I am studying the rate of climb of turbojets, I don't know how the thrust varies with altitude and in particular which are the differences between necessary thrust and effective thrust. Hope being clear, I can't translate properly maybe so ask and edit !
The thrust variation with altitude would be highly engine specific, but the general trend is nicely depicted in the image below:
Read this for further details.
Thrust is produced by accelerating air. The exhaust air leaves the engine nozzle at a fairly fixed velocity, so the acceleration is mainly controlled by the difference between the exhaust and incoming airspeeds. The faster the aircraft speed, the less acceleration is being created on the intake air. Therefore thrust decreases with increasing airspeed.
In level flight, an aircraft could not be accelerated above the engine exhaust gas speeds because then the incoming air would be faster than the exhaust air - resulting in a decelaration.
Most jets are operated as max speeds much less than their exhaust gas velocity - about half of V-exhaust I think.
Since higher air-speeds are normally used at higher altitudes, thrust generally decreases with an aircraft's altitude. But increasing altitudes can erode thrust because the mass of air being consumed is also decreasing as the air gets increasingly more rarified.
To summarize: At a constant airspeed (ignoring airspeed measurement nuances) thrust decreases as air density decreases with increasing altitude; at a constant altitude, thrust decreases with increasing airspeed.
Note that max thrust is found when stationary, just before take-off, since that's when incoming air is at its slowest. Also, at max thrust, (when airspeed is zero) there is no work being done and hence the power produced is zero right before takeoff.
As an aircraft increases in altitude, the density of air also decreases. Thrust available = Q(V1 - V2). The important part of this equation is Q. Q = (rho)AV which means that the smaller rho (density ratio) becomes, the less mass airflow there is which results in lesser thrust at high altitudes.