The first stage of development for MyState will to be define the factors of production and devise laws of motion to shape their development. In this process, we will often start with unrealistic assumptions – which may be modified at an appropriate juncture – but this is a necessary step in order to provide mouldable material.
First, we shall assume that there three factors of production which determine total output:
Y = Ka (AN)(1-a)
Y = output, K = capital, A = total factor productivity, alpha = elasticity of income with respect to capital
In accordance with economic evidence, we shall assume that the capital income share (alpha) is 0.33. For simplicity, we will assume a constant elasticity of substitution.
Next we require laws of motion to determine how each variable evolves through time. Intuitively, we can imagine the explanatory variables:
△K = f( expected return, risk appetite, depreciation)
When an investor makes the decision to borrow money, she must form an idea of the expected return from that investment. For if the expected return were negative, then she would not borrow money on those terms. The expected return is a function of the following variables:
Expected return = f(interest, expected sales, expected input costs, depreciation)
The interest is the cost of the loan – say 5%. All production is for the purpose of selling, so the investor must form an idea of consumption (sales) in the future. They must also form an idea of the expected costs of production, as well as the depreciation on the capital stock. This forms the basis of a decision rule whether to invest or not.
But there is another factor: uncertainty. If wider economic uncertainty increases, then I will become less sure of my return and less willing to invest. This is related to the investor’s risk appetite. For now we shall assume that this is exogenously determined. Lastly there is the depreciation rate of capital which erodes away at the existing capital stock.
The law of motion for capital