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Consider the Solow grow model. Suppose for each unit of savings, the government consumes a fraction...

Consider the Solow grow model. Suppose for each unit of savings, the government consumes a fraction τ , so only the fraction 1 − τ would accumulate the capital stock. In other words, the law of motion for capital becomes:

K1= (1 − δ)K + (1 − τ )sY

where δ is the depreciation rate, s is the saving rate, and Y is aggregate output. Suppose production function is Y = zF(K, N). Follow the same steps we did in class to derive the equation that determines the steady state capital under this new law of motion. Then, mathematically show whether output per capita falls or rises with τ , i.e., determine the sign of dy/dτ . Explain your result briefly

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