14

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


10

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 ...


8

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 ...


7

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 (...


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

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 ...


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 ...


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

According to the orthodox economist, in the real world, firms do not consciously try to calculate $MC$ or $MR$. Nor do they consciously try to produce/sell at the point where $MC=MR$. Instead, the theory you have learnt is simply theory. This theory argues that: If firms are maximizing profits, then they must be producing/selling at the point where $MC=MR$....


3

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 diminishing returns holds. Thus, the more you hire workers, the more you produce, but at a diminishing rate. I am not so sure what your professor has in mind ...


3

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 wages $w$). I am about to show you how to write this problem (and how to solve it) from consumer's alone, and then from both, firm's and consumer's points of ...


2

A firm requieres capital $K\in\mathbb{R}_+$ and labor $L\in\mathbb{R}_+$ to produce the final good $Q$. The technology is of Cobb-Douglas type $Q:(K,L)\mapsto K^{\alpha}L^{1-\alpha}$, here $\alpha=0.75$. Denote the capital rent by $r$ and the worker's wage by $w$. Production costs are then given by $C:(K,L)\mapsto rK+wL$. Instead of maximizing profits, the ...


2

Since the OP "recovers old-ground", let's turn the flashlight on some dark spots of this ground. It is almost "automatic" to think that "marginal revenue" is the price at which the additional unit of output will be sold 9so that it is "the revenue that the additional unit brings in"), and that "marginal cost" is what this additional unit will cost. We ...


2

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 $f(\overrightarrow{x})$ is homothetic, $$ C(\overrightarrow{w},y)=h(y).C(\overrightarrow{w},{1}) $$ Substituting in the profit function gives; $$ \pi(p,w) = \mathop{max}...


2

Sorry I don't have enough reputation yet in the Economics community to comment. But the answer provided by @Alecos Papadopoulos can be illustrated further. Please feel free to move my "answer" to comments of his answer. With the assumption of only $F' > 0$ and $F > 0$ and $h' > 0$, then there is a simple case where the minimization problem has no ...


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