nation 1 produces 8 units of cloth per labour hour and nation 2 produces 6 units of wheat per labour hour. At the exchange rate 8X for 8Y, nation 1 exports 8 units of X for 8 units of Y. Thus nation 1 gains (8Y - 2Y) = 6units of Y by participating in the trade. At the same time, nation 2 imports 8 X for 8 units of Y exported to nation 1. Nation 2 takes less than 1.5 hours to produce 8Y, now by importing 8X which is equivalent to 2 labour hour worth of time, nation 2 could use this 2 hours to produce 12units of Y. By exporting only 8Y, it gains (12Y- 8Y) = 4Y.

SECOND PART-

(a) (i) comparative advantage is the ability of a nation to produce a commodity at a lower opportunity cost. For nation 1, the opportunity cost of producing X in terms of Y is given by 1/2 = 0.5.

(ii) Now, from the table, opportunity cost of producing X for nation 1 = 1/2 = 0.5, and opportunity cost of producing X by nation 2 = 10/8 = 1.25. since the opportunity cost of producing X is lower in nation 1, nation 1 has comparative advantage over nation 2 in the production of X, and nation 2 has comparative advantage over nation 1 in the production of Y. Thus, Nation 1 has comparative advantage in X and nation 2 has comparative advantage in Y.

(ii) by specialising in the production of commodities of its comparative advantage, nation 1 produces X and nation 2 produces Y. The range of trade is 2X- 8Y.

THIRD PART-

(a) Q = KL^{​​​​​2}​

Cost function,C = 10K + 15L

Min Q =KL^{​​​​​2}​ subject to C = 10K + 15L

dQ/dK = 2L

dQ/dL = 2KL

Lagrange function, π = KL^{​​​​​2} -10K - 15L

dπ/dK = 2L - 15 = 0

L = 7.5

dπ/dL = 2KL - 10 = 0

2*K*7.5 = 10

K = 10/15 = 0.67