# Tag Info

15

This is when the attempt at accuracy creates confusion and misunderstanding. Back in the day, growth models were not incorporating technological progress, and led to a long-run equilibrium characterized by constant per capita magnitudes. Verbally, the term "steady-state" seemed appropriate to describe such a situation. Then Romer and endogenous growth ...

9

Necessary Caveats When Discussing Slavery: First before tackling this question it is important to note that this issue is broad and complex. This is because there is no single 'slavery'. For example, slavery under the Roman Empire was not the same as slavery practiced in US south (see Tamin; 2017). Furthermore, even within a given society there might be ...

7

So, let me start with your second question. No you cannot multiply by 365. You could approximate it by $$\log(\text{Annual Return})=365*\log(\text{Daily Return}),$$ but for what you are doing, it does not make sense to do so. You are correct in your annualized rate of return. It is 2069063%. It should be obvious as to why you would not want to do this. ...

5

Following the conversation with user @denesp at the comments of my previous answer, I have to clarify the following: the usual graphical device we use related to the basic Solow growth model (see for example here, figure 2) is not a phase diagram, since reasonably we call "phase diagrams" those that contain zero-change loci, identify the crossing points of ...

4

Although I'm not sure that Piketty ever directly discusses the exact definition of $r$, he does make it clear indirectly. On page 52 of the hardcover English-language edition of his book, Piketty declares his "first fundamental law of capitalism": Piketty obtains the share of income $\alpha$ from capital in national income from the income side of the ...

4

The paper is assuming that some form of "law of large numbers" (LLN) applies for the continuum. The expected value of capital for an individual agent is $$\mathbb{E}[R\cdot 1_{R\geq R^*}]=\int_{R^*}^1 R\,dR\tag{1}$$ The LLN assumption says that when we have a mass-1 continuum of agents, their actual total will equal their expectation in (1). What justifies ...

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 ...

4

Not 100% sure of what you need help with, but ill throw some things here and if it doesn't help tell me and ill delete this answer. Since you asked to "mathematically show why this is the case", i will try to show why $\beta = 1$ in your example. If $\varepsilon_t$ is the part of the nominal return not explained by inflation, than it should respect ...

3

At time $(t-1)$, the investor buys some risk free bond, $B_{t-1}$ and some risky asset $X_{t-1}$ at price $P_{t-1}$, such that the budget constraint holds, i.e. $$W_{t-1} = B_{t-1} + P_{t-1}X_{t-1}$$ At period $t$, one unit of risk free bond pays off one unit, so $B_{t-1}$ units of risk free bonds pays off $B_{t-1}$ units of wealth at $t$. For a risky ...

3

According to your calculations MPK is not increasing in $K$. The Solow model assumes $0< \alpha < 1$, thus $\alpha - 1 < 0$ and $K^{\alpha - 1}$ is decreasing in $K$.

