18
votes
Accepted
Monopolies are just a mathematical misunderstanding
$PQ(P)=TR$, Total Revenue.
$\frac{∂Q}{∂P}P+Q$ is the derivative of $PQ(P)$ with respect to $P$.
$MR$, Marginal Revenue, is the derivative of $TR$ with respect to $Q$.
So in general $\frac{∂Q}{∂P}P+...
- 8,311
9
votes
Why are firms taken to be profit-maximizing? Shouldn't that make them risk-neutral?
Why would a [risk-neutral] firm need to diversify if all it wanted to do was maximise profit?
Suppose there is a risk-neutral firm that has two strategies it could follow: risky and safe. The safe ...
- 16.9k
7
votes
Accepted
Profit Function: Just revenue maximization subject to constraint? if so where is $\lambda$?
The problem
$$\max py(x) $$
$$s.t. wx \leq \bar{C} $$
could be interpreted as revenue maximization subject to an operational budget contraint. However the solution of this can differ from the solution ...
- 28.6k
7
votes
Accepted
When can one drop time subscripts? Example from Angrist and Kugler (2003)
Because "adjustment costs are linear and there is no aggregate uncertainty", the FOC for $N_t$ is $$f'\theta g_N(N_{t}, I_{t}) - w_N = \phi \lambda C_N$$. Notice that this is exactly the ...
- 2,339
6
votes
Why are firms taken to be profit-maximizing? Shouldn't that make them risk-neutral?
Firms maximize profit, not expected profit. If they want to take a lower guaranteed value than the expected value because they are risk averse, then they're still maximizing profit based on their ...
- 6,578
6
votes
Why is AC = MC in the monopoly?
Suppose the marginal cost is constant and equal to $c$, that fixed costs are $K>0$, and that revenue is $R(q)$. You seem to understand that MR=MC must be true for profits to be maximized: $R'(q)=c$....
- 16.9k
6
votes
Accepted
If house prices appreciate, why do developers sell them?
They are different businesses.
Developers make more money developing than landlording. Some do both. But they are different businesses entirely. Also, there is a limited supply of capital and ...
- 1,101
5
votes
Monopolies are just a mathematical misunderstanding
To complement @AdamBailey to-the-point answer, the purpose of this post was to alert interested readers to the consequences of changing decision-variables in our thinking.
We are accustomed to think ...
- 33.4k
5
votes
Accepted
Solving for profit function $\pi (w,p)$ given the output of production function $f(z) = \sqrt{2z_1 + 3z_2}$
The production function has a particular feature: the inputs are perfectly substitutable. One unit of input 1 can be substituted by 2/3 of input 2 to produce the same quantity of output.
Intuitively, ...
- 887
5
votes
Solving for profit function $\pi (w,p)$ given the output of production function $f(z) = \sqrt{2z_1 + 3z_2}$
Given the production function $\sqrt{2z_1+3z_2}$, cost function can be obtained by minimizing cost:
\begin{eqnarray*} \min_{z_1, z_2} \ \ w_1z_1+w_2z_2 \\
\text{s.t.} \sqrt{2z_1+3z_2} \geq q\end{...
- 8,208
4
votes
If house prices appreciate, why do developers sell them?
The simple answer is that if it is widely expected that the value of an asset will increase in the future, then the value should rise today as people bid up the price of the asset by trying to get the ...
- 691
4
votes
If house prices appreciate, why do developers sell them?
Why not hold onto the property, and sell it later at a higher price?
Here is a non-exhaustive list of why not:
Real estate bubbles going burst.
Depreciation and maintenance costs.
A location may ...
- 1,765
4
votes
Decision over "max" production function:
Hint
For profit maximization, either $x_1$ or $x_2$ (but not both) must be zero. If not, say $x_1^*>x_2^*>0$ at the optimum, then one could increase profit by lowering cost by reducing $x_2^*$ ...
- 15.3k
4
votes
Opportunity profits vs. opportunity costs
Opportunity cost is simply the value not obtained of the highest value alternative. It can be positive or negative; meaning it doesn't really make sense to define the opposite as opportunity profit. ...
