Consider the Solow growth model in which population evolves according to: N = (1 + n)N where N is the population (labor force) in the current period, N is the population (labor force) in the future period, and n is the population growth rate. There are public health expenditures that takes the form of government spending, G = gN, where G is the current period government spending on health care, g is the per-capita health spending in the current period. The production technology is given by Y = zKN1 where Y is the output of the consumption good, z is the total factor productivity, K is the current period capital stock, aN is the labour input, and 0 < < 1 is a parameter. Consumers save a constant fraction, s, of their disposable income, where 0 < s < 1.

(a) Suppose that the economic is hit by a pandemic (e.g. Covid-19). The government responds to the pandemic by raising the public health spending per person (e.g spending on vaccination) temporarily (i.e. one-period only). Using the Solow growth model, assess the impact of the pandemic.

(b) Suppose that the economic is hit by a pandemic (e.g. Covid-19) which causes a temporary decrease in total factor productivity, z, as certain sectors in the economy (e.g. entertainment, travel etc.) cannot deliver the same quantity of output with physical distancing measures. In order to counteract the decrease in z due to the pandemic, the government increases temporarily G (i.e. spending on vaccines) which eliminates the pandemic in the future period completely. Using the Solow growth model (i.e. equations, graphs, and words), discuss the changes in economic variables in both periods.