Q1, Solow Growth Model. {1 [1 marks) Consider the production ftmctjon for a closed economy r = 2 avatar-tr\" Assume that the savings rate 3 equals 20% and the depreciation rate 6 equals 5%. Further, assume the growth rate of the labor force ,9\" is 3% and the growth mte of technological progress 3,, is 2% per year- a. Find the steady-state values of (i) capital per effective worker, {ii} output per effective worker, {iii} the growth rate of output per effective worker, {iv} the growth rate of output per worker, and {v} the growth rate of output. (2.5 marks) Now we modify the basic Solow growth model described above, by including government spending as follows. The government collects taxes T to finance its government spending G in every period. Government spending per worker is given by a constant g, where g= Gaff. Workers consume a Fraction of disposable income C= {f-sjtT-fj. Suppose that the government has a balanced budget. Also assume that A= f and the growth rates of technological progress and the labor force are zero, g= g~= l}. b. Write down the capital accumulation equation. With the help of a diagram, illustrate that there can be two steady-state values of capital per worker (I? =K'ri'v}. Careilly label your diagram. [3.5 marks} c. We can Focus on the high it\" and ignore the low t' because the low it" is an unstable steady state. What is the effect of an increase in g on At"? What are the effects of an increase in g on aggregate consumption C? Explain, [2 marks} d. How we modify the way we defme government spending. Suppose that government spending G is proportions] to aggregate output 1", where G= 2]". That is, government spending is a fraction .- of aggregate output If. Are there two steady-state values of capital per worker? What are the effects of an increase in a on capital per worker t2" and aggregate consumption C? Explain. {2 marks}