00:02
We have to determine the value of m in the production function.
00:06
That is f bracket k comma l bracket close is equal to 4k to the power l to the power 13 added to 3k.
00:15
So we can check for homogeneity a production function is said to be homogeneous of degree m if it satisfies the following property f tk comma tl is equal to t to the power m multiplied by f bracket open k comma l bracket close.
00:37
So in this case, we have f k comma l is equal to 4k l.
00:45
Sorry 4k to the power l to the power 13 added to 3k.
00:54
So now let's consider f bracket tk comma tl.
00:58
So f tk comma tl is equal to 4tk to the power tl to the power 13 added to 3 bracket tk.
01:14
So now let's compare this with t to the power m multiplied by f comma kl.
01:20
Sorry f bracket k comma l.
01:22
So t to the power m multiplied by f comma l bracket close is equal to t to the power m multiplied by 4k to the power l to the power 13 added to 3k.
01:45
So for the two expressions to be equal we need 4tk to the power tl to the power 13 added to 3tk is equal to t to the power m multiplied by 4k to the power l to the power 13 added to 3k.
02:08
So now let's equate this exponent and coefficient.
02:12
So exponents to the power tl to the power 13 is equal to t to the power m for the first term t to the power 1 is equal to t to the power m for the second term coefficients 4tk to the power tl to the power 13 is equal to 4t to the power mk to the power l to the power 13 for the first term then 3tk is equal to 3t to the power mk for the second term...