# How do the factors of production map to the GDP identity?

How do the 4 factors of production (nature / capital / labour/ entrepr.) map to the GDP components in: $$Y=C+I+G+(X-M)$$

To me it seems that all factors map to all GDP components, simply because it's fully a different perspective to breakdown the GDP. Is that correct / why?

thanks!

• Your expression is the expenditure measure of GDP. There are also the income measure (wages, profits and other income) and production measure (gross output less intermediate consumption to give value added) which should in theory give the same results. Your factors of production can be considered to be contributing to the production measure Jun 2 '20 at 23:35
• "simply because it's... a different...breakdown of the GDP"---it's not just that. $Y = f(\cdots)$ describes the production technology $f$ that transforms production factors to output $Y$. After production takes place, $Y = C + I + \cdots$ describes how output is allocated between consumption/investment/etc. This involves parameters describing economic agents behavior, instead of the production technology---e.g. the $c_1$ in $C = c_0 + c_1 Y$ (from answer below) is the agent's marginal propensity to consume. Jun 3 '20 at 4:22

They all map through production function to output $$Y$$. Since output is produced from these factors we have

$$Y=f(K,L,E,N,...)$$

Where, $$K$$ would capital, $$L$$ labor, $$E$$ would be entrepreneurship and $$N$$ nature - you can also include any arbitrary number of factors and also note while entrepreneurship is in some textbooks considered factor, nature is often just included under the land label.

The right hand side of the identity is all determined by output.

Consumption is determined by output as its function of disposable income based on output. A simple undergraduate example would be:

$$C=c_0+c_1(Y-T)$$

Where $$c_0$$ and $$c_1$$ are parameters $$Y$$ is output and $$T$$ taxes. You can have more complex consumption functions but they will all be functions of $$Y$$.

Investment $$I$$ depends on the $$c_1$$ parameter which determines what proportion of income people save. That is $$(1-c_1)Y=S$$ where $$S$$ is saving and $$I=S$$ (assuming balanced budget).

$$G$$ is again determined by the output - in the long run government can only spend maximum what the society can produce and what government can extract from society through taxes $$G=T$$.

$$X-M$$ tracks the movement of some of the home output abroad and import of some of the foreign output.

So to sum up, the factors of production map to GDP as they through production function map to $$Y$$ and the right hand side of the equation is just all determined by what $$Y$$ is.

• thanks @1muflon1 so you are confirming that they are different ways to break down Y. that is $Y=F(K,L,H,...)$, $Y=C+I+G+(X-M)$, or for that matter $F(K,L,H,...)=C+I+G+(X-M)$, right? Jun 2 '20 at 16:45
• @elemolotiv you are welcome also I updated the names of factors to match your question, I originally wanted to use more common ones but then I decided to just follow the ones in your question not to create confusion. Also yes that equality would hold you can replace Y with prod function in fact many growth models do just that
– 1muflon1
Jun 2 '20 at 16:48
• great I got it. Can one push a step further say that there is some $f(K,L,E,N)$ in every component? I mean $C=c(K,L,N,E)$, $I=i(K,L,N,E)$, $G=g(K,L,N,E)$ etc. ? For example, food consumers buy surely contains some capital, labour, land, entrepreneurship and that goes in $C=c(K,L,N,E)$ Jun 2 '20 at 16:57
• @elemolotiv it’s correct to say consumption is a composite function of the inputs. A more correct way would be to write C(Y(f(K,L,N,E))).. you can also extent it to other components but you will get more and more complex composite functions - but essentially yes the GDP is all determined by production which depends on inputs so all variables there are ultimately some composite functions of input.
– 1muflon1
Jun 2 '20 at 17:00