Let us consider a Solow growth model augmented with government spending financed by a proportional income tax re (0,1). Therefore, the total tax revenue at time / denoted by T can be written as: T = TY where Y, denotes the aggregate output/income at time & produced according to the following Cobb-Douglas production function: Y = AK *LY where a E (0,1) denotes the labour share of output, A > 0 stands for aggregate productivity, Ke is the aggregate stock of physical capital at time / and &, represents the aggregate labour input at time & which is equal at every period to the population size denoted by N, which grows at the constant rate n 2 0: Ni+1 = (1 + n)N. The equation of motion for the aggregate physical capital from time & to time t+I is given by: Ke+1 - Ke = he -K where I, denotes the aggregate investment at time &and $ 6 (0,1) represents the depreciation rate. At every time & aggregate private consumption denoted by C, is a constant fraction y c (0,1) of the disposable income: C = V(Y - T.) where y e(0,1) stands for the marginal propensity to consume. Let S, denote aggregate private saving at time + which corresponds to the disposable income not consumed: SEY -T, - C Let us assume that government spendings at every time & denoted by G, always balance Its budget: Let ye = Y:/N, denote the output per capita, let k, = K /N, represent the physical capital per capita and let c = C/N, stand for the consumption per capita. a. Write-down the production function in per capita units. (4 points)