Lecture 17
General Equilibrium: Production Economy (part I)
Microeconomic Theory II (2008)
By Kornkarun Kungpanidchakul Ph,D.
Robinson Crusoe Economy
Consider what we call Robinson Crusoe Economy. This is the case of one
consumer lives in the isolated islands. He has to make the decision about his
consumption and production by himself.
Pareto Optimal
Since there is only one person here, Robinson Crusoe, the pareto optimal
allocation is the choice of times he allocates to work (or leisure) and the amount of
coconuts he consume. His objective function becomes:
Max U (C , L )
s.t. C  f ( L)
Then the pareto optimal allocation is such that:
U f ( L) U

0
C L
L
f ( L)
U / L

or MRT = MRS
L
U / C
Coconuts
Indifference curve
y*
Production function
MRSc ,  f ( )
*
24
Labour
Market Equilibrium
To make things simpler, we will separate his production and consumption
decision as if it comes from different agents.
Production
Robinson Crusoe as a firm has to make decision how many labors (amount of
time) he should employ and how many coconuts he should collect (produce). The
objective is to maximize profit. Normalize the price of coconuts to $1. (Coconuts are
numeraire goods).
of  * .
  f ( L)  wL
The first order condition is:
f ( L )
 w or MPL = wage
L
At the optimal level :
 *  C * wL *
So we can draw the iso profit line which has the slope of w and the y-intercept
Consumption
Consumption
Isoprofit
Isoprofit
3
2
1
y*
Isoprofit:
y
 w
*
p
Labour
*
24
Consumer Side
Robinson Crusoe as a consumer has to decide how much he wants to consume
and how much he wants to work (or rest). He has the endowment equal to  * , the
profit of his firm. Then his objective as a consumer is to maximize his utility s.t. the
budget constraint.
Max U (C , L )
s.t. C    wL
The first order condition becomes:
U / L

 w or MRS = price ratio.
U / C
Consumption
Indifference
curve
y*
*
24 Labour
Market equilibrium
Combine the production and consumption side together to get the market
equilibrium, we will have the equilibrium is such that MRS = MRT = wage, which is
the pareto optimal allocation as well.
Coconuts
Indifference
curve
y*
Isoprofit = budget line
Production function
MRSc ,
*
w
 f ( ) 
p
24
Labour