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Chapter Two
2. A basic model
The
following model is used to demonstrate an approach to the analysis of regional
impacts from implementing economic reforms.
The model
represents just two regions producing two products. Product X is the
only output of region 1, and product Y is the only output of region 2.
Each of the regions is represented by just one aggregate regional consumer. The
aggregate consumer of each region consumes some part of the region’s
product. Another part of the region’s product is used for exchange with
the other region. As in most classical trade models, we exclude transaction
costs.
Each region
consists of perfectly competitive firms and there is no problem of aggregation
of the firms’ production functions into one industry function. Thus, the
production function for each of the two regions can be represented as:
 (2.1)
 (2.2)
Supply of
both commodities is represented as increasing functions of prices
 and
 :
 (2.3)
 (2.4)
The
quantity demanded for the product of both sectors/regions
 and
 depends upon prices for both
products and
as well as upon the level of
income of the aggregate consumer:
 (2.5)
 . (2.6)
It is
assumed that there is no income apart from the wages of employees
 and
 in both sectors, and that the
wage rates  and
 are constant:
 . (2.7)
The
assumption about constant wage rates is not conventional in the traditional
microeconomic analysis. However, it simplifies the model and also reflects the
non-flexibility of wages as found in the majority of developed nations current
industrial relations environment, especially in the short run.
We will be
using the model for comparative static analysis. Such an analysis assists in
answering the question, how changes in some exogenous variables and/or
structural parameters lead to changes in output, relative prices, income
distribution and welfare. We will interpret economic reforms as a change either
in structural parameters, or exogenous variables, or both.
A
conventional technique will be used to transform the model (2.1)-(2.7) in terms
of log-derivatives representing small relative changes. If all the production,
supply, demand and income functions involved in the model (2.1)-(2.7) are
assumed as differentiable and homogenous, then they can be rewritten in the
following form:
 , (2.8)
 , (2.9)
where
 ,
 ,
 ,
 >0 are constant factor
elasticities of outputs X and Y;
 , (2.10)
 , (2.11)
where
 ,
 >0 are price elasticities of
supply;
 , (2.12)
 , (2.13)
where
 , <0 are price elasticities of demand,
 , >0 are cross price elasticises of demand, and , >0 are income elasticises of demand;
 ; (2.14)
where
 and
 .
This form
of the model will be used for further analysis. Meanwhile, try to do the
following exercises using the differential form of the model – equations
(2.8) – (2.14):
- Modify the model to
reflect an increase in internal efficiency in one of the
industries/regions.
- The federal income tax
is raised or lowered. Which equation and/or structural parameter absorbs this
change in governmental policy?
- Use the model to show
the introduction of an
excise tax
on commodity X produced in region 1.
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