# Production Function

Yes.. I know this is a math forums but there is no economics.stackexchange.com :(.

An undeveloped economy produces goods and services which rely heavily on natural resources. It is described by the following production function:

$$Y = T * K^{1/4} * Z^{1/2} * L^{1/4}$$

where Y is real GDP, T is technology, K is physical capital, Z is natural resources, and L is aggregate hours of work.

If there is no growth in labor productivity, and both the capital stock (K) and natural resources (Z) are constant, with population and labor hours growing at 2 percent per year, what is the growth rate of technological progress in this economy?

So, what I got it that there is no growth in labor productivity meaning Y/L = a constant. K and Z are constant meaning K/L and Z/L is 0. However, I dont know how to use the fact that population and labor hours are growing at 2%/yr.

Thanks!

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"K and Z are constant" does not mean "K/L and Z/L is 0". It might be true that $\frac{dK}{dt}$ and $\frac{dZ}{dt}$ are 0, but you don't really need that restatement here.

You seem to have decided that you want to look at $Y/L$ so you get

$$Y/L = T \times K^{1/4} \times Z^{1/2} \times L^{-3/4}.$$

But some of these are constant so you have

$$\text{constant} = T \times \text{constant} \times \text{constant} \times L^{-3/4}$$

and that gives you a relationship between $T$ and $L$ so you can work out how $T$ changes if $L$ changes by a specified fraction each year.

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