Answer to Question #127365 in Macroeconomics for som

Question

1. Consider the following aggregate production function: Y=100×√L×√K, where A is the total factor productivity, K is the amount of capital in the economy, L is the labour force, and Y is the GDP. Is this aggregate production function exhibiting the constant returns to scale and diminishing marginal product of capital? Explain how you know
2. In 1867, the government employed 6% of the country’s workers. Since then, the country’s labour force has been growing an average 0.5% a year while the government’s employment has been growing an average 1% a year. What is the share of the government employment in the country’s labour force by 2011?
3. Investopedia.com explains that “Bitcoin is a digital or virtual currency created in 2009.” Is Bitcoin money?

Answer 1

1.

At the first stage (when L is from 0 to 4), there is an increase in the return of the variable resource (i.e., the mean product APL grows), the marginal product of labor MPL also increases and reaches its maximum value. Then the marginal product stops growing (MPL = max, at L = 3) and reaches its maximum point (sometimes called the decay point of the marginal product). At the same time, the average product APL continues to grow to its maximum value (in our example, APL = max at L = 4).

At the second stage (at L from 4 to 7), a decrease in the return of the variable resource is observed (i.e., the average product APL decreases), the marginal product MPL also continues to decrease and reaches zero (MP = 0 at L = 7). In this case, the volume of the total product TP becomes the maximum possible and its further increase due to the increase in only variable resources is no longer feasible.

At the third stage (L> 7), the marginal product acquires a negative value (MP <0), and the total TP product begins to decrease.

To achieve the most effective results and minimize costs, the firm should use a variable resource in the amount corresponding to stage 2. At stage 1, the additional use of a variable resource leads to a decrease in average costs. At stage 3, the total output and average costs are reduced (i.e., profitability falls).

The reason for this behavior of the production function lies in the law of diminishing marginal returns:

The law of decreasing marginal return. Starting from a certain point in time, additional use of a variable resource with a constant amount of a constant resource leads to a reduction in the marginal return, or marginal product.

2.

labor resources increased by 105.8%

the number of employees in the public sector is 25.1%, which is 19.1% more than in 1867 (25,1-6=19,1)

3.Bitcoin is virtual money and can be used to pay for goods and services, and they participate in the commodity-money-commodity cycle