Consider the extension of the Solow model to encompass a second type of capital, called government capital, which consists of publicly funded infrastructure such as roads and ports. Let x denote the quantity of government capital per worker, k the quantity of physical capital per worker, and y the quantity of output per worker. The economy's production function is: y = A k1/3 x1/3 We assume that the government collects a fraction 1: of national income in taxes and spends all of this revenue producing government capital. We also assume that a constant fraction )1 of after-tax income is invested in producing physical capital. Both government capital and physical capital depreciate at rate 6 . The equations describing how government capital and physical capital change over time are thus: Ax = rAkax'g 6x Ak = y(1 T)Ak\"x3 6k (a) Solve for the steady-state level of output per worker. (b) What value of T will maximize output per worker in the steady state