Question

The automobile assembly plant you manage has a Cobb-Douglas production function given by p = 10x^0.2 y^0.8

Answer 1

Answer:

The variation needed for the daily buget to follow the increase in production for the first year is 12.38 $/year.

This value of Δy is not constant for a constant increase in production.

Step-by-step explanation:

We know that the production function is $p = 10x^{0.2} y^{0.8}$, and in the current situation $p=1200$ and $x=130$.

With this information we can calculate the actual budget level:

$p_0 = 10x^{0.2} y^{0.8}\\\\1200=10*130^{0.2} y^{0.8}\\\\1200=26.47*y^{0.8}\\\\y=(1200/26.47)^{1/0.8}=45.33^{1.25}=117.62$

The next year, with an increase in demand of 100 more automobiles, the production will be $p_1=1300$.

If we calculate y for this new situation, we have:

$y_1=(\frac{p_1}{10x^{0.2}} )^{1.25}=(\frac{1300}{26.47} )^{1.25}=49.10^{1.25}=130$

The budget for the following year is 130.

The variation needed for the daily buget to follow the increase in production for the first year is 12.38 $/year.

$\Delta y=y_1-y_0=130.00-117.62=12.38$

This value of Δy is not constant for a constant increase in production.