Closed Economy Aggregate Production Function: Computing Output for t = 10, 20, 30

To compute Yt for t = 10, 20, and 30, we need to calculate the values of Kt and Lt for each period.

Given: K0 = 1 L0 = 1 Population growth rate = 2% = 0.02 Investment share = 20% = 0.2

To calculate Kt and Lt for each period, we can use the following equations:

Kt+1 = 0.95Kt + It It = 0.2Yt Lt+1 = (1 + 0.02)Lt

Let's calculate the values of Kt and Lt for t = 10, 20, and 30:

For t = 0: K0 = 1 L0 = 1

For t = 1: It = 0.2Y0 = 0.2F(K0, L0) = 0.2√(1)^2 + (1)^2 = 0.2√2 = 0.4 K1 = 0.95K0 + I0 = 0.95(1) + 0.4 = 1.35 L1 = (1 + 0.02)L0 = (1 + 0.02)(1) = 1.02

For t = 2: It = 0.2Y1 = 0.2F(K1, L1) = 0.2√(1.35)^2 + (1.02)^2 = 0.2√2.5625 + 1.0404 = 0.2(1.6 + 1.0202) = 0.324 K2 = 0.95K1 + I1 = 0.95(1.35) + 0.324 = 1.52825 L2 = (1 + 0.02)L1 = (1 + 0.02)(1.02) = 1.0404

Continue this process to calculate Kt and Lt for t = 10, 20, and 30.

For t = 10: It = 0.2Y9 K10 = 0.95K9 + I9 L10 = (1 + 0.02)L9

For t = 20: It = 0.2Y19 K20 = 0.95K19 + I19 L20 = (1 + 0.02)L19

For t = 30: It = 0.2Y29 K30 = 0.95K29 + I29 L30 = (1 + 0.02)L29

Once we have calculated the values of Kt and Lt for t = 10, 20, and 30, we can substitute them into the production function Yt = F(Kt, Lt) to find Yt.