Emerta A. Aragie; November 2023; Addis Ababa, Ethiopia. Constrained Multiplier Analysis

1. Emerta A. Aragie
November 2023
Addis Ababa, Ethiopia
Constrained Multiplier Analysis

2. Dropping a key assumption
• The three assumptions
• Unconstrained multipliers assume that factor resources are unlimited or
unconstrained
• such that any increase in demand is matched by increased supply.
• We now drop this assumption by preventing/constraining changes in some
sectors’ production levels.
• This is true in the case of resource constrained activities such as agric, mining
and govt services.
• For the sectors with constrained supply, it is net exports that now decline
when demand increases
• (i.e., imports increase to replace any shortfall in domestic production).

3. Constrained multiplier formula (1)
• Earlier, we derived the following demand equations
• We now distinguish between supply unconstrained (Z1), and those with
supply constraints (Z2).
• Previously exogenous components of demand are now treated as endogenous
(E2) (i.e., net exports will now be able to change if domestic production
cannot).
• As with the unconstrained multiplier formula, we group exogenous
components onto the right-hand side…
( ) ( )
11 1 1 1 1 1 12 2 1 2 2 2 1
1-a b -c v b Z -a b -c v b Z =E
+
( ) ( )
21 1 2 1 1 1 22 2 2 2 2 2 2
-a b -c v b Z 1-a b -c v b Z E
+ =
( ) ( )
11 1 1 1 1 1 1 12 2 1 2 2 2
1-a b -c v b Z =E a b c v b Z
+ +
( ) ( )
21 1 2 1 1 1 2 22 2 2 2 2 2
-a b -c v b Z E 1-a b -c v b Z
- = -

4. Constrained multiplier formula (2)
• The equation above can be expressed in matrix format…
• The first term on the left-hand side is the identity matrix (I) minus an
adjusted coefficient matrix (M*). We will call the first term on the right-
hand side the B-matrix.
• Finally, by rearranging terms, we arrive at the constrained multiplier
formula.…

5. Constrained Multiplier Model → Exercise 5 (Task 5)
Complete “Task 5 Worksheet.xls” in the
“Exercises” folder. The solution file is in the
“Solutions” sub-folder.
Task 5:
Constructing a Constrained Multiplier
Model
• Activity: Calculate constrained multipliers
• Translate the mathematical equations presented above into Excel
• Use the MINVERSE and MMULT Excel functions
• Answer the questions in red at the bottom of the worksheet
• Interpret the multipliers