1. Suppose a country's production function is Y = 4 + 9*K. If the level of...

1. Suppose a country's production function is
Y = 4 + 9*K.
If the level of capital (K) is 17, then what is the marginal productivity of the 18 unit of capital?

2. Suppose a country's production function is
Y = 4 + 9*K^0.5
If the level of capital (K) is 17, then what is the marginal productivity of the 18 unit of capital?

3. Assume the production function for a small country is
Y = 7*K^0.5.
If 20% of capital is lost to depreciation every year and the country uses 24% of output as investment, what is the level of investment if K= 35?

4. Assume the production function for a small country is
Y = 5*K^0.5.
Also assume that 24% of capital is lost to depreciation every year and the country uses 19% of output as investment. What is the steady state level of K?

5. North Solonia has 96 machines (K=96).
South Solonia's output is twice that of North Solonia.
How many more machines does South Solonia have? The production function for each country is Y = 3*K^0.5.

Expert Solution

Answer1:-

Marginal productivity is the outcome of employing one extra unit of capital. Initially when capital was 17, productivity was Y = 4 + 9*K, i.e., Y = 4+ 9*17 = 157. With K = 18, Output will be Y = 4+ 9*18 = 170. So, Marginal productivity with 18 units = 170-157 = 13 units.

Answer2:-

Y = 4 + 9*K0.5 = 4 + 9*17*0.5 = 80.5
Y = 4 + 9*18*0.5 = 81+4 =85
In this case Marginal productivity for 18 units will be 85 -80.5 = 4.5 Units

Answer3:-

Production when K is 35. Out of this 20% i.e., (35*20%= 7) investment is lost due to depreciation; K will become 28.
Y = 7*K*0.5 = 7*28*0.5 = 98 Units
Out of this 24% output will be used as investment.
So level of investment will be = 98 + 28% of 98 = 98 + 23.52 = 121.52.

Answer 4:-

Steady state level of capital is when Capital is just enough so that the growth level does not change over the years. The increase in capital is equal to increase in depreciation so that a steady level of output is maintained.

Answer 5:-

North solonia has machines - 96.
Production of North Solonia = 3*K*05 =3*96*0.5 =3*48 = 148 units

Since production of South Solonia should be doubles machines required:-
148 * 2 = 3*K*0.5
K = 48*4 = 196 machines is reqd.

Rahul Sunny answered 1 year ago

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