28

One possible answer is that Mankiw's argument takes consumer demand for airline tickets as fixed and given. I would speculate that cheap last-minute tickets are a substitute good for regularly priced tickets, and that if enough people came to prefer them, demand for regularly priced tickets would fall and the airlines would lose revenue. In other words, ...


20

Do airlines actually do anything like the above? Yes, in fact now you will see on many airports specialized companies/windows that will offer last-minute flights very cheap. For example, in the past, I used to frequently fly to Vienna Schwechat airport, and there used to be a window where you could get cheap tourist flight but the catch was you could not ...


13

Pricing of last minute tickets for airlines is a tricky problem. Yes, discounting fares may attract customers who would not have flown otherwise. But buying a flight is a bit more complex than buying some gadget on discount on Amazon. Few customers can make such last-minute decisions. They usually need that flight, but also a flight back, and the schedules ...


7

One problem with trying to price goods or services at their marginal cost is that customers may hold off on making immediate purchases of goods or services they expect to be available cheaper at a later time. If there aren't enough people who would have any interest in a particular flight to fill it even if tickets were only \$1 each, but the number of ...


7

How is marginal utility interpreted as the additional "happiness" gained from consuming one more unit of some good? Not sure what you mean. Utility is not interpreted as some biological measure of happiness. A bundle of goods with high utility is prefered by the consumer to bundles with lower utilities. This is all that utility describes; it is a ...


6

As noted in the comments, it is not true that homothetic preferences must have constant marginal rates of substitution. To see this, recall that preferences given by the utility function $$ u(x,y) = x^\alpha y^{1-\alpha} $$ are homothetic. (More generally, Cobb-Douglas preferences are homothetic.) However, the marginal rate of substitution is $$ \text{...


6

It is perfectly consistent for the marginal revenue to increase in $q$, even if the demand curve decreases. Marginal revenue is $$p(q)+ q p'(q).$$ The first term says "if I sell one extra unit then I will receive an extra $p$ in revenue". The larger is this effect, the higher is the MR. The second term says "in order to sell one extra unit, I will have to ...


5

Marginal utility (of $x$) in your case is $U_x(x,y)=2xy^2$. You use the sign of the derivative of MU, namely $U_{xx}$, to tell whether MU is increasing, constant, or decreasing. Specifically, you have increasing MU if $U_{xx}>0$, constant MU if $U_{xx}=0$, and decreasing MU if $U_{xx}<0$. In your case, assuming that $y>0$, you'd have $U_{xx}&...


5

Your intuition is correct. First, you're right that "marginal cost only depends on variable cost", since \begin{equation} MC(q)=\frac{\mathrm dTC(q)}{\mathrm dq}=\frac{\mathrm d(FC+VC(q))}{\mathrm dq}=\frac{\mathrm dVC(q)}{\mathrm dq}. \end{equation} Next, if marginal cost is some constant $k$, then variable cost must be $VC(q)=kq$, because we can ...


5

I think the other answers covered well why airlines don't usually do quite what Mankiw described. But everything I have read about airline pricing says they are acutely aware of marginal costs. Even if the discounted seats are sold well before the flight, it can be seen as charging less than otherwise desired to avoid ending up with an empty seat. The ...


4

I'll offer a less algebraic alternative to Alecos's answer. In short, yes and no. The "no" part Normally the MC and AC curves would look like the following, with MC intersecting AC from below AC's minimum point. Suppose price $P_0$ were below this point. Then the firm would sell at a quantity below $Q_1$. But what does this imply for the firm's ...


4

You are missing the average cost curve in the same diagram. Basic algebra gives us the following. Let's find the minimum of the $AC = C/Q$. We have $$\frac {\partial AC}{\partial Q} = \frac {MC\cdot Q - C}{Q^2}$$ For this to be equal to zero, we must have $MC \cdot Q = C \implies MC = AC$. So when $AC$ is at its minimum, it equals $MC$. But we also ...


4

The reason why marginal benefit is measured in cans of soda is that this economy only has two goods: pizza and soda. So instead of using money we may as well use soda. Alternatively, in the absence of money this economy is an exchange economy, and the only way to pay for pizza in that case is with soda. When you move beyond two goods willingness to pay is ...


4

Utility functions as ordinarily used are not a measure of well-being comparable among people, but a representation of preferences. Moreover, preferences could principally be elicited from choice experiments. A utility function assigns real numbers to alternatives so that one alternative is preferred to the other if and only if it is assigned a higher number. ...


4

The profit of a firm $i$ is given by: $$ \pi_i(p) = p q_i - C_i(q_i) $$ where $p$ is the price, $q$_i is the output of firm $i$ and $C_i(.)$ is the cost function which differs across firms. The first order condition gives: $$ p = \frac{\partial C_i(q_i)}{\partial q_i} = MC_i(q_i^\ast) $$ This shows how to obtain the optimal supply of firm $i$, i.e. where $MC(...


