# How does a positive capital shock cause an increase in land price?

I am trying to determine the exact theoretical mechanism for a positive capital shock to create an increase in land price.

Assuming output is a function of land ($L$), labour ($N$) and capital ($K$) :

$$Y = A f (L, N, K)$$

I am unsure if I am correct, but so far I have,

Positive capital shock -> increase in the MPK -> labour demand rises -> wage rises -> qty supplied of labour rises -> MPN rises -> with more workers available to work the land, each additional unit of land is able to produce more output -> MPL rises -> price of land rises.

If you know any papers that deal with this particular mechanism please let me know also.

• Positive capital shock raises directly not only the MPK, but also the MP-Land (usually). – FooBar Nov 9 '15 at 17:26

I think you got the answer, to give more detail: assume a Cobb-Dougblas production function: $Y=AL^{\alpha_1}N^{\alpha_2}K^{1-\alpha_1-\alpha_2}$. The marginal product of land i.e. price is then:$$MPL = \alpha_1 A L^{\alpha_1-1}N^{\alpha_2}K^{1-\alpha_1-\alpha_2}$$ Simulate this model with various factor values. You can build the story yourself using this basic textbook explanation, don't need a paper for empirical evidence.
$Y=A L^{\alpha_1} N^{\alpha_2} K^{1-\alpha_1-\alpha_2}$