00:01
Hey guys, let's do problem 12.
00:03
In this problem, we need to find what is the marginal product of studying supply and demand problems for will and for david.
00:14
And the information such as the production function, great production function for both of them are given here.
00:21
So let's do the problem.
00:24
It is given that for wheel, the production function is 2 .5, 8 to the power 0 .36.
00:32
And r2 d .04 0 .64.
00:34
We know that marginal productivity of studying supply and demand problems, which is denoted as mpr, is the change in grid due to change in number of hours wheel studied supply and demand problems.
00:53
Therefore, the marginal productivity of wheel is going to be change in the production function with respect to our and when we do this differentiation here 2 .5 and a to the power 0 .36 is a constant so it will come out of the differentiation and we will differentiate r to the power 0 .64 with respect to r and when we do this we get 0 .64 multiplied by r to the power 0 .64 minus 1 and this calculation gives us 1 .6 a to the power 0 .36 r to the power negative 0 .36 or we can write 1 .6 a to the power 0 .36 divided by r to the power 0 .36 and in a simplest form it gives us 1 .6 in the bracket it by r to the power 0 .36 which is wills marginal productivity.
02:05
Similarly we can now find out what is david's marginal productivity.
02:10
The production function is given as 2 .5 a to the 1 .0 .25 or to the bar 0 .75 for david therefore his marginal productivity is this one 0 .25 a to the bar 0 .25 or to the bar 0 .75 we need to take the differentiation when we take that it will come out.
02:32
Because a and 0 .25 these are constants and this differentiation gives us 1 .87 a to the power 0 .25 or to the power negative 0 .25 or we can write this as david's marginal productivity...