c3 solow model

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Economics 70-XA, Ateneo de Cagayan-Xavier University, AY 2011-2012

Basic Macroeconomics, June 23, 2011 lecture Page 1

GROWTH ACCOUNTING1

Growth accounting pertains to the decisions regarding how much

inputs should be utilized to attain a certain level of production. It answersquestions such as: which inputs played a big role in growth?

So, when does output grow? Every economics student must know the

right answer to this basic macro question. Thus, this handout is an econ

student-friendly guide to help you out.

a.) Define a Production Function (PF) without technology:Y = f (K, N)

b.) Assume: only K, N are the inputs. Any increase in these inputs will leadto an increase in output. (Simply, MPK and MPL are positive).2

c.)Assume further: The economy is competitive (i.e., it has technologicalprogress = A). In this case, technological progress means that there is nochange in inputs but only better and efficient production. So, the PFbecomes:

Y = A [f (K, N)]

Note: Technology in this case is called Total Factor Productivity (TFP)because it augments both capital and labor. But in most cases, technologycan be:

1. Labor augmenting: Y = f[K, AN]; saves labor2. Capital augmenting: Y = f[AK, N]; saves capital

Now that you know the basics, we shall determine the growth model:

d.) Fundamental Growth Equation (or Solow, neoclassical growthmodel).

This section will help you understand how much change in output (Y) isattained when capital, labor and technology changes (i.e., K, L, A).

1For inquiries, email me [email protected] . Proof reading is taken for granted.

2You should already know by now the meaning of Marginal Productivities of Labor and Capital (MPL and MPK) from your

Microeconomics class.
mailto:[email protected]:[email protected]:[email protected]:[email protected]


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Economics 70-XA, Ateneo de Cagayan-Xavier University, AY 2011-2012

Basic Macroeconomics, June 23, 2011 lecture Page 2

S1.) Define the PF:

Y = A [f (K, N)]

S2.) Take the Y as:

Y = (MPL)(N) + (MPK)(K) + [f(K,N)] (A)

Where:

1st term = additional labor productivity (i.e. additional output of the new labor)multiplied to the additional labor or population.2nd term = same idea, only that its capital.3rd term = output without technology multiplied to the introduction to newtechnology or an improved production method.

S3.) Divide everything by Y (Y/Y means growth rate of output.3).

Y/Y = (MPL/Y)(N) + (MPK/Y)(K) + [f(K,N)/Y] (A)

Simplifying, we can see that:4

Y/Y = (MPL/Y)(N) + (MPK/Y)(K) + (A)/A

Another trick: Add N/N = 1 in the 1st term and K/K = 1 in the 2nd term.5

Y/Y = [(MPL)(N)/(Y)] (N/N) + [(MPK)(K)/(Y)] (K/K) +(A)/A

S4.) If I pay labor (N), then MPL= w=wageIf I pay capital used (K), then MPK=c= capital payments

We can see that:

Y/Y = (wN/Y) (N/N) + (cK/Y) (K/K) + (A)A

3Recall that in order to get the growth rate of output, you need to do horizontal analysis: Present value- previous value and

divide everything by the previous value (i.e. Y/Y ).4

Note further:

Y = A[f(K,N)]

We can get:

f(K,N) = Y/A and A = Y/ [f(K,N)].5

This doesnt affect the equation at all because it is the same as multiplying the terms by 1. Thus, it is needless to add the same

expression on the Left-hand side (LHS) of the equation. A good question would be, w hy not add something to the 3rd

term? We

dont have to since it is a strong assumption in the Solow model that technological progress changes exogenously . This means

that, we have no control of it and so we take it as given.


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c3 solow model

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