Consider the Solow model given by the following equations kit+ (18)kt-1 Yt = Akt_1 (1) (2)...

  

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Consider the Solow model given by the following equations kit+ (18)kt-1 Yt = A·kt_1 (1) (2) it = s. yt Yt = ct + it R₁ = a ·A.k(-1) Wt = (1 - a) Yt (4) (5) (6) where s is the constant savings rate, a is the capital share in production, A is the exogenous level of total factor productivity (TFP) and d is the constant depreciation rate of capital. All the variables, except for the interest rate R₁ and the wage rate w+ are in per capita term, so, for example, ct is consumption per person in the economy. A) assuming s = 0.25, A = 5, 6 = 0.1 et a = 0.4. Find the value c* and y* at the steady state. B) Assume now that A = 6, ie there is a permanent increase in TFP. Calculate the new level of consumption per capita c* following this increase in TFP. Has consumption per capita increased or decreased following the gain in productivity? How do you explain this result? C) Assume now that A = 5 but s = 0.20, ie there is a permanent decrease in the savings rate. Calculate the new level of consumption per capita c* following this decrease in the savings rate. Has consumption per capita increased or decreased? How do you explain this result? D) Assume now that A = 5 but 6 = 0.125, ie there is a permanent increase in the depreciation rate of capital k. Calculate the new level of consumption per capita c* following this increase in the depreciation rate. Has consumption per capita increased or decreased? How do you explain this result? E) Assume again that A = 5 but s = 0.20, ie there is a permanent decrease in the savings rate. What is the minimum percentage (%) increase in TFP that needs to materialize to ensure that consumption per capita (a measure of standards of living) remains the same as that found in A), despite the lower savings rate? Consider the Solow model given by the following equations kit+ (18)kt-1 Yt = A·kt_1 (1) (2) it = s. yt Yt = ct + it R₁ = a ·A.k(-1) Wt = (1 - a) Yt (4) (5) (6) where s is the constant savings rate, a is the capital share in production, A is the exogenous level of total factor productivity (TFP) and d is the constant depreciation rate of capital. All the variables, except for the interest rate R₁ and the wage rate w+ are in per capita term, so, for example, ct is consumption per person in the economy. A) assuming s = 0.25, A = 5, 6 = 0.1 et a = 0.4. Find the value c* and y* at the steady state. B) Assume now that A = 6, ie there is a permanent increase in TFP. Calculate the new level of consumption per capita c* following this increase in TFP. Has consumption per capita increased or decreased following the gain in productivity? How do you explain this result? C) Assume now that A = 5 but s = 0.20, ie there is a permanent decrease in the savings rate. Calculate the new level of consumption per capita c* following this decrease in the savings rate. Has consumption per capita increased or decreased? How do you explain this result? D) Assume now that A = 5 but 6 = 0.125, ie there is a permanent increase in the depreciation rate of capital k. Calculate the new level of consumption per capita c* following this increase in the depreciation rate. Has consumption per capita increased or decreased? How do you explain this result? E) Assume again that A = 5 but s = 0.20, ie there is a permanent decrease in the savings rate. What is the minimum percentage (%) increase in TFP that needs to materialize to ensure that consumption per capita (a measure of standards of living) remains the same as that found in A), despite the lower savings rate?

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A Given s025 A5 01 04 At steady state k 1k sY Y Ak R Ak1 w 1Y Solving the model c 075Y 0755k04 3375 ... View the full answer