Answer :
The steady-state level of capital per worker is approximately 3.52, output per worker is approximately 6.19, consumption per worker is approximately 4.67, savings and investment per worker is approximately 0.80, and depreciation per worker is approximately 0.07.
To calculate the steady-state level of capital per worker, we use the equation k* = (sY* - δk*) / (n + g), where k* represents capital per worker, s is the savings rate, Y* is output per worker, δ is the depreciation rate, n is the population growth rate, and g is the technological progress rate. Since the population growth rate is given as 0, n = 0. The technological progress rate is also not specified, so we assume it to be zero, g = 0. The depreciation rate is 2% per year, which means δ = 0.02.
Substituting the given values into the equation, we have k* = (0.128 * 6.19 - 0.02 * k*) / (0 + 0). Solving this equation, we find k* = 3.52.
Next, we can calculate output per worker (Y*) using the production function Y = 10(K^(1/4))(L^(3/4)). Since we know k*, we can substitute it into the production function and solve for Y*. Plugging in k* = 3.52, we find Y* = 6.19.
To calculate consumption per worker, we use the equation c* = Y* - δk*. Substituting the values, c* = 6.19 - (0.02 * 3.52) = 4.67.
Savings and investment per worker are equal to sY*, which is approximately 0.128 * 6.19 = 0.80.
Depreciation per worker is equal to δk*, which is approximately 0.02 * 3.52 = 0.07.
In conclusion, the steady-state level of capital per worker is approximately 3.52, output per worker is approximately 6.19, consumption per worker is approximately 4.67, savings and investment per worker is approximately 0.80, and depreciation per worker is approximately 0.07.
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