An economist has invented an “index of economic well-being”. The value of the in

Question

An economist has invented an “index of economic well-being”. The value of the index in year t is:

Where W(t) = average industrial wage (in dollars per hour)

                        R(t) = yield on a 30-day treasure bill (in percent)

                        U(t) = unemployment rate (in percent)

The economist has defined the “coefficient of economic velocity at time t” to be . At a particular time t0, the economist has found that the average industrial wage per hour is 11 dollars, the 30-day treasure bill rate is 5%, and the unemployment rate is 5%. Also, the economist has estimated that the average industrial wage is rising at a rate of 20 cents (per hour) per year, the 30-day treasure bill rate is constant at 5%, and the unemployment rate is dropping at the rate of 0.2% per year. Find the coefficient of economic velocity at time t0.  

Explanation / Answer

i=$11 and di/dt=$0.2

R=5. And Dr/dt=0

U=5 and du/dt=-0.2

di/dt=(1/R)*W*Dr/dt(-1/U^2)du/dt

So I=((11*0.2)/(-1/5^2)*-0.2)/5

I=0.00352

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