Date Page Ma. 1/2 a ) 4 = 10 k 2 2 1/2 Multiply K & L by, 10712 112 7 1/ 2 1/2 L A. LO K 2 . Power of x in 1 - production function is constant returns b ) y = 10 k L Divide both sides by L - 8 Lok 12 1 / L = 10 k'h L Let y - y & K - R C ) he * = 3025 sy S = 1601. = 0 x 6 Old= 107. = 0.1 Ah = 0 . 6 ( 1 on ? ) - 0 . Int = 0 . 6 ( 1 0 X 3 0 2 5 /2 ) - 0 - 1 ( 3025 ) = 330 - 302.5 = 27.5 RTH = 3025 + 27.5 = 3052.5 20 . 6 ( 10 X 30 5 2 . 5- 2 ) - 0. 1 ( 3251.5) 3 31. 496 - 305- 25 26 . 296 vijetaR = 3052 .5 +26. 276 = 3078. 746 ARE+2 : 0. 6 ( 10 X 3078. 746 ) - 0. 1 ( 3079. 796 = 25. 04 3078 . 746 + 25. 09 = 3103. 79 2 + = 4225 AR * = 0. 6 ( 10 X 72 25 2 ) - 0 . 1 ( 4225) = 390 - 422.5 = - 32-5 REH = 4225 - 32.5 = 4/92.5- A n * g = 0 . 6 ( 1 0 x 4 1 9 2 . 5 2 ) - 0. 1 ( 4192 .5) = 388 . 497 - 419. 25 = - 30- 75 K E + 2 = 4 192. 5 - 30. 75 = 4161 . 797 AREyz = 0. 6 ( 10 X 9161 - 797 2 ) - 0.1 ( 4161. 747) = - 29. 101 12 + + 3 = 4 161 . 247 - 29 . 101 = 4/32 . 641. An economy produces with the production function Y = 10K /21 /2. There is no population growth or technological progress. The depreciation rate is 10% and the saving rate is 60% a. Show that the production function is constant returns to scale. b. Show that the function can be written y = 10k /2 where y = +, and k = c. Assume k = 3025. Find Kt+1. kt+2, and kt+3 d. Now assume k = 4225. Again find kt+1, kt+2, and kt+3 e. Based on your answers above, without directly solving for the steady state, provide a range that the steady state of capital must fall within. f. Find the exact steady state capital per worker. Also find output per worker and consumption per worker at the steady state. g. Find the steady state capital per worker that maximizes consumption. What is consumption at this level? h. Assume the economy starts in the steady state corresponding to s = 0.6. If it adjusts its savings to the optimal level (i.e. the level that maximizes consumption in the steady state), what is consumption per worker immediately after the change in savings (i.e. before capital changes)? Draw a graph of consumption per worker over time as it adjusts to the new steady state. i. Thanos snaps his fingers and half the labor force disappears. Draw a graph of output per worker and total output over time