Suppose the economy of Poorland is described by the simple Solow model without technological progress or...

 

  

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Suppose the economy of Poorland is described by the simple Solow model without technological progress or population growth. The economy starts at the steady state. Suppose another country concludes that income per worker is too low in Poorland and therefore sends them at one-time development aid package (in form of capital) at period to- a. Show what happens as a result of this aid package in a graph showing the production function, investment function and depreciation function (all in per-worker terms). b. Show a time path of output per worker that shows the old steady state, the change due to the aid package and the transition to the long-run equilibrium over time. Briefly explain your graph. C. If Poorland would like to maintain the capital stock per worker that it had right after the aid package was received, what would it need to do? Question 31 Consider the simple Solow growth model without technological progress and without population growth. Assume that the production function has the same properties as we assumed in class. When we look at economic data we usually find that richer individual save a higher fraction of their income compared to poorer individuals. This problem will ask you to analyze how this will affect our model. Suppose that there is a specific threshold level of the capital stock per worker (), below which individuals save a fractions and above which individuals save a fraction ag of their income. Mathematically this translates into the following conditions: Furthermore the following is satisfied: A. 8=sy for 81 < 82 ss for e mf N < 2 T [)]*) [(G)]> * (*)* Note that the last two conditions represent inequalities that hold at the threshold level and do NOT represent conditions that hold for every 1 Show graphically how the above conditions affect the Solow model! Specifically, draw the investment function, the production function and the depreciation function. Also identify clearly all possible steady states! b. For each of the steady states identify if it is stable or unstable. If the economy starts with a capital stock per worker that is smaller than (), in which steady state will the economy end up? Suppose the economy of Poorland is described by the simple Solow model without technological progress or population growth. The economy starts at the steady state. Suppose another country concludes that income per worker is too low in Poorland and therefore sends them at one-time development aid package (in form of capital) at period to- a. Show what happens as a result of this aid package in a graph showing the production function, investment function and depreciation function (all in per-worker terms). b. Show a time path of output per worker that shows the old steady state, the change due to the aid package and the transition to the long-run equilibrium over time. Briefly explain your graph. C. If Poorland would like to maintain the capital stock per worker that it had right after the aid package was received, what would it need to do? Question 31 Consider the simple Solow growth model without technological progress and without population growth. Assume that the production function has the same properties as we assumed in class. When we look at economic data we usually find that richer individual save a higher fraction of their income compared to poorer individuals. This problem will ask you to analyze how this will affect our model. Suppose that there is a specific threshold level of the capital stock per worker (), below which individuals save a fractions and above which individuals save a fraction ag of their income. Mathematically this translates into the following conditions: Furthermore the following is satisfied: A. 8=sy for 81 < 82 ss for e mf N < 2 T [)]*) [(G)]> * (*)* Note that the last two conditions represent inequalities that hold at the threshold level and do NOT represent conditions that hold for every 1 Show graphically how the above conditions affect the Solow model! Specifically, draw the investment function, the production function and the depreciation function. Also identify clearly all possible steady states! b. For each of the steady states identify if it is stable or unstable. If the economy starts with a capital stock per worker that is smaller than (), in which steady state will the economy end up?