# Tag Info

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### How can I obtain Leontief and Cobb-Douglas production function from CES function?

The proofs I will present are based on techniques relevant to the fact that the CES production function has the form of a generalized weighted mean. This was used in the original paper where the CES ...

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### Why labour, capital, and output levels cannot be pinned down in perfect competition?

Thus, the furthest we can go in terms of characterising the equilibrium in this economy/firm relates to the optimal capital-labour ratio. In effect, nothing can be said about the level of inputs and ...
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### Lessons From Successfully small island economies

I like this question, in the sense that although it is broad, I think it can be answered concisely and factually. Singapore and China (from your previous question) are largely authoritarian countries....

### Is it true that $\frac{dL}{dq}=1/\frac{\partial q}{\partial L}$?

Question: is the following correct ? $$\frac{dL}{dq}=1/\frac{\partial q}{\partial L},\;\frac{dK}{dq}=1/\frac{\partial q}{\partial K}$$ In general, no. Since $q= f(L,K)$ is a multivariable, ...

### What exactly is L in a Cobb-Douglas production function?

It can be both. The number of working hours are of course easier to interpret. You can also make the assumption that every employee works some fixed number of hours, say 8 per day (or 220 per month, ...
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### How was the CES production function derived?

The CES function can be derived directly from the condition of constant elasticity of substitution. There are various ways to do this, but the simplest derivation occurs for a homothetic production ...

The idea is indeed to Taylor expand the production function. To justify it, you can start with the constant elasticity of substitution function, which in the two-factor case can be written as $$Y = ... 6 votes Accepted ### Aggregate production function and returns to scale I am assuming that you are interested in finding the aggregate production function when you have two plants and they use same inputs. So if you have k units of capital and l units of labor in ... 5 votes ### Is it true that \frac{dL}{dq}=1/\frac{\partial q}{\partial L}? It is valid but only in the short run with the assumption that the capital is fixed. By assuming that output depends on labor and capital you can write$$q=q(L,K)$$Now taking the total derivative ... 5 votes Accepted ### Financial investment in the composition of GDP What you're describing is a change in the capital account, not in GDP. They're related through the balance of payments, in that if a country is running a current account deficit (usually arising ... 5 votes Accepted ### What does it mean by 'intensive form'? The intensive form of the production function is derived from the following. Let us assume a production function, F, with inputs of capital, K, and labor and technology, AL. Thus, output, Y = F(K,AL)... 5 votes Accepted ### CES Production Function with \rho>1 The problem with \rho>1 is that it means the marginal product of factors is not decreasing (\rho<1) or constant (\rho=1) but increasing, which is an odd assumption. Such functions yield ... 5 votes ### Solow Model: Steady State v Balanced Growth Path Following the conversation with user @denesp at the comments of my previous answer, I have to clarify the following: the usual graphical device we use related to the basic Solow growth model (see for ... 5 votes Accepted ### How to show the production function is concave in K and L but not strictly so? So we want the Hessian to be NSD, so we need the PMs to alternate weakly. H=\begin{bmatrix} F_{kk} & F_{kl} \\ F_{kl} & F_{ll} \end{bmatrix}~~NSD \iff~~~F_{kk},F_{ll}\leq0~~~\&~~F_{kk}... 5 votes Accepted ### Returns to scale - Constant Function You want to find a relation between tF(z) and F(tz) for all t>1 (or 0 for CRS). So since 2t=tF(z)>F(tz)=2 for all t>1, we see decreasing returns to scale. 5 votes Accepted ### Is Artificial Intelligence a completely new (and underestimated) production factor? My guess is that it is not a new factor of production, but simply a type of total factor productivity. This is because: factors of production are a stock, which produce services. What is the stock of ... 5 votes Accepted ### Notation of a Cobb-Douglas function printed in 1989 Seems to be the second one, so$$ Q_t = A_t*(K_t^\alpha N^\beta_t T_t^\rho). $$Two clues: This is the usual specification. On the top of page 14 it is written that$$ w_t = \beta Q_t/N_t.  Given ...
Define the production function $Q=f(x_1,..,x_k)$, where $x_i$ denotes the ith input. Next recall that the total differential of output can be written as \$\Delta Q = \sum_{i=1}^{\ k}\frac{\partial Q}{\...