could you help?

wheather per capita variables should increase?

In this problem we study the effects of a big pandemic L'corona style'1 on economic growth using the Solow model. Total population in this economy.r is N. constant over time. However. not all the people will worlr. but only a fraction in of them [the fraction of healthy people at time t]. Thus the aggregate labor force is Lt = MN. and aggregate output is Y: = erKr where K: is aggregate capital. Note that the labor force depends on time only to the extent that the fraction ht may vary over time. The remaining of the model is standard. We have an aggregate resource constraint: {1+ It = H where U: is aggregate consumption. and I: investment. We assume that investment is always a fr action of out put: It=STEr where s E {0.1} is the saving rate. Finally. the law of motion for aggregate capital is Kt+1 = [1 ENG 4 It where .5 E {[1,1] is the depreciation rate. The benchmark [initial] economy is one where the fraction of healthy people is constant and equal to one: ht = 1 for all t. Please note that per capita Trariahles are always in terms of total population (y: = Iii/tn and so on]. For simplicity assume 3 = .5. a] Suppose that at time t = I] the economy is at the henchm ark steady-state. Then. at t= l the fraction h: permanently decreases as a result of a new dangerous virus. In particular. we have h; = [1.75. Explain how this permanent change affects the economy both in the short-run [on impact and throughout the transition] and in the long run. Specic ally. show [with pictures!) what happens with capital. output. investment and consumption over time [in per capita terms