- 473
4
votes
profit-maximization
My professor once said, when doing economics, don't get stuck in mathematics. Math is just a tool.
You know that the price will always be 24 per piece. For (iii), your cost is $C(q) = 10q$. What's ...
- 2,784
4
votes
Accepted
Competitive equilibrium for an economy with a consumer and a producer
This is the utility maximisation problem of the consumer:
\begin{eqnarray*}\max_{c_D, l_S} & \ c_D^a(24-l_S)^{1-a} \\ \text{s.t.} & \ pc_D = wl_S \\ \text{and} & \ c_D\geq 0 , 0\leq l_S\...
- 8,208
3
votes
Accepted
Utility maximization question setting up.
Consider a consumer whose preferences can be represented by the following utility function: $$u(x_1,x_2)=\dfrac{x_2}{(1+x_1)^2}.$$
Assume the agent's income is $y=5$. The price of one unit ...
- 8,208
3
votes
Why are firms taken to be profit-maximizing? Shouldn't that make them risk-neutral?
There are really three reasons why a risk neutral firm would buy insurance.
One is that the insurance market is under estimating the riskiness of an insurance product. In other words a firm might ...
- 201
3
votes
Profit maximization with Cobb-Douglas function
Should I solve for $L^∗$ by separating $K^∗$ from the equation and plugging into $pMP_{L}$
Yep, that's about it.
Wouldn't this yield a very complicated solution?
Somewhat. The math is available ...
- 41
3
votes
How do calculate whether selling a product leads to profit?
The process for solving this type of problem is very general--it's not a set of rules. You don't need to attribute fixed costs to one good or the other (if there is only one fixed cost).
Here's the ...
- 836
3
votes
Expectations in Gali's classical monetary model
As for your first question, we are not just assuming $\partial U/\partial B > 0$. We simply assume monotonicity of preferences, which for the model here is a plausible condition. In simple terms ...
- 6,128
3
votes
Accepted
Homothetic production function and Profit Function
I have figured this as the answer to this question;
As we know profit maximization problem is given as,
$$
\pi(p,w) = \mathop{max}_{\textbf{y}}\quad p.y - C(\overrightarrow{w},y)
$$
When $f(\...
- 616
3
votes
Accepted
Duality of cost minimization and profit maximization
If $F(K,L)$ is a homogeneous function of degree one then so is
$$
\Pi(K,L) = F(K,L) - R \cdot K - w \cdot L.
$$
This follows straight from the definition of homogeneity. (A definition of homogeneous ...
- 28.6k
3
votes
Accepted
CES production function profit and supply function
Hint: Solving for the FOC's assumes that the solution is interior, in this case, that profits are positive and smaller than $\infty$. I would recommend you to derive the cost function $c(y)$ and then ...
- 4,188
3
votes
Opportunity profits vs. opportunity costs
First off some terminology: opportunity cost are not necessarily avoided profit. Profit is a term that is used for firms, but opportunity cost does not just apply to firms. Moreover as @clinical coder ...
- 2,375
3
votes
Why does the profit function in standard neoclassical theory have exactly one maximum?
Mathematically, most neoclassical models assume that the profits are concave. This guaranties the uniqueness of the maximum. In economic terms, the Neoclassical theory usually assumes that the law of ...
- 4,188
3
votes
Utility function_maximazation
This is quite a loaded question you asked here. I answered it in a few parts: first I introduce you to the idea of Robinson's economy, then I add a company to the equation (as you also asked about the ...
- 911
3
votes
Accepted
How to find the maximum profit in a graph?
Short answer:
Shift the profit line parallel downward until it only touches the loss function in only one point. That's the point where the maximum gap occurs.
Reason:
The maximum occurs where ...
- 6,128
3
votes
Accepted
Static Profit Maximization Short Run Shut Down Decision
In the short run, you cannot sell your capital. To do so would be a violation of "short run" and would instead be the "long run".
Case 3 (and I would also contest Case 2) are ...
- 3,467
Only top scored, non community-wiki answers of a minimum length are eligible