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Consider an extension of the simple Solow model to encompass a second type of capital, called government- provided health capital, which consists of publicly funded health infrastructure such as sanitation, hospitals, and nutrition programs. Let x denote the quantity of government health capital per worker, k the quantity of physical capital per worker, and y the quantity of output per worker. The economy's production function (in per-worker terms) is: y = A Assume that the government collects a fraction t of national income in taxes and spends all of this revenue producing health capital. Also assume that a constant s fraction of after-tax income is invested in producing private physical capital. Both government health capital and private physical capital depreciate at rate 8. The equations describing how health capital and physical capital change over time are thus: Ax = ty - ox Ak = s(1-t)y - 8k Solve for the steady-state level of output per worker. What value of t will maximize output per worker in steady state? Hint: Variables x and k will not change in steady state. Use this idea to solve for steady state y from the equations above. Please show your work