ECON6002 Tutorial 1 (Solow Model)
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ECON6002
Tutorial 1 (Solow Model)
NOTE: The tutorial problems are covered by the online tutor. If you have any ques- tions about the tutorial questions that are covered by the tutor, please post the ques- tions (after you have tried working on the problems) on Ed and the tutor will respond. Please use this as a learning mechanism and not just a channel to get the solutions.
1. Speed of Convergence.
(a) Consider a first order approximation of k(˙) around k* .
k(˙) ≈ − 
k=k * × (k − k* )
Using the formula above, argue that the speed of convergence of the economy from any value of k0 towards k* is directly proportional to the distance between k0 and k* .
(b) The derivative above equals
λ 三 
k=k * = (1 − α(k* ))(n + g + δ)
Find and interpret the expression for α(k* )
(c) Assume that α = 
, δ = 0.05, n = 0.03 and g = 0.03. How long (in years) does it take for an economy to converge halfway to their balanced growth path (i.e. (k − k* ) = 
possibility of “miracle growth” episodes in the past vis-a-vis the present?
2. Describe how, if at all, each of the following developments affects the break-even and actual investment lines in the basic diagram for the Solow model:
(a) The rate of depreciation falls.
(b) The rate of technological progress rises.
3. Suppose that the production function is Cobb-Douglas.
(a) Find expressions for k* , y* , and c* as functions of the parameters of the model, s, n, δ , g, and α .
(b) What is the golden-rule value of k?
(c) What saving rate is needed to yield the golden-rule capital stock?
4. Factor payments in the Solow model. Assume that both labour and capital are paid
their marginal products. Let w denote ∂F(K, AL)/∂L and r denote ∂F(K, AL)/∂K − δ .
(a) Show that the marginal product of labour, w, is A[f(k) − kf′ (k)].
(b) Show that if both capital and labour are paid their marginal products, constant returns to scale imply that the total amount paid to the factors of production equals total net output. That is, show that under constant returns, wL + rK = F(K, AL) − δK.
(c) The return to capital (r) is roughly constant over time, as are the shares of output going to capital and to labour. Does a Solow economy on a balanced growth path exhibit these properties? What are the growth rates of w and r on a balanced growth path?
2023-08-21