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A natural application of trigonometric functions is in the analysis of spatial data. An example is the Weber problem in location theory - finding the point which minimises the sum of transport costs …

Firstly, the formula you have used for FV is equivalent to that shown here. What it calculates, with your numbers, is the value after 7 years of investing 200,000 annually at a compound rate of 7% (as …

Suppose the probability of an error in the $n$th cycle since the most recent maintenance is $a+bn$, and let the number of tasks (cycles) between maintenance be $x$. I'm assuming here that the tasks ca …

There is no clear right and wrong about this, it's just a matter of convenience. The current-value Hamiltonian is likely to be more convenient when the objective function includes a discount factor. F …

It is theoretically possible, but extremely unlikely if the random sample is large. To see that it is possible, consider the very simple case shown below in which the population consists of just four …

As pointed out by mark leeds, the chapter appears to be part of an incomplete text by Peter Thompson - see here.

One of the most fundamental distinctions in economics is that between stocks, measured at a point in time, and flows, measured over a period of time or as instantaneous rates. The construction of dyna …

A textbook on dynamic optimization which treats transversality conditions at some length is Chiang Elements of Dynamic Optimization. See especially sections 7.2 - 7.4 and 9.1.

The term $\lambda_2(x_1-1)$ in your Lagrangian is incorrect; it treats the second constraint as an equality rather than an inequality. To allow for the constraint being an inequality you can include a …

If GDP is measured (as it usually is) for a period such as a year, then number of hours worked ($h$) should be measured for the same period. Thus $h$ is dimensionless and the dimension of the right h …

A useful starting-point would be Nordhaus's Nobel Prize Lecture, especially the sections headed Integrated Assessment Modelling and Mathematical Representation, and the references at the end of the Le …

Turnpike theory uses fairly sophisticated mathematics to obtain results (which may appear surprising to many) about optimal economic growth over the long term. The theory appears to have its origin i …

The problem is soluble by taking your formula for the industry sector share $f(t)$ at time $t$ and differentiating with respect to $t$ to determine its gradient at $t$, with the maximum where the grad …

In the given scenario, the optimal social outcome from a Coasian bargain is not in general the same as the optimal social outcome from a Pigouvian tax, although there is a special case in which this i …