Answer to Question #165352 in Economics for Saron Gebre

Question

Compute the ơ for a CES technology y=( z1Ȣ+ z2Ȣ)1/ Ȣ . And what do you think will the value of ơ be for linear production function?

Now, what are the laws governing the production function in the short run and in the long run production?

Answer 1

In the short term, only one-factor changes. The expansion of production is subject to the principle of diminishing returns from a variable factor (diminishing productivity).

In the long run, all factors of production change, and the principle of economies of scale of production operates. With this technology, the increase in output is carried out by a proportional increase in all production resources up to a certain limit.

$$y=(z_1^8+z_2^8)^{\frac {1}{8}}$$

$$\frac {\delta y}{\delta z_1}=\frac{1}{8}\times8z_1^7(z_1^8+z_2^8)^{-\frac {7}{8}}$$

$$\frac {\delta y}{\delta z_2}=\frac{1}{8}\times8z_2^7(z_1^8+z_2^8)^{-\frac {7}{8}}$$