00:01
In question 9, we have to deal with this cope douglas production function, which is y equals to a times, sorry, a times k to the power of one -third, one -third, and l times 2 to the power of 2 -3rd.
00:31
Where y means production and the a is a parameter k is capital l is labor.
00:39
So we know that the marginal product of labor is just this y take derivative with respect to l and we already got the answer here, which is 2 3rd times a times k divided by l to the power to the power.
01:03
Of one third.
01:06
All right and we just have to plug in all the numbers here.
01:10
So we know p the price of the output is 2 and a is 3.
01:17
This is just a parameter and k is 10 to the power of 6.
01:26
1 million.
01:28
And then l is 1 ,000 so 10 to the power of 3.
01:34
All right, so with all these numbers, we can answer question a.
01:41
Question a, calculate the amount of output produced, so calculate y, and the dollar value of output, p, y.
01:52
So to calculate y, we just have to plug in a, which is 3, because here we have a, so this is a times what is k to the power of 1 third.
02:06
So that is going to be 10 to the power of 2, because 6 divided by 3 is 2, right? and then l to the power of 2 3 3 3 ,000, which is 10 to the power of 2.
02:21
Okay, so the y here is 3 to the power.
02:27
Okay, i'll just write 30 ,000 here.
02:32
So 3 times 10 to the power of 4, right? and what about the value so we time this output amount by the price here so it is going to be 60 ,000 all right question three calculating the wage and the real wage so what is the wage here we know that the wage is going to be the value of marginal product of labor which is p times mpl.
03:14
So we first, we have to calculate this mpl in this setting.
03:18
So two third times a, which is three times k divided by l is 10 to the power of three, right? so 10 to the power of three times one to the power of third, which is just 10.
03:40
So we know that in this question.
03:43
The npl is 20.
03:48
So since we have npl, we can calculate wage, which is p is 2 times 20, which is 40.
03:58
So the wage is 40.
04:00
What about the real wage? so the real wage is wage times divided by the price of the economy, which is equal to just the mpl here.
04:13
So the marginal product of labor is equal to the real wage, which is 20 in this case.
04:24
All right, question c, calculating the labor share, which by definition is w times l divided by p, divided by p times y.
04:42
So labor share is how many proportion of the value output is devoted by labor.
04:53
So we already have this w which is 40, right? and 40 times labor.
05:00
So i was write 40 times 10 to the power of three.
05:08
So divided by py, what we already have is here.
05:12
So it is 60 and also to the 10 to the power of three.
05:19
So the labor share is to third.
05:23
All right.
05:27
So question d calculate what happens to output wage, the real wage, and the labor share in each of the following scenarios...