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Econ 222 Assignment 3

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Econ 222

Macroeconomic Theory I

Assignment #3

Question 1: The Solow growth model

Consider the following production function:

Y (t ) = F (K (t ),A(t )N (t )),

(1)

where Y (t ) denotes output, K (t ) denotes total capital input, A(t ) denotes “knowledge”,

and N (t ) denotes total labour input. F (•, •) is the aggregate production function. Note that

A(t )N (t ) is commonly referred as effective labour, and technological progress that enters

the production function in this fashion is known as labour-augmenting or Harrod-neutral.

a) Derive the intense form (per unit of effective labour) of the production function, using

the abstract production function above.

b) We know the actual production function is

Y (t ) = K (t )α [A(t )N (t )]1−α .

(2)

Denote the population growth rate as n, the depreciation rate as d, the growth rate of

knowledge as д, and the saving rate as s. First derive the steady state condition for this

economy (involving investment per unit of effective labour), and then solve for the steady

state level of capital per unit of effective labour, k ∗ (t ).

c) Given the result in b), solve for the steady state level of output per worker y ∗ (t ), and

consumption per worker c ∗ (t ).

1

d) Solve for the Golden rule level of capital per worker, kG . If the government can choose

a saving rate for the economy, what saving rate should the government choose, assuming

that it wants to achieve kG in the steady state.

e) Suppose the economy is at a steady state, and there is a decrease in the saving rate

s. Explain the impact of this shock regarding steady state variables, with the help of a

diagram. Label your graph appropriately.

Question 2: Learning-by-doing and endogenous growth

This question explores the idea of learning-by-doing as a source of economic growth.

Consider the same production function as in...

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