6

You cannot completely ignore the RHS. Starting with $$\frac{U'(c_{t+1})}{U'(c_{t})}=RHS,$$ replace $t+1$ by $t+\Delta t$ to get $$\frac{U'(c(t+\Delta t))}{U'(c(t))}=RHS_{\Delta t},$$ where $RHS_{\Delta t}$ is the modified version of $RHS$ which contains terms depending on $\Delta t$, e.g. the modified discount factor. Expanding around $c(t)$ (and neglecting ...


6

One way to see (intuitively) the connection between the left hand sides is to write the discrete case as: $$ \frac{u'(c(t + \tau))}{u'(c(t))}, $$ for $\tau = 1$. Now if we generalise this to a setting where $\tau$ is now a variable in $\mathbb{R}$, this becomes a function of $\tau$. Taking the derivative with respect to $\tau$ and evaluating at $\tau = 0$, ...


5

The answer of @tdm shows you how it is done using De L'Hospital's rule. If you want to avoid this rule you can write $u(c)=\frac{c^{1-\theta}-1}{1-\theta}$ and note that for $\theta\ne 1$ this implies $u(1)=0$. Differentiating with respect to $c$ then gives you $u'(c)=c^{-\theta}$ and therefore $\lim_{\theta \to 1}u'(c)=c^{-1}$. Then integrate again to get $\...


5

This does not seem to have anything to do with calculus. The idea is that the income not consumed $Y_d - C$ is saved (usually denoted by $S$). This saving is then lent out to companies (via banks) who invest it (usually denoted by $I$), and the accumulated capital is used in production. I am guessing this is denoted by $A$? And the change of $A$ in time is ...


4

Have a look at CentralBankNews.info.


4

The derivative of $a^{x}$ with respect to $x$ is equal to $a^x \ln(a)$. As such, using the chain rule, the derivative of $c^{1-\theta}$ with respect to $\theta$ equals $c^{1-\theta} \ln(c) (-1)$ L'Hospital gives: $$ \lim_{\theta \to 1} \frac{c^{1-\theta}-1}{1 - \theta}\\ = \lim_{\theta \to 1} \frac{(c^{1-\theta}-1)'}{(1-\theta)'},\\ = \lim_{\theta \to 1} \...


3

Mathematically, a higher risk aversion leads to a lower intertemporal elasticity of substitution (there is an inverse relationship). But why? The (relative) measure of risk aversion is measured as: $$ r(x) = -x\frac{u''(x)}{u'(x)} $$ Consider an intertemporal utility function $u(x_1) + \beta u(x_2)$. Maximising this with respect to an intertemporal budget ...


3

You have most of this; it seems like you might have a miscalculation when differentiating the fraction: $$ \begin{align*} \frac{dk_t}{dt} = \frac{d\frac{K_t}{N_t}}{dt} & = \frac{\frac{dK_t}{dt}N_t - \frac{dN_t}{dt}K_t}{N_t^2} \\ & = \frac{\frac{dK_t}{dt}}{N_t} - nk_t \end{align*} $$ thus $$ \frac{\frac{dK_t}{dt}}{N_t} = \frac{dk_t}{dt} + nk_t, $$ and ...


3

They consider a model with two islands: a Production island and a Leisure island. Every transition from a period $t$ to a period $t+1$ is split into two parts. People who are in the Production island at the end of period $t$, start on the Leisure island in the beginning of period $t+1$ with probability $\sigma$, and stay on the Production island with ...


2

here are several reasons for that. First, if we look beyond the simplified version Philips curve, to the more appropriate modern version of Phillips curve we discover that what matters is not just inflation but that inflation is higher than expected inflation. For example, following Romer Advanced Economics pp 261, the Phillips curve will look like: $$\pi_t= ...


2

There are multiple answers to this question. In any model you can always make a thought experiment where you hold certain variables fixed. So one answer, although not very satisfying one, is that you can view it as a thought experiment. For example, in physics distance traveled equals velocity times time or $D=tv$ and you can always make a thought ...


2

I had the same question and I figured out the answer! I am looking into FAOSTAT> Value of Agricultural Production (http://www.fao.org/faostat/en/#data/QV) and there they have: Gross Production Value (constant 2014-2016 thousand US\$) Gross Production Value (constant 2014-2016 thousand I\$) So, my understanding is that in the first one (constant... US$), ...


