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18

$PQ(P)=TR$, 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 $\frac{∂Q}{∂P}P+Q \neq MR$

11

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 equivalently, we can solve the maximization problem with respect to $P$ (and not w.r.t. $Q$). More over, "price elasticity of demand" involves the derivative of $Q$ with ...

9

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 $\Pi^c = P \cdot q - C(q)$. That is, they seek to maximize profits, facing an exogenous price to sell goods and where costs are a function of amount produced. If everything is nice and ...

8

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 strategy (e.g. holding a diversified portfolio) yields a profit of $1$ every year forever. The risky strategy (e.g. not diversifying) yields a payoff of $2$ with (...

7

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 same form for each period. The same is for $I_t$. This means that a firm will choose the same labor inputs in all periods. In other words, the firm gets into the ...

6

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: $R'(q)=c$. We also know that average costs are given by $AC=(K+qc)/q$. But note that $AC=(K+qc)/q>c=MC$. Thus, when profits are maximized we have $AC>MC=R'(q)$. So ...

6

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 offer of full-priced goods that presumably have much higher margins. This is pretty much the definition of https://en.wikipedia.org/wiki/Cannibalization_(...

6

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 of the profit maximization problem, as costs do not appear in the goal function. $\lambda$ here would show by how much an additional dollar spent on ...

6

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 carrying that capital has a cost. For example. Let's say Bob the Builder borrows $10M to develop a project. The bank lends on the development. Not the completed ... 5 Firms maximize profit, not expected profit. If they want to take a lower guaranteed value than the expected value because they are risk averse, then they're still maximizing profit based on their preferences and/or constraints. You're right that they wouldn't be maximizing expected profit. Profit could also have diminishing marginal returns. To add a little ... 5 To complement @AdamBailey to-the-point answer, the purpose of this post was to alert interested readers to the consequences of changing decision-variables in our thinking. We are accustomed to think of Demand as either "price depending on quantity" or "quantity depending on price". But on the production-cost side, we automatically tend to ... 5 The production function has a particular feature: the inputs are perfectly substitutable. One unit of input 1 can be substituted by 2/3 of input 2 to produce the same quantity of output. Intuitively, a producer would optimally use only one output to produce. Suppose the production plan is$(z_1,z_2)$. By choosing$(z_1-1,z_2+2/3)$, the firm produces the same ... 5 Given the production function$\sqrt{2z_1+3z_2}$, cost function can be obtained by minimizing cost: \begin{eqnarray*} \min_{z_1, z_2} \ \ w_1z_1+w_2z_2 \\ \text{s.t.} \sqrt{2z_1+3z_2} \geq q\end{eqnarray*} Solving it we get conditional input demand as follows: \begin{eqnarray*} (z_1, z_2) = \begin{cases} \left(\frac{q^2}{2}, 0\right) \ \text{if } \frac{w_1}{... 4 The simple answer is that if it is widely expected that the value of an asset will increase in the future, then the value should rise today as people bid up the price of the asset by trying to get the higher return it can provide. In other words, if an asset is trading at a specific price, the average investor (a term I won't make precise here) should think ... 4 Why not hold onto the property, and sell it later at a higher price? Here is a non-exhaustive list of why not: Real estate bubbles going burst. Depreciation and maintenance costs. A location may become less attractive in the long term due to mass emigration, criminal activity going up, collapsed economy, business could relocate to somewhere with incentives.... 4 Hint For profit maximization, either$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^*$without affecting output and thus revenue. Let$z=\max\{x_1,8x_2\}$. The profit function can be written as \begin{equation} p[3(x_3)^{1/3}(z)^{1/3}]-w_3x_3-... 4 Opportunity cost is simply the value not obtained of the highest value alternative. It can be positive or negative; meaning it doesn't really make sense to define the opposite as opportunity profit. There is only two ways to go about it rationally, either you are profiting from doing something, or you are not profiting by not doing something, which is ... 4 My professor once said, when doing economics, don't get stuck in mathematics. Math is just a tool. You know that the price will always be 24 per piece. For (iii), your cost is$C(q) = 10q$. What's the cost per piece to produce it? Is it more or less than what you could sell? If it's the former, you're guaranteed to make profit for each piece you make. If it'... 3 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 believe they have a 10% chance of losing \$1m but there are insurance companies willing to wear that risk for less than $100k. This can happen if insurance ... 3 Should I solve for$L^∗$by separating$K^∗$from the equation and plugging into$pMP_{L}$Yep, that's about it. Wouldn't this yield a very complicated solution? Somewhat. The math is available at many places, like section 4 here. But you can surely do it yourself! 3 The process for solving this type of problem is very general--it's not a set of rules. You don't need to attribute fixed costs to one good or the other (if there is only one fixed cost). Here's the procedure: Write out the whole profit function Find the maximum of the profit function If the maximum is less than the scrap value, then scrap it. If your ... 3 As for your first question, we are not just assuming$\partial U/\partial B > 0$. We simply assume monotonicity of preferences, which for the model here is a plausible condition. In simple terms this means that "more is better". Hence, the consumer will always choose to spend all of his budget for current or future consumption, given by$C$and$B$... 3 If$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 function can be found here.) This means that if a maximal profit exists it is zero. Otherwise you could increase all inputs by say 100%, thereby increasing both ... 3 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 are assets of the company and affect internal and external accounting, especially accounting of value of publicly traded companies. Goods as assets are likely ... 3 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 tort. While grocers do carry products liability insurance, the policies require that stores adopt certain standards of practice. It should make sense that ... 3 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 standard for any firm, though. How Google in particular and these big firms in general (Amazon, Microsoft, etc.) estimate demand curves is somewhat different ... 3 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 of good$1$is$p_1=1$. For each unit of good$1$the agent buys, he qualifies to buy up to one unit of good$2$at an additional price of$p_2=1$. In other ... 3 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 study its derivative. If the marginal cost is always smaller than the price of the good (probably it is assumed to be 1) then producing more is always better ...

3

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 points out the opportunity costs are not avoided profits but the value of the best alternative forgone. For certain firm decisions that may be forgone profit, ...

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