3

If $Y = C \cdot X$ where $C$ is constant and $\frac{\dot{X}}{X} = g$ then we can solve for $\frac{\dot{Y}}{Y}$ as follows: $$\frac{d}{dt} Y = \frac{d}{dt} C \cdot X = C \cdot \frac{dX}{dt} = C \cdot \dot{X} \Rightarrow$$ $$\frac{\dot{Y}}{Y} = \frac{C \cdot \dot{X}}{ C \cdot X} = \frac{\dot{X}}{X} = g$$ Therefore, as you concluded, they both grow at rate $... 2 Ignoring the expectations operator, your lagrangean has two mistakes: first the constraint is per-period so it is also multiplied by the discount factor. Second, the way you have wrote the time indexes is inconsistent, as regards their interpretation for capital and bonds. If$K_t$denotes "capital at the beginning of period$t$" (as it does), you should ... 2 I don't think that on yearly returns, a day more or less matters too much. In the unlikely case it actually does, you could interpolate the final day. A first approximation would be the average over June 12th and June 11. 2 Leveraging is done with debt. Most high net worth individuals are debt free and even if they take out loans, it is to reduce taxes. However, high net worth individuals normally have their wealth in a form of equities or stocks. For example Bill Gates' wealth is mostly in Microsoft stock, Warren Buffet's is in Berkshire Hathaway's, etc. The corporations that ... 2 Because the papers which use these methods are not properly refereed. That's why you should read papers published in high impact factor journals. 2 My students also frequently make the mistake of thinking they "understand the basic idea of" something, when what they actually know is a formula to calculate some aspect of it. Average costs being equal to marginal costs in the break even point is not the basic idea, it is a mathematical property that only holds given certain assumptions (e.g., price ... 2 When you are finding the break even point, you are looking for a price-point. The price is essentially the average (and marginal) revenue. Suppose price of good$x$is$p$. Revenue =$p * x$. Average Revenue = Revenue /$x$=$p$. So what you are really doing when looking for p is to set Average Revenue = Average Cost. At that point, you will also have ... 2 I agree with Dan it is likely a typo. Some definitions (using your notations) Investment :$f_0$Investment one year later :$f_1$Net income :$f_1 - f_0$ROI:$-1 + \frac{f_1}{f_0}$It follows that the correct code should be ROI = (goog/goog.tshift(-365) -1)*100 2 @chsk gives the correct answer if the firm has to raise funds using the equity market and the cost of those funds is the same as that for the firm. However, I would recommend that this firm do the project. As indicated in the project, the risk free rate of return is 10%, and this project "...will earn a 13% rate of return for certain into the indefinite ... 2 Dividends have to be taxed as income, as otherwise people can incorporate, have their wages taxed as revenue for the corporation, and then pay themselves a dividend. (Canada adjusts taxes on dividends in an attempt to make these two approaches equivalent for taxes purposes.) Capital gains are at a lower rate for reasons that are debatable. However, in order ... 1 Your figures reports ex-post (say end of year) returns on capital investments. Ex-ante (beginning of the year, or before the investment) these returns are random and unknown, and there is a trade-off between return and risk. If investor$i$is investing rationally her assets in firm$j$instead of$k$, according her specific risk aversion and information set ... 1 Edit: after OP made changes to his question and clarification this answer became less relevant. I am still keeping it here because OP said some parts of it and references are still useful. There are several reasons why even if all markets were perfect rates of return would not equalize. I will just focus on some major ones. Many countries have some capital ... 1 Let's first clarify one concept. Risk premium is the extra expected return that an investor demands (not of the market, here is the key) over the return of risk-free asset (usually government bonds). Then it becomes clearer that a higher market risk premium during a crisis does not mean the market is expected/able to achieve higher returns. It rather ... 1 Risk premium is the excess expected return of the market over that of the risk-free asset. (There is no "(expected) risk premium".) It is a property of the expected returns of two assets. It is an indication of investor's willingness to bear risk. High risk premium means less risk-bearing capacity in the market, where market participants are in risk-off ... 1 Assuming that the project has the same beta as the firm's existing assets -- and assuming I'm remembering what I learned in my introductory CorpFin class correctly --, you are indeed right. The present value of future cash flows is, in general, $$\mathrm{PV} = \sum_{t=1}^T \frac{ \mathbb{E}[ \tilde{c}_t ] }{ (1 + \mu_t)^t }$$ where$$\mu_t = r_f + (\mu_M -... 1 I am not sure I understand your question. In most projects, the bulk of the investment is a down payment, so the ROI is meant to capture precisely that. I.e. the average return that the money you put in the project will yield. This has in mind that the total investment is mostly done today and the returns come in the future. If you restrict the denominator ... 1 Your formula is wrong. The derivation for the cost of equity$r_E$is actually:$r_A = r_D(1-t)\frac{D}{V}+r_E \frac{E}{V}\\ r_E \frac{E}{V} = r_A - r_D(1-t)\frac{D}{V}\\ r_E = r_A \frac{V}{E} - r_D(1-t)\frac{D}{V} \times\frac{V}{E}\\ \mathbf{r_E = r_A \frac{V}{E} - r_D(1-t)\frac{D}{E}}$Since$\frac{D}{V}=\frac{D}{D+E}=0.09091$when$r_A=0.1941$, then$...

1

Several thoughts in this area: 1) Capital stock lasts over time. I may trade 1 euro for 1 unit of capital. This capital returns 0.01 euros every period forever. It pays itself off eventually. 2) If one has an incredible high rate of return and a sufficiently low discount rate, one might have divergent consumption paths, ex: I spend all of my money on ...

1

Should housing be considered a form of capital for the purpose of capital gains taxation? Chamley-Judd's proposition aims at avoid[ing] unlimited growth in tax compounding as the horizon extends. Criticism of the Chamley-Judd model is centered on the "assumption regarding infinite lives". But I think the distinction between short-term and long-term ...

1

I think there are a few different ways one can go about examining the topic and general question you bring up. For that reason, I'd like to highlight that this isn't my primary field, and so my answer might not align with a more expert view from that field. However, to get the ball rolling... First, we should probably take a short digression and consider ...

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