Consider the full version of the Solow model with both population growth and technology: Y; = F (K a, LtEt). We will extend this version of Solow to also explicitly include the government. The national income accounts identity becomes: Yt=0t+It+Gt where G1; is government spending in period t. In order to fund its spending the government collects a tax Tt. Suppose for simplicity that the government runs a balanced budget G; = I} and that the tax collected is a constant fraction 0 of output: 6': = T; = UK. The remaining disposable income for households each period is (1 cr)Yt. As in Solow we still assume that households save/ invest a constant fraction 3 of their (now disposable) income. The population growth rate is n, techonolog'y grows at g, and the depreciation rate is 6. (a) Assume for now that there is only private and no public investment (i.e all government purchases are spent on consumer goods and none of GE is used to invest in capital). Write down the stande system the equations for output, consumption, investment, and the capital accumulation equation