f(k ) means Y/EN?? but since f'(k) is the marginal product of capital, so f(k) means the capital ? please try!

bxample:z=2 llf(K.EuN)=X then l'"(2K,b2N)=2Y. Note that we have written the production function so that a 10 percent increase in E has the same effect on production as a 10 percent increase in N. In order to analyse what happens to production when E and N change over time, or between countries, it is useful to think of EN as the e'ective number of workers. if we choose 2 = % we get an expression relating production per effective worker to the capital stock per effective worker: p (ix, Lav) .. i y, EN EN EN thatis. Y K = _'1 . EN F(151v ) Production per efective worker is a function of the capital stock per q'ective worker. With constant returns to scale, the size of the economy does not matv ter. Countries with the same technology 8 and the same capital per worker K/N will have the same GDP per worker independent of their size. This seems reason- able, at least as a rough approximation.\" To simplify notation, we use lower case I: to denote the capital stock per worker: K k= EN and we also use the simplied notation f(k)=F(E%, 1). Note that f ' (k) is the marginal product of capital: f' (k) = F;- (k, 1). We see that the marginal product of capital depends on how much capital there is per effective worker. With this notation, the steady state capital stock per effective worker, k', is determined by the following condition: '2