Show your work and explain in detail complete all parts of the questions below:
- Assume that a leader country has real GDP per capita of $40,000, whereas a follower country has real GDP per capita of $20,000. Next suppose that the growth of real GDP per capita falls to zero percent in the leader country and rises to 7 percent in the follower country. If these rates continue for long periods of time, how many years will it take for the follower country to catch up to the living standard of the leader country? Explain in detail show your work.
To determine how long it will take for the follower country to catch up to the living standard of the leader country, we can use the concept of exponential growth. The formula for future value in terms of growth is given by:
[
FV = PV \times (1 + r)^t
]
Where:
- ( FV ) is the future value (real GDP per capita in this case),
- ( PV ) is the present value (current real GDP per capita),
- ( r ) is the growth rate,
- ( t ) is the number of.
Step : Up the
.Leader: Current GDP capita ((PV_{}\ $,
- rate(_{}\ % .- Future value (\ years ((FV_{}\ $, (ains)
. **Follower: Current GDP capita ((PV_{}\ $,
- rate(_{}\ % .
- value (\ years(_{}\
[
_{} , \ ( +007t### : the Values
find when follower catches to the leader country we ({}\ equal ({}\20000times1 .)^ =40000### :ify EquationDivide sides ,:
[
1 +0.)^ =frac4000020000\This to(.)^ =2### : fort)
solve (\ we take logarith of sides\((.)^) ()
]
the ofms allows to the exponent down\tcd (.) \log()
]
, (\t {()}log107### : (\Using calculator find logarith:
\log2 \ .0)
\log107 \approx 0.0291)
Now substitute these values into equation\tapproxfrac0301}{.1 \ .
]
ConclusionIt take **. years for the follower country catch to living of leader, that follower maintains real per growth rate of 7% and the leader country stagnant a rate of %.This analysis demonstrates growth significantly the convergence countries despite at lower level consistent growth lead substantial in standards time