# Tag Info

14

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 ...

5

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. ...

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

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 ...

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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 $... 3 Although I'm not sure that Piketty ever directly discusses the exact definition of$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$from capital in national income from the income side of the ... 3 At time$(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 ... 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 @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 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 ... 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 Normally, in the Solow model, there are not increasing marginal returns because by construction, Solow model assumes that marginal return of capital is decreasing. In fact this feature ensures the catch up between countries? which is the main insight of this model. There is another branch of literature on endogeneous growth models which has taken into ... 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 Because the papers which use these methods are not properly refereed. That's why you should read papers published in high impact factor journals. 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 ... 1 I put the article through translate and it appears that this is the (translated) section you are talking about: "To achieve this selection of 50 nuggets, the Tech Tour did not scan only the continent, but the whole world. The overall result for Europe is very encouraging since there are 284 companies (including 38 French) , compared to 121 in 2015. They are ... 1 Its legal to borrow and lend money, but if you become anything close to a bank, (take deposits, make loans, take risks, make a business out of it) then you will be regulated. You will be insured by the FDIC, and since you are insured, you will then be required to follow certain guidelines regarding how you asses risk and which risks you can take or not. ... 1 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. IfK_t$denotes "capital at the beginning of period$t$" (as it does), you should ... 1 I believe he assumes that there is no arbitrage and also that there are no pricing bubbles. So two assets that have the same price today would have the same net present value. Let$P_t$denote the price of an asset in year$t$,$d_t$the dividend (or rental income or cashflow) you get from said asset in year$t$and let$r\$ denote the interest rate (which I ...

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Nothing about marginal productivity theory depends on the exact truth of a simple aggregate production function with capital defined by a single number Different sorts of capital used as separate production technologies prevent clean aggregation to a representative form of capital but does not prevent capital from being paid its marginal product. To make ...

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