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, & the quantity of physical capital per worker, and y the quantity of output per worker. The economy's production function is: y = Ak1/3 x1/3 We assume that the government collects a fraction r of national income in taxes and spends all of this revenue producing government capital. We also assume that a constant fraction y 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 = TAK* x - 5x Ak = y(1 -T)Ak x5 - 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