# Tag Info

Accepted

### Why are cost functions often assumed to be convex in microeconomics?

There are several reasons: Didactic Reasons: Other users seem to have missed it but in your question you specify you are talking about "(introductory) microeconomics" [emphasis mine]. Well ...
• 57k
Accepted

### Fixed cost of a firm

It is the first one, $TC(0) = FC$. This is the definition. Also consider that it is not clear what is "transformed by $q$ in some way". In case of $$\frac{5q}{q+1} + \frac{5}{q+1}$$ are the two ...
• 29.3k
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### Properties on conditional demand correspondence from the textbook of Mas-Colell et al

Let $z_1$ and $z_2$ be $\geq 0$ and solution to $$\min_z \{w^\top z\lvert f(z)\geq q\}$$ then clearly $f(z_1)\geq q$ and $f(z_2)\geq q$ and since $\{z\geq 0\lvert f(z)\geq z \}$ is convex it then ...
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### Intermediate Case of Bertrand and Cournot

These papers could be interesting to you. First, a classical contribution: Singh Nirvikar and Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of ...
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### 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 ...
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### Walras Law in a production economy with fixed costs

Partial answer: for simplicity let $P_c =1$. The budget constraint: $c= wn + \Pi$ Simplify (plug in $\Pi$): $c= F(n)- fc$ Goods clearing: $c = F(n)$ The household's budget constraint is inconsistent w/...

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### Does the contract curve always have to connect the initial points on an edgeworth box? Why or why not?

The contract curve is the locus of Pareto optimal points in an Edgeworth box. What we get from that: To be P.O., an allocation must be feasible. So, the contract curve does not extend beyond the ...
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### Why does a homothetic function have constant ratio of marginal products along rays?

A homothetic function can be characterized as follows: Let $f(\mathbf x)$, $\mathbf x \in \mathbb R^n$ be a function homogeneous of degree $r$. Let $g()$ be a function with $g'\neq 0$. Then G(\...
• 33.9k
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### Why was activity analysis abanadoned as a field of research?

In Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society: Series A (General), 120(3), 253-281. which is widely seen as the starting point of ...
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### Why are cost functions often assumed to be convex in microeconomics?

Increasing and convex costs are a result of decreasing returns to scale. These are mainly due to the limited availability of (local) input factors. Other contributing factors are the decline of ...
• 6,994
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### Micro: proving that cost minimizing input vector for producing y cannot produce more than y

I don't think you need convexity. However, I think you do need to assume some monotonicity condition. The following should work (but might not be the minimal set of assumptions that provides the ...
• 12.4k
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### How do you calculate the contribution of each factor of production to the value of the final product?

You can do this in various ways for a value of output (e.g. goods and services) firm produces but not really very reliably for value of firm itself. Value of Output When it comes to value of output ...
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The standard definition is that a production function $F(\vec{x})$ has constant, increasing, or decreasing returns to scale if $F(a\vec{x})$ is equal to, greater than, or less than $a F(\vec{x})$ (...