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 [tex]p = 10x^{0.2} y^{0.8}[/tex], and in the current situation [tex]p=1200[/tex] and [tex]x=130[/tex].
With this information we can calculate the actual budget level:
[tex]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[/tex]
The next year, with an increase in demand of 100 more automobiles, the production will be [tex]p_1=1300[/tex].
If we calculate y for this new situation, we have:
[tex]y_1=(\frac{p_1}{10x^{0.2}} )^{1.25}=(\frac{1300}{26.47} )^{1.25}=49.10^{1.25}=130[/tex]
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.
[tex]\Delta y=y_1-y_0=130.00-117.62=12.38[/tex]
This value of Δy is not constant for a constant increase in production.
