<p>The short answer is no.</p>
<p>If you recall the simple intensive form (capital-labor ratio) of the Solow model:
<span class="math-container">$$
y_t = k_t^\alpha,
$$</span>
with <span class="math-container">$0 &lt; \alpha &lt; 1$</span>, you would realize that it exhibits decreasing returns to scale (to capital-labor ratio). When the competitive firm maximizes its profit, it chooses the optimal capital-labor ratio.</p>
<p>In Varian's words, the decreasing-returns-to-scale is just constant-returns-to-scale but with the presence of a fixed factor (such as land). Say you have a production function with labor <span class="math-container">$L$</span> and land <span class="math-container">$T$</span>
<span class="math-container">$$
Y_t = L_t^{\alpha} T_t^{1-\alpha}
$$</span>
This is CRTS. But by fixing the land factor: <span class="math-container">$T_t = \bar{T} = 1 \ \forall t$</span>, you have a DRTS technology:
<span class="math-container">$$
Y_t = L_t^\alpha
$$</span>
You can solve this model (profit maximization) in 2 ways.</p>
<p>(2) The first way is to solve it as a DRTS model
<span class="math-container">$$
\max L^{\alpha} - wL
$$</span></p>
<p>(2) The second way is solving it as a CRTS model
<span class="math-container">$$
\max L^{\alpha} T^{1-\alpha} - wL - qT
$$</span>
and then imposing the land market clearing condition in equilibrium <span class="math-container">$T_t = \bar{T} = 1 \ \forall t$</span>.</p>
<p>The results are the same regardless of how you solve it as a DRTS or CTRS-in-disguise. For more exposition, please read Hal Varian's Microeconomic Analysis (p.352).</p>

CC BY-SA 4.0
2024-04-23T07:30:09.440Z
Hi teddi! Having read your answer, I don't understand what question "*The short answer is no.*" applies to? Could you please elaborate?
Giskard
CC BY-SA 4.0
2024-04-23T09:37:35.037Z
Thank you that's extremely helpful!
georgetbarber
CC BY-SA 4.0
2024-04-23T10:45:08.583Z
@Giskard Hi. I think what I meant was the production function can have CRRS on the scale level, but when you consider the intensive form, it is actually DRRS. So it's not problematic, just 2 faces of the same coin. Also, without DRRS to the capital-labor ratio, there will be no unique steady state.
teddi
CC BY-SA 4.0
2024-09-20T09:44:51.397Z
@georgetbar if you think the answer is "extremely helpful" then pls. as a minimum upvote it and perhaps even consider accepting it.
Jesper Hybel
CC BY-SA 4.0
2024-04-23T02:18:28.387Z
2024-04-23T02:18:28.387Z
teddi
<p>I understand with IRS we have explosive growth and a single firm would eventually dominate the market since MC &lt; AC, and hence P &lt; AC, so firms would leave the market. I am struggling to find what would happen if we had the opposite case - DRS. Would it be similarly problematic?</p>

CC BY-SA 4.0
2024-04-22T08:04:02.343Z
"*Would there still be [...] perfect competition?*" Perfect competition is a modelling assumption, not a result, so I am not sure what you are asking here?
Giskard
<macroeconomics><economic-growth><solow><balanced-growth><returns-to-scale>
What would happen if we had decreasing returns to scale in the solow-swan growth model? Would there still be a steady state and perfect competition?
georgetbarber
# What would happen if we had decreasing returns to scale in the solow-swan growth model? Would there still be a steady state and perfect competition?

(Asked by: username_0 on 2024-04-21)

I understand with IRS we have explosive growth and a single firm would eventually dominate the market since MC < AC, and hence P < AC, so firms would leave the market. I am struggling to find what would happen if we had the opposite case - DRS. Would it be similarly problematic?

**Tags:** macroeconomics, economic-growth, solow, balanced-growth, returns-to-scale

> **Comments:**
> **username_1**: "*Would there still be [...] perfect competition?*" Perfect competition is a modelling assumption, not a result, so I am not sure what you are asking here?  

---

## 1 answers

### Answer by username_2 on 2024-04-23. Score: 2

The short answer is no.

If you recall the simple intensive form (capital-labor ratio) of the Solow model:
$$
y\_t = k\_t^\alpha,
$$
with $0 < \alpha < 1$, you would realize that it exhibits decreasing returns to scale (to capital-labor ratio). When the competitive firm maximizes its profit, it chooses the optimal capital-labor ratio.

In Varian's words, the decreasing-returns-to-scale is just constant-returns-to-scale but with the presence of a fixed factor (such as land). Say you have a production function with labor $L$ and land $T$
$$
Y\_t = L\_t^{\alpha} T\_t^{1-\alpha}
$$
This is CRTS. But by fixing the land factor: $T\_t = \bar{T} = 1 \ \forall t$, you have a DRTS technology:
$$
Y\_t = L\_t^\alpha
$$
You can solve this model (profit maximization) in 2 ways.

(2) The first way is to solve it as a DRTS model
$$
\max L^{\alpha} - wL
$$

(2) The second way is solving it as a CRTS model
$$
\max L^{\alpha} T^{1-\alpha} - wL - qT
$$
and then imposing the land market clearing condition in equilibrium $T\_t = \bar{T} = 1 \ \forall t$.

The results are the same regardless of how you solve it as a DRTS or CTRS-in-disguise. For more exposition, please read Hal Varian's Microeconomic Analysis (p.352).

> **Comments:**
> **username_1**: Hi username_2! Having read your answer, I don't understand what question "*The short answer is no.*" applies to? Could you please elaborate?  
> **username_0**: Thank you that's extremely helpful!  
> **username_2**: @username_1 Hi. I think what I meant was the production function can have CRRS on the scale level, but when you consider the intensive form, it is actually DRRS. So it's not problematic, just 2 faces of the same coin. Also, without DRRS to the capital-labor ratio, there will be no unique steady state.  
> **username_3**: @georgetbar if you think the answer is "extremely helpful" then pls. as a minimum upvote it and perhaps even consider accepting it.  

---

