<p>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.</p>

CC BY-SA 3.0
2015-11-09T18:34:54.763Z
2015-11-09T18:34:54.763Z
london
<p>You might want to assume a Cobb-Douglas production function for the sake of simplicity. </p>

<p>$Y=A L^{\alpha_1} N^{\alpha_2} K^{1-\alpha_1-\alpha_2}$</p>

<p>Hint: Look at to the cross derivatives.</p>

CC BY-SA 3.0
2015-11-09T16:22:32.813Z
2015-11-10T03:23:43.720Z
2015-11-10T03:23:43.720Z
RegressForward
<p>I am trying to determine the exact theoretical mechanism for a positive capital shock to create an increase in land price.</p>

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

<p>$$ Y = A f (L, N, K) $$</p>

<p>I am unsure if I am correct, but so far I have,</p>

<p>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. </p>

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

CC BY-SA 3.0
2015-11-09T17:26:12.073Z
Positive capital shock raises  directly not only the MPK, but also the MP-Land (usually).
FooBar
<production-function>
How does a positive capital shock cause an increase in land price?
Kelly
# How does a positive capital shock cause an increase in land price?

(Asked by: username_0 on 2015-11-09)

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.

**Tags:** production-function

> **Comments:**
> **username_1**: Positive capital shock raises  directly not only the MPK, but also the MP-Land (usually).  

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## 2 answers

### Answer by username_2 on 2015-11-09. Score: 2 | Accepted answer

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.


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### Answer by username_3 on 2015-11-09. Score: 3

You might want to assume a Cobb-Douglas production function for the sake of simplicity.

$Y=A L^{\alpha\_1} N^{\alpha\_2} K^{1-\alpha\_1-\alpha\_2}$

Hint: Look at to the cross derivatives.


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