Economics

Economics Assignment

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a. The function Y=K1/2L1/2 has a constant return to scale. A production function is represented mathematically as a costant return to scale as λY= F(λK, λL) if λ is a positive number. Therefore, if we multiply λ by both the amount of labour and capital and then multiplying λ with the amount of output. By doing this for the function Y=K1/2L1/2 we find that it has a constant return to scale. Constant return to scale means that the input and the out are proportional to each other.

b. The production function as a function of labor and capital is given as the follows:

Y=K1/2L1/2

Therefore, to get the function of output per worker we divide both sides of the functions by L. This result in the following function:

Y/L= K1/2L1/2/L

Y/L=.

Y/L=. 1

Y/L=

In the steady state, it means that the state at which the capital per worker and output per worker is not changing. The steady state is given as follows:

sY/L= δK/L

Where δ is the depreciation rate per capital. Now substituting the equation into the first equation to find:

s=δ

K/L=s2/ δ2

Therefore, the steady state per worker in this situation is s2/ δ2

To obtain the output per worker we plug the value of per capital in the first equation.

Y/L=

Y/L= (s2/ δ2)1/2

Y/L= s/ δ

Therefore, the steady state of output per worker is s/ δ.

c. As from the above equations the steady state output per worker is given by the equation s/ δ. Using the given value we find that the value of s is 0.2 and that of δ is 0.05 0.2/0.05=4 therefore, the output per worker is 4.

d. Just like in the previous question, the steady state output per worker is 0.6/0.05=12. Therefore, the steady state output per worker in this situation with an increase in s is 12. The value has increased than when the value of s is less. This means an increase in the saving means that the output per worker increases.

1. a. Growth in technology causes productivity to increases. The economy grows and manufactures tend to automate their productivity. The result is that the manufactures produces more products using less labour.

In the short run the demand for labor drops but shift to the right. The following is the graph for the short run. In the short run the equilibrium of worker demand decreases.

In the medium run, the technological development cannot meet the demand for producing new output. The manufacturing companies will need to come up with new products that the existing technology can offer. Therefore, in this situation the labor starts to increase. Therefore, the companies as they require more people to carry out the manufacturing the demand for more labor is seen. In the end the labor demand will finally get back to where it was. Labor also starts to stabilize within the market until a new technological development is achieved. The graph below illustrates what happen in the medium run (Czaja, & Moen, 2004).

b. The best example can be obtained from the british lesson when they were changing from agricultural activities to industrialization. During this, time machines replaced most of the laborers. The farmers started using more machines in the farms and the result was that most individuals lost their jobs in the farm. This was in the short run where many of the people lost jobs. The level of equilibrium during the short run in the labor market dropped. In the medium run, there arouse more work as there was need for laborers who could carry the manufacturing of the machines. Therefore, again there was a rise in the demand for workers. Therefore, in the medium run the labor equilibrium level rose.

c. The research and development spending is determined by a number of factors. The first factor is the number of people involved in the research and development. If there are a large number of people then the spending is high. However, when the number of people is less than the spending is less.

Another factor that determines the research and development spending is the technology in use. The use of high-end technology might be expensive in the short run but in the medium run, it is cheap for the company. The use of outdated technology on the other hand is expensive in the medium run. However, in the short run it would be expensive for the company.

References

Czaja, S. J., & Moen, P. (2004). Technology and employment.