Consider the Solow-Swan growth model, with a savings rate, s, a depreciatic 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 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/ (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 canita terms to write the fundamental
Consider the Solow-Swan growth model, with a savings rate, s, a depreciatic 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 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/ (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 canita terms to write the fundamental
Chapter1: Making Economics Decisions
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only part e solution is needed
Transcribed Image Text:Problem 1
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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