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Returns to scale - Constant Function

You want to find a relation between $tF(z)$ and $F(tz)$ for all $t>1$ (or $0$ for CRS). So since $2t=tF(z)>F(tz)=2$ for all $t>1$, we see decreasing returns to scale.
Kitsune Cavalry's user avatar
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Does returns to scale always lead to economies of scale?

Excellent question (I am assuming your intended question is "does increasing returns to scale always leads to economies of scale"): The two concepts are related but Returns to scale (RS) is ...
Dayne's user avatar
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4 votes

Does returns to scale always lead to economies of scale?

Since my previous answer is quite long, posting here another answer for giving some (non-technical) references with brief description (as suggested by Michael in the comment to previous answer). All ...
Dayne's user avatar
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Economies of scale v.s. technological change

The problem is to distinguish between changes along the production function, from $f(K_1, L_1)$ to $f(K_2, L_2)$, and changes of the production function, from $f(K_1, L_1)$ to $g(K_1, L_1)$. A very ...
user11629's user avatar
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4 votes

Diminishing returns and economies of scale

In production with more than one input, "diminishing returns" refers to what happens when we increase one input while keeping all the rest constant. "Economies of scale" is a more informal term for "...
Alecos Papadopoulos's user avatar
4 votes

Can a monopoly INCREASE the market surplus compared with a competitive market?

Under standard assumptions (some of which you state in your question: no externalities, etc.), no. This follows from the First Welfare Theorem. Perhaps there are departures from standard models that ...
Theoretical Economist's user avatar
3 votes

Why do banks offer less interest on larger deposits?

When you lend your money to a bank (by depositing it), they don't just make money off of lending out your money. They also make money out of charging you for banking services. If the bank makes more ...
BKay's user avatar
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finding the returns to scale of a production function

What you have proven is that $$f(tx_1, tx_2) > tg(x_1,x_2)$$ which translates "scaled $f$ is higher than some other, homogeneous function $g$ scaled by the same factor". This does not prove ...
Alecos Papadopoulos's user avatar
3 votes
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Mathematic notation of scale returns

Quoting from the question: $F(aK,aL)$ : simultaneous and proportional inputs increase $aF(K,L)$ : output increase But $F(aK,aL)$ is an output increase, that is why it starts with $F$. It ...
Giskard's user avatar
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Shouldn't big tech want to split up?

This is going to be a hard find because it is not true. These companies have increasing returns to scale over the relevant range and for the foreseeable future. Many technologies, particularly ...
RegressForward's user avatar
3 votes

Does returns to scale always lead to economies of scale?

I think you wanted to ask "Do returns of big scale always imply economies of scale?" The answer is no. Diseconomies of scale exist too. You can get big, get economies of scale, then get even ...
KarmaPeasant's user avatar
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2 votes

Term for partial resource use economics

I think what you are looking for is known as overselling.
VARulle's user avatar
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Is there any empirical evidence for the so-called "law" of diminishing returns

The above chart is from Agroecosystems, nitrogen-use efficiency, and nitrogen management by Cassman KG, Dobermann A, Walters DT, and it deals with this sort of question quite extensively for those ...
Roger's user avatar
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Why doesn't economy of scale bring down prices of food?

In the US at least, purchases and wages cost more than rent for a fast-food type business: Purchases include some other hidden labor costs (drivers for transportation etc.) I'm not sure what's in the ...
got trolled too much this week's user avatar
2 votes

Economies of Scale, texbook example

The surface area of a pipe with length $l$ and radius $r$ is $l2r\pi$. This is approximately proportional to how much material you need to make the pipe,1 so it is proportional to the cost of the pipe....
Giskard's user avatar
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2 votes
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Why $\gamma(c,i)=cv(i)$ means diseconomies of scale?

You wrote: It means per unit cost of transating goods is independent of the volume transacted.\ But in this equation $c$ is left so I wonder how can we say that "it is independent of the volume ...
BakerStreet's user avatar
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2 votes

Constant returns and (weak/strict) concavity

No, it is not generally true that the rank of the Hessian of a CRTS production function with $K$ inputs is equal to $K-1$. Example 1. Let $x$ be a vector of $K$ inputs, and consider the quadratic ...
Bertrand's user avatar
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2 votes

How to calculate Returns to Scale for Translog production function with two inputs?

The typical translog production function $q \left(K, L\right)$ satisfies \begin{equation} \ln \left( q \left(K, L \right) \right) = \ln \left( A \right) + \alpha \ln \left( K \right) + \left( 1 - \...
Thomas Favory's user avatar
1 vote

What are the best criticisms of economies of scale?

What are the best criticisms of economies of scale? As mentioned by Michael in the comments economies of scale is a property of a production function, its not an philosophical idea, policy proposal ...
1muflon1's user avatar
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1 vote

What are the motivations for two non-profit Hosptials to merge?

What possible market motivations are there for Hospital A to acquire Hospital B? Economies of scale - when economies of scale exist the cost per unit will decrease with scale of production. If ...
1muflon1's user avatar
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1 vote

Mathematic notation of scale returns

Returns to scale is directly related to homogeneous functions: For a homogeneous function $F(x,y)$ given $\theta>0$, for simplicity, $$F(\theta x,\theta y) = \theta^r F(x,y)$$ where would we ...
Brennan's user avatar
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1 vote

What's the econ word for "Savings and efficiencies gained via consolidation"?

If you are looking for term for the reason why the efficiencies occur it would be the increasing returns to scale.
1muflon1's user avatar
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1 vote

Economies of scale: when is it disadvantageous?

I would give you a simple answer: when the marginal cost is equal to the marginal income. This would be the equilibrium and beyond that the company would lose money.
Ignacio Valdés Zamudio's user avatar
1 vote

Can a monopoly INCREASE the market surplus compared with a competitive market?

Trying to avoid posting further comments above. Ok, as you suggest, let's assume that demand curve does not shift, because P=ATC condition moves the price along the deman curve. The only situation ...
london's user avatar
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1 vote

Returns to scale - Constant Function

I would say it exhibits no returns to scale. What follows is a counter argument to the idea that it can exhibit returns to scale. A 'return to scale' means that production will change in response to a ...
ahorn's user avatar
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