Using the production function approach $($augmented model$),$ answer the following questions. For

simplicity, assume that there are two countries: a poor country $($with low living standards$)$ and a rich

country $($with high living standards$).$ Explain and illustrate how convergence works in the following

cases. Briefly explain how each scenario a$$ects the speed with which the poor country converges with

the rich country. Unless otherwise noted, assume each country has the same MPK and that their

productivity levels are di$$erent$,$ with AP $<$ AR$.$

$($a$)$ Foreign direct investment into the poor country leads to an increase in its access to technology.

$($b$)$ The rich country experiences an increase in human capital through government funding of education.

$($c$)$ The poor country experiences an improvement in political stability through the signing of a peace

treaty between warring factions.

$($d$)$ A sovereign debt default by the poor country$$s government leads to an increase in the risk premium