2

Well first if actually the cryptocurrency we are talking about would be created by central bank, then the rules that were used to create it would be by definition monetary policy even if supply of money would be fixed, since monetary policy is central bank’s control of money supply either directly or via interest rate (see Yeyati, Sturzenegger (2010), or ...


2

You are wrong/vague here: the rupee (INR), is appreciating against, say, the USD, it possibly means that there is a high demand for the former. If the rupee becomes more expensive w.r.t. the dollar, demand for the rupee usually decreases, as Indian exports are now more expensive to pay for when measured in dollars, and hence fewer people seek to convert ...


2

Yes inflating asset prices does not count as an inflation generally speaking although your friend's explanation is incorrect. Fed is not an authority that decides how inflation is defined. Inflation is generally in academic literature simply defined as (Lebow & Rudd, 2016) Inflation measurement is the process whereby changes in the prices of individual ...


2

Dividing equation 25 by $\gamma$ gives: $$ Y_t = C_h + \frac{\gamma}{1-\gamma} C_h^\ast. $$ Then using 7 and 7a to substitute for $C_h$ and $C_h^\ast$, we get: $$ Y_t = (1-\gamma) \frac{P_t}{P_h} C_t + \frac{\gamma}{1-\gamma}(1-\gamma) \frac{P_t^\ast}{P_h^\ast} C_t^\ast. $$ Then multiply both sides by $P_h$ and use $C_t^\ast = C_t$ to get: $$ \begin{align*} ...


2

I don't know the paper nor the notation, so I am just guessing here. I gues $N(a,t)$ is the number of agents of age $a$ at time period $t$. Let's follow the number of age $B$ accross generations: $$ \begin{align*} N(B,t) &= e^f N(B, t- B),\\ &= e^{2f} N(B, t - 2 B),\\ &= \ldots,\\ &= e^{f t/B} N(B,0),\\ &= e^{\eta t} N(B, 0). \end{align*} ...


2

Let's guess that the value function is of the form $a + b \ln(k)$. Then substituting for $V(k) = a + b \ln(k)$ in the Bellman equation gives: $$ a + b \ln(k) = \max_{k'}\left(\ln(k^\alpha - k') + \beta(a + b \ln(k')\right) $$ The first order condition is given by: $$ \begin{align*} &\frac{-1}{k^\alpha - k'} + \beta b \frac{1}{k'} = 0,\\ \to & k' = \...


2

First, something that was not explicitly mentioned in your question is that in both cases you refer just to indexation, so answer will also be given in context of indexation. Second, your premise is false. Datasets & research do not use just multiples of 10 but also multiples of 5 often. For example, for HICP Eurostat choose year 2015 as base year. ...


1

Question : Is what I wrote above accurate? There is a bit more nuance to it but 1-3 points are 'corect-ish'. I guess what I'm getting at is: Is there some connection to the bank making loans, and those loans being used to fund additional productive activities* than otherwise possible (say, given the agent's initial budget constraints), and long run growth ...


1

I think this boils down to misunderstanding what saving in macroeconomics is. Saving does not cancel each other out. In closed economy, private saving is difference between income (which is by definition equivalent to output so I will be using output and income interchangeably) and consumption $S=Y-C$ and public saving is difference between government ...


1

Does savings always equal investment? If we are talking about national accounts then yes. Output of closed economy is given by: $$Y = C+I+G \tag{1} $$ Private saving $S_p$ is by definition is disposable that is not consumed (see further explanation in Blanchard et al. Macroeconomics an European Perspective pp 55) so: $$S_p= Y- T-C \tag{2}$$ Public saving $...


1

After reading a few more chapters, the authors in their, by now very known, terse and often imprecise style, state that a financial repression is a method used by some governments to obtain indirectly more revenue. This channel works when the government makes bank accounts as the main possible saving tool available to the common folk. Afterwards, the banks ...


1

If the demand curve SHIFTS to the right (due to a thriving economy and an increase in transactional demand for money) and the central bank keeps the money supply the same, the result would be deflation? Yes, this would result in deflation ceteris paribus. In fact Mankiw Macroeconomics 8ed also mentions that in passing on pp 335, but you are right it does ...


1

Hypothetically, if the US was to fall into sub-unity velocity, would there be a clear interpretation $V$ is by definition the average number of times 1 unit of currency is used (See Fed explainer on that). A clear interpretation of $V<1$ is that there are some units of currency that were never used during the measurement period. If an hypothetical ...


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