Problem 2 Suppose that the growth of the national economic output of a country Y depends on how much capital K is available in the economy and also on the progress of technolog- ical innovation 3 according to the following aggregate production function: Hg, K) : 0.5gK. Suppose furthermore that the evolution of technological growth and that of the aggre- gate capital stock over time t are given as g\") 2 V 1 + t! KG) 2 10:20-93. The chain rule tells us that the total derivative dY / d t of national output with respect to time is: dY _ BY dg BY dK aga+' '\" (a) Provide an economic interpretation of the formula (4:). (b) Use the chainrule formula (ac) to compute the total derivative dY/dt of national output with respect to time given the functional forms Y(g, K), g(t), and K(t) spec- ied above. Make sure to express the formula you compute for dY/dt solely as a function of t