Consider the Solow-Swan growth model, with a savings rate, s, a depreciation rate,8, and a population...

  

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Consider the Solow-Swan growth model, with a savings rate, s, a depreciation rate,8, and a population growth rate, n. The production function is given by: Y = AK + BK¹/2 H¹/4L¹/4 where A and B are positive constants. Note that this production is a mixture of Romer's AK model and the neoclassical Cobb-Douglas production function. (a) Express output per person, y =Y/L, as a function of capital per person, k =K/L. (b) Write down an expression for y/k as a function of k and graph. (Hint: as k goes to infinity, does the ratio y/k approach zero?) (c) Use the production function in per capita terms to write the fundamental equation of the Solow-Swan model. (d) Suppose first that sA <d+n. Draw the savings curve and the depreciation curve. What number does the savings curve approach as k goes to zero? As k goes to infinity, the savings curve approaches a number: what number is that? Is it zero? (e) Under these parameters, will there be positive growth in the long run? (Remember that A and B are constants). Why? Consider the Solow-Swan growth model, with a savings rate, s, a depreciation rate,8, and a population growth rate, n. The production function is given by: Y = AK + BK¹/2 H¹/4L¹/4 where A and B are positive constants. Note that this production is a mixture of Romer's AK model and the neoclassical Cobb-Douglas production function. (a) Express output per person, y =Y/L, as a function of capital per person, k =K/L. (b) Write down an expression for y/k as a function of k and graph. (Hint: as k goes to infinity, does the ratio y/k approach zero?) (c) Use the production function in per capita terms to write the fundamental equation of the Solow-Swan model. (d) Suppose first that sA <d+n. Draw the savings curve and the depreciation curve. What number does the savings curve approach as k goes to zero? As k goes to infinity, the savings curve approaches a number: what number is that? Is it zero? (e) Under these parameters, will there be positive growth in the long run? (Remember that A and B are constants). Why?

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a OUTPUT per person y y YL CAPITAL per person k K L y AKL BK13H13L13L y Ak Bkhl Explanation In the production function we divide both sides by per per... View the full answer