Question
0.5 Suppose that an economy has the per-worker production function given as: Vt 4kt, where y...
0.5 Suppose that an economy has the per-worker production function given as: Vt 4kt, where y is output per worker and k is capital per worker In addition, national savings is given as: St0.20Y where S is national savings and Y is total output The depreciation rate is d 0.05 and the population growth rate is n 0.05 The steady-state value of the capital-labor ratio, k is 64.00 The steady-state value of output per worker, y is 32.00. The steady-state value of consumption per worker, c is 25.600. Use the same production function as before, but now let the savings rate be 0.30 rather than 0.20 St0.30Y, The depreciation rate is d 0.05 and the population growth rate is n 0.05. (Enter all responses as decimals rounded up to three places.) What is the new steady-state value of the capital-labor ratio, k?
Answers
s = 0.3
In steady state, following relationship holds:
s / (d + n) = k / y
0.3 / (0.05 + 0.05) = k / 4k0.5
0.3 / 0.1 = k0.5 / 4
k0.5 = 1.2 / 0.1
k0.5 = 12
Squaring both sides,
k = 144.000
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