Question

A firm has the production function f(x,y)=x

1.40
y
1.40
. This firm has decreasing returns to scale and diminishing marginal product for factor x. constant returns to scale. decreasing returns to scale and increasing marginal product for factor x None of the above. increasing returns to scale and decreasing marginal product for factor x.

Answer 1

the firm has decreasing returns to scale and diminishing marginal product for factor x

Step-by-step explanation:

The production function f(x,y) = x^1.40 * y^1.40 exhibits decreasing returns to scale.

Returns to scale refer to the relationship between proportional changes in the inputs of production and the resulting proportional change in output. If a production function exhibits decreasing returns to scale, this means that if we increase both inputs x and y by the same proportion (for example, we double both of them), the resulting increase in output will be less than double. To determine the returns to scale of the given production function, we can use the formula:

f(tx, ty) / f(x,y)

where f(tx, ty) is the output produced when we multiply both inputs by the same factor t, and f(x,y) is the output produced by the original inputs.

Substituting the given production function into this formula, we obtain:

f(tx, ty) / f(x,y) = (tx)^1.40 * (ty)^1.40 / x^1.40 * y^1.40

= t^1.40 * t^1.40 = t^2.80

Since t^2.80 decreases as t increases, this indicates decreasing returns to scale for the given production function.

Furthermore, the production function has diminishing marginal product for factor x, which means that as we increase the amount of factor x while holding factor y constant, the additional output produced by each additional unit of x will decrease.

Therefore, the correct answer is: the firm has decreasing returns to scale and diminishing marginal product for factor x.

Answer 2

The Water-splashing Festival is a New Year festival of the Dai, Achang, Blang, Wa, Deang and other ethnic minorities in China and some ethnic groups in Indochina Peninsula. It is the grandest traditional festival of the Dai people in a year. The Dai festival in China is in the sixth and seventh months of the Dai calendar (about ten days after the Qingming Festival). It is now fixed on April 13-15 in the Gregorian calendar. During the festival, people pour water on each other, and hold activities such as Buddha worship, dragon boat racing, raising and lighting Kongming lanterns. After the founding of the People's Republic of China, new contents such as parades, art performances, film evenings, exhibitions and material exchanges were added. Thailand, Myanmar, Laos and other countries celebrate this festival in the middle of April every year.

The Water-splashing Festival is a comprehensive stage to show the traditional culture of Dai nationality, such as water culture, music and dance culture, diet culture, dress culture and folk worship. It is an important window to study the history of Dai nationality and has high academic value. The artistic performances such as Zhangha and White elephant dance displayed in the Water-splashing Festival help to understand the Dai people's national characteristics of feeling nature, loving water and respecting Buddha, and being gentle and quiet. At the same time, the Water-splashing Festival is also an important link to strengthen the unity of the people of all ethnic groups in Xishuangbanna, and plays a positive role in the friendly cooperation and exchanges between Xishuangbanna and Southeast Asian countries, and in promoting the social, economic and cultural development of the whole state.

On May 20, 2006, the folk custom was approved by The State Council to be included in China's first batch of national intangible cultural heritage list.