Question #44838

A country produces only commodity 1 and commodity 2 using capital (K) and
Labor (L) as inputs. Assume that the production of commodity 1 uses 10 units of
capital for each worker, so that K1 =10L1 , while the production of commodity 2
uses 2 units of capital for each worker, so that K2 =2L2 . The total supply of
capital is 400 units and the total supply of labor is 100 units.
(a) Determine the amount of both inputs of production, that is, capital and labor,
used in each commodity and the output levels.
(b) Now assume that the number of workers increases to 140 due to immigration,
keeping total capital fixed at 400. Solve for the amount of capital and labor in
used in each commodity and for the output levels. Relate your findings in (a) and
(b) to a theoretical result of the Standard Trade Theory.

Expert's answer

Assume that the production of commodity 1 uses 10 units of capital for each worker, so that K1 =10L1 , while the production of commodity 2

uses 2 units of capital for each worker, so that K2 =2L2 . The total supply of capital is 400 units and the total supply of labor is 100 units.

(a) Determine the amount of both inputs of production, that is, capital and labor, used in each commodity and the output levels.

According to the data above:

L1 + L2 = 100, K1 + K2 = 400.

As K1 =10L1 and K2 =2L2, so 10L1 + 2L2 = 400.

We have the system of equations:

L1 + L2 = 100

10L1 + 2L2 = 400

L2 = 100 - L1

10L1 + 200 - 2L1 = 400

L1 = 25, L2 = 75

So, K1 = 250, K2 = 150

So, the amounts of inputs for production of commodity 1 and 2 are (250;25) and (150;75).

(b) Now assume that the number of workers increases to 140 due to immigration, keeping total capital fixed at 400. Solve for the amount of capital and labor in

used in each commodity and for the output levels.

Now we have another system:

L1 + L2 = 140

10L1 + 2L2 = 400

L2 = 140 - L1

10L1 + 280 - 2L1 = 400

L1 = 15, L2 = 125

So, K1 = 150, K2 = 250

So, the amounts of inputs for production of commodity 1 and 2 are (150;15) and (250;125).

uses 2 units of capital for each worker, so that K2 =2L2 . The total supply of capital is 400 units and the total supply of labor is 100 units.

(a) Determine the amount of both inputs of production, that is, capital and labor, used in each commodity and the output levels.

According to the data above:

L1 + L2 = 100, K1 + K2 = 400.

As K1 =10L1 and K2 =2L2, so 10L1 + 2L2 = 400.

We have the system of equations:

L1 + L2 = 100

10L1 + 2L2 = 400

L2 = 100 - L1

10L1 + 200 - 2L1 = 400

L1 = 25, L2 = 75

So, K1 = 250, K2 = 150

So, the amounts of inputs for production of commodity 1 and 2 are (250;25) and (150;75).

(b) Now assume that the number of workers increases to 140 due to immigration, keeping total capital fixed at 400. Solve for the amount of capital and labor in

used in each commodity and for the output levels.

Now we have another system:

L1 + L2 = 140

10L1 + 2L2 = 400

L2 = 140 - L1

10L1 + 280 - 2L1 = 400

L1 = 15, L2 = 125

So, K1 = 150, K2 = 250

So, the amounts of inputs for production of commodity 1 and 2 are (150;15) and (250;125).

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