4 votes
Accepted

Arguments for Concavity or Quasi-concavity

I will try to address your queries in the order you've asked them by providing the necessary definitions and procedures to find the answers you're looking for. The first approach is valid and it is ...
mynameparv's user avatar
3 votes
Accepted

Could you give an example of production function such that involves sunk costs?

Concepts: Production function Measured in units of output, depends on inputs. It has no information on prices or costs, so it cannot directly include fixed/sunk costs. The only way it can imply the ...
Giskard's user avatar
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3 votes

A problem with "Returns to Scale"

Assume that $Y$ has constant returns to scale, which means that if for all $t > 0$ $$ (-z_1, -z_2, q) \in Y \to (-tz_1, -tz_2, tq) \in Y $$ We want to show that $\overline{Y}$ has non-increasing ...
tdm's user avatar
  • 12k
3 votes
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CRS, Homothetic Functions, and constant MRTS

I think I’m generally missing the added value of a homothetic function vs homogenous function. The added value of homothetic functions is that they are a wider class with respect to homogeneous ...
BakerStreet's user avatar
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3 votes
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Derive cost function from production function

$z_2$ is included in the production function. Please see the production function $f:\mathbb{R}^2_+\rightarrow\mathbb{R}$: \begin{eqnarray*} f(z_1,z_2) = \left(\min(\lfloor z_2\rfloor, 1)\right)z_1^\...
Amit's user avatar
  • 8,466
3 votes

In a box diagram, why does efficiency locus lie on one side of the diagonal, if both sectors haves constant returns to scale function?

Assuming that the total endowment of labor and capital is both equal to $1$, consider these examples with CRS technologies and efficient points on both sides of the diagonal of the box: Example 1: $x =...
Amit's user avatar
  • 8,466
2 votes

Why is the Cobb-Douglas production function so popular?

The Cobb-Douglas production function $^1$ $$Y=F(K,L)=AK^{\alpha}L^{1-\alpha}\; 0<\alpha<1, A>0 \qquad (1)$$ as pointed out in the other answers, is very popular because of several formal ...
BakerStreet's user avatar
  • 3,697
2 votes

Optimal production plan in monopol

To produce $Q$ units at the minimum cost, we can obtain the optimal values of $q_1$ and $q_2$ using $\text{MC}_1$ and $\text{MC}_2$ and get: \begin{eqnarray*} q_1 = \min\left(2 + \frac{1}{5}Q, Q\right)...
Amit's user avatar
  • 8,466
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
  • 3,351
2 votes
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Mixed Partial Derivatives in Profit Function

In my classes, they’re called Marshallian or uncompensated demands, as in consumer theory. The partial derivative on the right hand side means to directly differentiate the demand for $z$ (the ...
Nicolas Torres's user avatar
2 votes

What could a negative output elasticity of an input imply?

What could a negative output elasticity of an input imply? If this would be actual rigorously and properly estimated result it would imply that when you increase the said input, you will get less ...
1muflon1's user avatar
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2 votes

Derive the input requirement set from production set

The input requirement set is defined as the set of all inputs required to produce at least the quantity $y$, or in other words, with a production function given by $y=f(x),$ $$ V(y)= \{x: f(x) \geq y \...
Bertrand's user avatar
  • 3,351
1 vote
Accepted

Solow model with three input factors

With the production function you specified you won’t get ‘clean’ per capita production function. However, to get it in per capita terms you just literally have to divide both sides of equation by $L$ ...
1muflon1's user avatar
  • 56.4k
1 vote

How do I derive optimal tax on pollution causing intermediate products?

In Chapter 1. General Framework, the authors introduce their model there and explain it step by step. [...] The two inputs, $Y_c$ (clean) and $Y_d$ (dirty), are produced using labour and sector-...
bajun65537's user avatar
1 vote
Accepted

How to derive the input demand functions from a perfect substitutes production function

Let $w:= w_1 = w_2$ The optimization problem you'd solve is profit maximization: $\max \Pi = P (x_1 + x_2)^\frac{1}{2} - w x_1 - w x_2$ The first order condition for the $i$-th factor is $\frac{\...
Nicolas Torres's user avatar
1 vote

Optimal production plan in monopol

That is not correct. Your solution results in more than the optimal Q since the firm solves the monopolists profit maximization problem for each plant. If $Q^\star$ is the the output that maximizes ...
A. Miller's user avatar
  • 151

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