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18 votes
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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+...
Adam Bailey's user avatar
  • 8,519
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 ...
Ubiquitous's user avatar
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7 votes
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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 ...
Giskard's user avatar
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7 votes
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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 ...
Alalalalaki's user avatar
  • 2,419
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 ...
Kitsune Cavalry's user avatar
  • 6,638
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: $R'(q)=c$....
Ubiquitous's user avatar
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6 votes
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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 ...
FreeMarketUnicorn's user avatar
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 ...
Alecos Papadopoulos's user avatar
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, ...
GuiWil's user avatar
  • 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{...
Amit's user avatar
  • 8,891
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 ...
Ege Erdil's user avatar
  • 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 ...
Iñaki Viggers's user avatar
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 $x_2^*$ ...
Herr K.'s user avatar
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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. ...
Clinical_Coder's user avatar
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 ...
Art's user avatar
  • 2,794
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\...
Amit's user avatar
  • 8,891
4 votes
Accepted

Why is a firm's profit maximized when MC=MR? Why not stop one unit before where it will still make a profit?

Because profit is maximized at MC=MR. If MC<MR, then firm could still earn more profit by producing little bit more. Also firms do earn positive profit at point where MC=MR. Practical example: Firm ...
1muflon1's user avatar
  • 56.8k
4 votes
Accepted

Net product marginal in Acemoglu's article "Modeling inefficient institutions"

Calculate the first-order-condition (FOC) wrt labour: $$\begin{align}\frac{\partial}{\partial l_t^j} \left( \frac{1 - \tau_t^j}{1 - \alpha} (A^j)^\alpha (k_t^j)^{1-\alpha} (l_t^j)^\alpha - w_t l_t^j - ...
uninterestedacademic's user avatar
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 ...
Amit's user avatar
  • 8,891
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 ...
Frank Shmrank's user avatar
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 ...
android16.5's user avatar
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 ...
farnsy's user avatar
  • 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 ...
BB King's user avatar
  • 6,168
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 ...
Regio's user avatar
  • 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 ...
Maarten Punt's user avatar
  • 2,373
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 ...
Regio's user avatar
  • 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 ...
bajun65537's user avatar
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 ...
BB King's user avatar
  • 6,168
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 ...
RegressForward's user avatar

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