4

Nuance matters: In the comments under 1muflon1's answer the quote given is The demand curve represents marginal benefit. The vertical distance at each quantity shows the mount consumers are willing to pay for that unit. Willingness to pay reflects the benefit derived from each unit. So the actual claim is not that the demand curve is the same as the ...


4

I am not sure why you expect method two to work, as generally $$ \frac{\partial F(K,N)}{\partial N} \neq \frac{\partial F(K,N)}{\partial K}\frac{\partial K}{\partial N}. $$ These are partial derivatives. Unless information to the contrary exists $$\frac{\partial K}{\partial N} = 0.$$ You can easily see that these formulas are not connected by calculating the ...


4

To expand on @1muflon1's answer. The theory of rational addiction assumes that the utility of a consumer at time instance $t$ depends both on current consumption of the addicitve good, say $c_t$, and the consumption of the addictive good in the past. For simplicity say $c_{t-1}$. So at period $t$ the instantaneous utility looks something like: $$ u(c_t, c_{t-...


4

The claim is not that capital decreases marginal productivity, but that the marginal productivity of capital is decreasing. (See "diminishing returns.") That is, the first "unit" of capital increases productivity the most, the second unit still increases it but less so, the third unit increases productivity even less and so on. Thus when ...


3

Marginal utility tells you how the utility changes as you alter x. That is the first derivative, which here is a function of x. This means it is increasing. The rate of that increase is constant as long as y is fixed (second derivative).


3

The marginal cost is 3. Marginal costs do not depend on the fixed cost, and when your variable costs are constant, then the marginal cost and the variable cost are the same. Note that your total cost is $C=FC+3q$ and the marginal cost is always the derivative of your total cost, in this case, $3$. As for the fixed costs, 4000 is definitely part of it, but ...


3

In general, you are right to be mystified: specifying a point (consumption bundle) isn't enough to compute MRS and indifference curves. However, in this problem, I would suggest you take the first sentence seriously as a description of her preferences. She likes fries. (She doesn't care about what box they come in!) Let $v(f)$ represent her utility as ...


3

The marginal profit you calculate is correct. We can rearrange the solution of the problem you are given. This is equivalent to $$ \frac{dP}{dq} = 192 -176q + 48q^2 -4q^3$$ This derivative has as primitive function the following profit function: $$P(q) = c + 192q -88q^2 + 16q^3 - q^4$$ where $c$ is a constant (e.g. $c=0$). This is clearly different ...


3

Having worked on these issues myself for quite some time, I am not aware of any study on this for New Zealand. For a back-of-the-envelope calculation of the revenue-neutral flat tax rate, you'd need the following: The tax base $Y$, i.e. the amount of income subject to income tax. Most probably, the New Zealand Treasury has published statistics on this. Note ...


3

The following is from Thomas Piketty and Gabriel Zucman (2015, From Handbook of Income Distribution, Volume 2, Chapter 15, Part 15.5.3 which is hard to link to directly but get it here): Take a CES production function $$Y=F(K,L)=(a⋅K^{\frac{\sigma-1}{\sigma}}+(1−a)⋅L^{\frac{\sigma-1}{\sigma}})^{\frac{\sigma}{1-\sigma}}$$ Me: $\sigma$ is the elasticity of ...


3

Seems like the only function $f$ that fits your description $$ \forall i: \frac{\partial f(\mathbf{x})}{\partial x_i} = c_i $$ is $$ f(\mathbf{x}) = A + \sum x_i c_i. $$ (Frequently $f(\mathbf{0}) = 0$ is assumed. The assumption is referred to as "no free lunch".) Then you can apply the definition of returns to scale.


3

Your marginal revenue is not calculated correctly. Marginal revenue $(MR)$ is the derivate of total revenue which is equal price times quantity $TR=PQ$. In your case $TR$ should be: $$TR=(k+aQ)Q \implies MR = \frac{dTR}{dQ} = k+2aQ$$ If the demand is given as: $P = 120−2Q$ then: $$TR= (120-2Q)Q \implies MR = \frac{dTR}{dQ} = 120-4Q $$ Also made a graph for ...


3

The Cobb Douglas production function with constants returns to scale $$y = \prod_i x_i^{\alpha_i} = A \prod_i \left(\frac{x_i}{\alpha_i}\right)^{\alpha_i} ,$$ where $A:= \prod_i \alpha_i^{\alpha_i}$ annoying constant. Cost minimization with perfect competition $$\min_x \ \ p^\top x\ \lvert \ y = \prod \left(\frac{x_i}{\alpha_i}\right)^{\alpha_i},$$ implies ...


3

You can think of it as the marginal benefit per person. The first piece of pizza you eat is amazing, it has a very high marginal benefit. But say you eat five whole pizzas in one sitting and then are immediately offered another slice. That next slice doesn’t seem so appealing, does it? You’re already full and starting to get sick of it. That slice has a low ...


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