Economic Equilibrium Modeling with GAMS

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Good
Y
Agent
A
Figure 7. The Edgeworth-Bowley Box
` is the value share of leisure (Shl),
LEIS is the benchmark demand for leisure,
LSUP is the benchmark supply of labor, and
is the compensated labor supply elasticity.
Ay’
Bx’
*
Ax’
E
Endowment
Good
X
5. The Pure Exchange Model
Partial equilibrium analysis forms the basis of most economics courses at the undergraduate
level. In these models we focus on price, supply and demand for a single commodity.
The partial equilibrium approach neglects indirect e ects, through which changes in the
demand or supply for one good may in uence the market for another good.
In the previous section, we focused on the choices of a single consumer. In the present
section, we will explore the implications of interactions between many consumers with
heterogeneous preferences. Furthermore, the analysis will explore the potentially important
interaction between market prices and income which are determined jointly in a general
equilibrium.
The most widely-used graphical framework for multi-agent exchange equilibrium analysis
is the Edgeworth-Bowley box as illustrated in Figure 7. In this diagram we model the
following economy:
Two types of consumers, denoted A and B. We consider A and H to each represent
many households, each with the same endowments and preferences. (This assumption
justi es an assumption of perfectly competitive, price-taking behavior.) There are two
commodities in the model, denoted x and y Each consumer has xed endowments of both
goods. The horizontal axis measures the total world endowment of good x. The vertical
axis measure the total world endowment ofgoody. Anypointinthebox then represents
an allocation of goods between the two agents. The agent H allocation is measured with
respect to the lower left origin. The agent F allocation is measured with respect to the
upper right origin.
Each agent has a given initial endowment, here denoted point E. Furthermore, we
assume that there is no possibility for trade. The indi erence curves through point E
therefore represent autarchy welfare levels.
Agent
B
By’