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Given a discount function $g(t)$, the discount rate is the rate at which the discount function declines over time. If time is discrete, then the (possibly time-varying) discount rate is $$\rho(t)=-\frac{g(t)-g(t-1)}{g(t)}.$$ If we divide each period into $n$ equal intervals and let $n\to\infty$, then we get the discount rate in ...

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You are right the two series closely follow each other for the reasons you mention. During quite some time the discount rate actually used to be a ceiling for a funds rate. This is precisely, because if the federal funds rate was below the discount rate, most banks adjusted their reserve positions in the federal funds market and when the federal funds rate ...

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Well this is 'exponential discounting'. An infinite sum of geometric series: $$\sum R+ R\delta + R\delta^2.... R\delta^t = \frac{R}{1-\delta}, \text{ if } |\delta|<1$$ Now lets call the denominator rho $1-\delta= \rho$. The exponential discounting is there since its an infinite sum of geometric series. Edit: In response to Giskard's +1 comment I tried to ...

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An answer (I am not sure this is the right one) is if the "positive rate $\rho$" refers to an interest rate. Sometimes interest rates are referred to as discount rates. In this case we would have a discount factor of $1/(1+ \rho)$, and the usual present value formula for a perpetual annuity yields $$\frac{R}{1+ \rho} + \frac{R}{(1+ \rho)^2} + \frac{... 2 In the version of the McCall search model I'm familiar with, once you accept an offer of wage w, you receive that wage w in every period starting from the period of acceptance. Hence, from the perspective of the current period, your utility from accepting that offer is$$ w + \beta w + \beta^2 w + \cdots =\frac{w}{1-\beta}  In case this equality ...

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As Kitsune rightly points out the usual reason for the inclusion of the time preferences for money into the discount formula (or Ramsey fomula) is that we observe this kind of behaviour in people. Given that many economists take a positive approach towards the study of economics, that is a logical stance. That being said the last word is not spoken on this, ...

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To be clear, we are assuming that the nominal investment value is a constant $K$. As such, if we calculate the NPV in the future, that future NPV will rise. Of course, we do not work with future NPV’s, we are making a decision now, and so we need to discount that future NPV by the discount rate, to get an apples-to-apples comparison. I will now look at the ...

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They are related but they are not same. An interest rate is broad term for what you pay for the use of assets as a percentage of the value of the asset or principal. See for example definition here. A discount rate can be the interest rate that Fed charges at its discount window, or it is often in theory used more broadly as the rate at which people ...

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Economically, they are both loans against financial instruments. The difference is the collateral posted - repos by the Fed are generally against Treasury securities. This is not a small difference: it makes it much easier for a bank to access liquidity, since not all of its assets are Treasury securities. There’s a mechanical difference: a discount window ...

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You're missing the distinction between costs and benefits. In your first probem you have positive NPVs and therefore the equivalent annual value is the equivalent annual cashflows that comes in. In your second problem you have costs only. Converting that that to an EAV means converting it to an annual cash flow that goes out. Obviously you want the former ...

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The yield to maturity is the internal rate of return on the bond assuming no default. Given a series of promised cashflows in the future, to quote Prof. John Cochrane, "... the yield is just a convenient way to quote the price." In the case of a zero-coupon bond with price $p_0$ and face value $c_t$ due $t$ periods in the future, the yield to maturity is ...

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An increase in the discount rate increases the cost of borrowing for commercial banks. Their normal response would be to (a) Offer higher interest rates to depositors to replace loans from the Reserve System, and (b) Increase commercial interest rates on the loans they offer to pass on their higher costs to customers. This makes it more attractive for ...

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A type of model you might be interested on is one where the depreciation rate is endogenous. This means, it depends on the value of other variables in the model, instead of being exogenous and constant (naturally, you can have a variable depreciation rate but exogenous, but that is as ad-hoc as a constant depreciation rate). One example is this model. ...

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I think one can answer this question by looking at what affects saving rates. Age According to the life-cycle model of household savings*, young and old people save less than middle-aged people. Young people who are starting a new family have many expenses and a lower income due to lack of work experience. Thus, young people save less and value money more ...

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