Question

4. (a) The following table presents data on the economy of Macroland.

Period	Quantity of Labor (L)	Quantity of Capital (K)	Total Output (Y)
1	50	50	200
2	50	60	215
3	50	70	225
4	50	80	230

1. Calculate Labor productivity for each period.
2. Calculate output per capital for each period.
3. Calculate marginal return to capital for each period.
4. Calculate the growth rate for each period.

(b) The following table presents data on the economy of Microland.

Period	Quantity of Labor (L)	Quantity of Capital (K)	Total Output (Y)
1	50	50	200
2	60	50	220
3	70	50	235
4	80	50	245

1. Calculate Labor productivity for each period.
2. Calculate output per capital for each period.
3. Calculate marginal return to labor for each period.
4. Calculate the growth rate for each period.

Answer 1

Q4 (a) Refer to the below table:

Macroland
Period	Qty of Labor (L)	Qty of Capital (K)	Total Output (Y)	Labor Productivity	Output Per Capital	Marginal Returns to Capital	Growth Rates (%)
1	50	50	200	4	4	_	_
2	50	60	215	4.3	3.6	1.5	7.5
3	50	70	225	4.5	3.2	1	4.7
4	50	80	230	4.6	2.9	0.5	2.2

1. Labor productivity measures the total output produced per unit of labor employed.

Labor Productivity = Total Output / Quantity of Labor

Column 5 in the above table shows the labor productivity in the respective periods. For example, in period 2 the labor productivity is given by 200/50 = 4

2. Output per capital measures the total output produced using per unit capital employed.

Output per capital = Total Output / Quantity of Capital

Column 6 in the above table shows the output per capital in the respective periods. For example, in period 2 the output per capital is given by 215/60 = 3.6

3. Marginal returns to capital show the ratio of change in total output to the change in capital input.

Marginal returns to capital = Change in Total Output / Change in Capital

Column 7 in the above table shows marginal returns to capital in the respective periods. For example, in period 3 :

Change in output = Output in Period 3 – Output in Period 2 = 225 – 215 = 10

Change in capital = Capital employed in period 3 – Capital employed in period 2 = 70 – 60 = 10

Thus, Marginal Returns To Capital in period 3 = 10/10 = 1

4. Growth rate of output in each period can be calculated by using the below formula:

Growth Rate = [(Current Output – Previous Year Output)/Previous Year Output] x 100

Column 8 in the above table shows growth rates in the respective periods. For example, in period 3 is given by :

Growth in Period 3 = [(Period 3 Output –Period 2 Output)/Period 2 Output] x 100

= [(225-215)/215] x 100

= (10/215) x 100

= 0.0465 x 100 = 4.7%

Q4 (b) Refer to the below table:

Microland
Period	Qty of Labor (L)	Qty of Capital (K)	Total Output (Y)	Labor Productivity	Output Per Capital	Marginal Returns to Labor	Growth Rates (%)
1	50	50	200	4	4	_	_
2	60	50	220	3.7	4.4	2	10
3	70	50	235	3.4	4.7	1.5	6.82
4	80	50	245	3.1	4.9	1	4.26

1. As explained above, Labor productivity for each period is calculated by the below formula in column 5:

Labor Productivity = Total Output / Quantity of Labor

2. As explained above, Output per capital for each period is calculated by the below formula in column 6:

Output per capital = Total Output / Quantity of Capital

3. Marginal returns to labor show the ratio of change in total output to the change in labor input.

Marginal returns to labor = Change in Total Output / Change in Labor Units

Column 7 in the above table shows marginal returns to labor in the respective periods. For example, in period 3 :

Change in output = Output in Period 3 – Output in Period 2 = 235 – 220 = 15

Change in labor = Labor employed in period 3 – Labor employed in period 2 = 70 – 60 = 10

Thus, Marginal Returns To Labor in period 3 = 15/10 = 1.5

4. As explained above, Growth rate of output in each period can be calculated by using the below formula: It is shown in column 8 of the above table

Growth Rate = [(Current Output – Previous Year Output)/Previous Year Output] x 100