economic essay

ariel857

session_7.pdf

Home >Business & Finance homework help >Economics homework help >economic essay

SESSION 7 25TH JANUARY 20

INTRODUCTION TO

ECONOMIC GROWTH

SOMASRI MUKHOPADHYAY

• Model in terms of Mathematics/Statistics • Model in the context of this course in Economics

Solow Model: The Basic Question

Solving the Model

Mathematical Model Finding the Values

of the Variables

In the Present Context of ECON333

We try to find out the Factors behind Growth

The Three Basic Equations • Y= f(L,K) • dK/dt = sY - ΩK

Model • Set of Equations

Describing Relationship Among “Endogenous” Variables

• Endogenous Vis-à-vis • Parameters and • Exogenous Variable

1000

2000

3000

4000

5000

6000

1960 1961 1962 1963 1964 1965 1966 1967 1968 1969

G D

P P

er C

ap ita

a t C

ur re

nt U

D S

Axis Title

Chart Title

Canada France United Kingdom Japan Korea, Rep. United States World Singapore Hong Kong SAR, China

Select Economies During 1960s

1000

2000

3000

4000

5000

6000

1960 1961 1962 1963 1964 1965 1966 1967 1968 1969

G D

P P

er C

ap ita

a t C

ur re

nt U

D S

Axis Title

Chart Title

Canada France United Kingdom Japan Korea, Rep. United States World Singapore Hong Kong SAR, China

Select Economies During 1960s

1000

2000

3000

4000

5000

6000

Canada France United Kingdom

Japan Korea, Rep. United States

World Singapore Hong Kong SAR, China

G D

P P

er C

ap ita

a t C

ur re

nt U

D S

Axis Title

Chart Title

1960 1961 1962 1963 1964 1965 1966 1967 1968 1969

Select Economies During 1960s

Solow Model : Understanding the Equations

• The Production Function � Y = f(L,K)

= kα L1-α

� Cobb-douglas Production Function Exhibiting constant Returns to Scale

• Assumptions � Large Number of firms in the Economy

�Perfect Competition Prevails �Firms are Price Takers

� Profit Maximisation Problem for the Frim is as under � Y = kα L1-α - wL-rK

�w = Wage paid per unit of labour �r = Rent paid per unit of capital �Price of output normalised to unity.

• Profit Maximisation Requires � MPL = w � MPK = r

�Firms will employ Labour and Capital to the level where the respective per unit contribution to output equals their remuneration

� Also, � w = (1-α) Y/L � r = α (Y/K)

� And, thus, � (wL)/Y = (1-α) � (rK)/Y = α

Solow Model : Understanding the Equations

• The Factor Shares are Constant over time

• Fact 5 of chapter 1

• Y = kα L1-α • Y/L = (kα L1-α ) / L • y = kα

• y = Y/L • k = K/L

• Rewriting the Production Function in terms of Output Per worker – as we are interested in knowing the factors affecting output per capita

Solow Model : Understanding the Equations

There is Enormous Variation in Per-Capita Income across Economies

Rates of Economic Growth Vary substantially Across Countries

Growth Rates are not Generally constant over time.

A country’s Relative Position in the World distribution of Per Capita Incomes is not immutable

USA Data …….

Growth in “output” and growth in International Trade are closely related

Solow Model : Understanding the Equations

y y = Kα

Output per worker = Y/L= y Capital per worker = K/L = k

• Per-capita Output As A Function Of Capital Labour Ratio

• With More Capital Per Worker Firms Produce More Output Per Worker

• Capital Accumulation is the addition of Capital during a period over and above the previous period. �K (t+1) – K (t)

�dK/dt = sY - ΩK • Thus …. Not Equal to the Gross Savings of an economy

during one particular period • Rewriting the Capital Accumulation Equation to suit our

need of analysing per capita growth…… �(1/y)dy/dt = α (1/k)dk/dt

Solow Model : Understanding the Equations

• Assumption: Labour force Participation Rate is Constant ¾ If Population Grows at the rate n, labour force participation

will also grow at the rate n. ¾ (1/L)dL/dt = n

• Assumption: n = .01 ¾ Population and thus labour force grows annually by 1 per

cent. ¾ Labour grows at an exponential rate n

¾L(t) = L0ent

¾(1/L)dL/dt = n

Solow Model : Understanding the Equations Refer Back – Capital was not the only factor……..

• Assumption: Labour force Participation Rate is Constant ¾ If Population Grows at the rate n, labour force participation

will also grow at the rate n. ¾ (1/L)dL/dt = n

• Assumption: n = .01 ¾ Population and thus labour force grows annually by 1 per

cent. ¾ Labour grows at an exponential rate n

¾L(t) = L0ent

¾(1/L)dL/dt = n

Solow Model : Understanding the Equations Refer Back – Capital was not the only factor……..

• dk/dt = sy – (Ω + n)k

Solow Model : Understanding the Equations

• Increase in Population by n • Depreciation of Capital by Ω Erodes away the Capita Per worker, which is technically the Capital Labour Ratio

• Obtaining Values of the Endogenous Variables with given values of Parameters and Exogenous Variables

• The two Basic Equations of solow Model are – y = (k)α

– dK/dt = sy – (n+Ω)K

Solving the Solow Model

The Basic Solow Diagram

The Basic Solow Diagram Solow Diagram with the Production Function