00:01
So here we've got a pretty complicated production question, right? we are given a production function and the marginal products here are pretty straightforward.
00:10
They are the marginal product of labor is just k plus 1, the marginal product of capital is equal to l plus 1, and we are told that the rate of return, sorry, the price of capital is equal to 1, but the wage is equal to this, and we are also told that the quantity produced has to be equal to 5.
00:28
So a, in the first case, we are imagining l is equal to something, k is equal to 0.
00:36
So this means that quantity, which has to be 5, is equal to k times 0 plus 0 plus l, and so we have l is equal to 5, right? we'll need 5 units of labor.
00:50
Now, the key thing is we use labor only if the marginal product of labor over the wage is greater than the marginal product of capital over r, right? because this is sort of units of output per dollar, and we want many units of output per dollar.
01:12
So if we substitute in here, right, what do we get? we get k plus 1 over w has to be less than or equal to l plus 1 over 1, which is equal to 6, right? because we know that l is equal to 5.
01:31
So this tells me, and this, sorry, k is, right, this is equal to 1 over w.
01:37
So this tells me that if i sort of cross multiply that w has to be, or let me put it the other way around, that, sorry, 1 over w, divide both sides by 6, we get 1 over 6, multiply both sides by w, we get w, and we get wage has to be less than 1 sixth, right? wage is less than 1 sixth...