# Questions tagged [cost-functions]

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

Why are cost functions typically assumed to be convex in producer theory of (introductory) microeconomics? For me this goes against the intuition of economies of scale. There are fixed costs (FC) ...
752 views

### Long Term Economic Profit for Perfectly Competitive market

When we consider a perfectly competitive market, in the short run we will run a firm if the total economic profit though negative till price is above shutdown point.In long run we will run at an ...
608 views

### Fixed cost of a firm

Suppose that a firm has a total cost function given by: $TC(q) = \frac{5}{q+1} + 5 + 5q + q^2$. What is the fixed cost? I seem to be able to come up with two "answers", which cannot be correct. My ...
267 views

### CobbDouglas: Constant marginal costs and constant returns to scale

A company has a production function: $$y=x_1^{\alpha}x_2^{1-\alpha}$$ where $0<\alpha<1$. Factor input 1 costs $w_1> 0$ and factor input 2 costs $w_2> 0$. The company wants to minimize its ...
58 views

### Constant returns to scale and cost function: $C(p,ty) = tC(p,y)$

How can I prove that for a production function $F:\mathbb X \rightarrow \mathbb R$ with constant returns to scale $$\forall x\in \mathbb X, \forall t > 0: \ \ F(tx) = t F(x)$$ and with the cost ...
380 views

### Decision over "max" production function:

I've been presented with the following problem: $$y=3(x_3)^{\frac13}(\max\{x_1,8x_2\})^{\frac13}$$ And the objective is to both maximize profit and minimize cost. First of all, if the problems are ...
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### Deriving long-run cost function

I'm a bit unsure about how to derive a long-run cost function. Suppose my production function was $X(L, K)=L^a K^b$, where $a+b>1$. I'm thinking about doing the following, but I'm not sure it's ...
65 views

### Solving the following cost minimization problem using Kuhn-Tucker conditions

I am currently getting my Masters in Economics. I did not get any exposure to optimization with inequality constraints in my undergrad. I would like to ensure that I am doing this problem correctly. ...
147 views

### Understanding the Diewertt Cost Function

The Diewert cost function (as described in Microeconomic Analysis by Hal Varian 3rd Edition) takes the form of: $$c(w,y)=y\sum_{i=1}^k\sum_{j=1}^kb_{ij}\sqrt{w_iw_j}$$ Varian goes on to say (page ...
361 views

### Under what condition is a cost function strictly concave in prices?

Define the unit cost function as $$c(w) = \min_{z\geq 0} w\cdot z$$ subject to $f(z)\geq 1$. Where $w$ is a vector of input prices, $z$ is the vector of inputs and $f$ is a production function. We ...
585 views

### What is the returns to scale of the production function q = min {K, L^(1/2)}?

I learned that when there is decreasing returns to scale, the average cost is always increasing. But the professor told us today that the other way around might not always be true. So if average cost ...
3k views

### Prove all cost functions are concave in input prices and demand for inputs is downward

I've seen proofs that cost functions are concave of the form $C(\lambda w + (1-\lambda)w',q) \ge \lambda c(w,q) + (1-\lambda)c(w',q)$ although this neither feels convincing nor does it seem like a ...
182 views

### what results can be derived from the average cost curve?

What is the practical use of knowing a firms average cost curve? The reason why I ask is because computational problems that a firm faces are either with regards profit maximization or cost ...
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### Derive the cost function and supply function from production function

I didn't study economics, but am quite interested in the topic. I came to the question whether I could derive the supply curve / marginal cost function from the production function and I actually ...
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### Revenues and cost functions

Let's assume that there is a firm that produces a single good, $q=f(x)$, where $x$ is a single input. The firm can sell it on the market at a price $p$. It's production cost is given by a cost ...
22 views

### Formula for splitting profit and loss for every person [closed]

I am looking for a formula to calculate even distribution of loss or profit between involved parties. Let's speak with some examples as I feel it will be easier. Example 1 Person 1 Balance: 2,000,...
A restaurant finds that less orders for their soup of the day are placed on warmer days so they discount the usual 7USD price to 5USD on warmer days. The cost of making the soup is given by  C = 0.1{...