Question

5. Government Spending and Long Run Economic Performance Consider the following variant of the basic growth model: We will include a government that consumes output (G) and pays for it by imposing lump sum taxes (T). The government balances its budget every period. With these modifications the model becomes: Y = A-. K.N.- N =1 Y = C, +1, +G I, =s.(Y, -T) T, = G, K,+1=K,:(1-5)+1, Suppose government spending is proportional to output. As the country grows, the government spends more and more. Specifically suppose government spending is G = 0 Y, where is between 0 and 1. a.) Plug the relevant equations into the capital accumulation equation to derive an expression for Khi involving only K (and some parameters). b.) There is no growth in the steady state (i.e. Kt+1/ Kt=1). Solve for the steady state capital stock K*. How do changes in affect the steady state?

Answer 1

Anas. Given that {avations. It Ya Alo Koivele to YH = CH+ If tht Iva S. (+-T) ET It = ht kitl = 4 (1-2) + I. Government Consumes output. (i) imposing lomp som taxestal. Now, we find out t o Lyte kvinde * : land # Igt= (kje] | Kitta kt(1-3)+It : + (1-4) 373-1) =kt (1-5)+J (y IkH] (kella kt (1-8) + 3 (J-Ikt)} Aktcon Dkt = J + (k)-3K = gaf&J: Sk f (- pression Ka gjat & la linedal

- Aft-Skt +Sy-SZkt-kot som IO:-8kt sx_dek : JK & dIk=dx 3k+dIk - dk? k(Std I) = $k² :C8+81):344-1 : KX-I = 8+81 *+= (2487) all It inedeases than steady' of capital i n decreases,