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+...
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  • 6,813
11 votes
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First Order Condition for Profit Maximization in Gambling Industry

The expression in question is in footnote $11$ of the referenced article. Reading the paper, we see that the decision variable here is "the payout rate", which is the reciprocal of $P$. So ...
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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 ...
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9 votes
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Can destruction be profitable?

It can be profitable for the monopolist to do so. For the conventional producer who is a price taker the profit objective function looks like this: $$\max_{q} \Pi^c $$ where $\Pi^c = P \cdot q - C(q)$....
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  • 15.8k
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 ...
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  • 2,099
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: $R'(q)=c$....
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  • 16.6k
6 votes

Can destruction be profitable?

Cannibalization Assuming that the [near] expired goods cannot be sold at full cost anymore, offering them for sale at a significant discount (instead of destroying them) will compete with your own ...
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  • 488
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 ...
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  • 6,409
6 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 ...
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  • 26.2k
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 ...
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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 ...
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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, ...
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  • 877
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{...
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  • 5,112
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 ...
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  • 671
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 ...
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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 $x_2^*$ ...
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  • 14.4k
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. ...
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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 ...
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  • 2,764
4 votes
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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\...
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  • 5,112
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 ...
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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 ...
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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 ...
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  • 806
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 ...
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  • 5,424
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 ...
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  • 26.2k
3 votes

Can destruction be profitable?

Simple answer: It cost companies money to do any, even doing nothing. The immediate issues with selling out of date food in most jurisdictions would be: Do nothing (stockpile non-perishable.) Goods ...
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  • 131
3 votes

Can destruction be profitable?

In addition to BKay's answer, selling expired food opens a firm to suit. This occurs either via breach of an implied warranty (that the food is fit for consumption) or, in many jurisdictions, strict ...
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  • 395
3 votes

How does Google price the items on Google Play?

The simple answer is they estimate the demand curves for each product and, using their cost structure and market characteristics (competition structure, etc.) set price to maximize profits. This is ...
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  • 1,040
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 ...
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  • 5,112
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 ...
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  • 4,148

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