Marginal Rate of Substitution
• MRS is the number of units of good Y that must be given up in exchange for an extra unit
X so that consumer can maintain the same level of satisfaction.
The value of marginal rate of substitution diminishes as X increase.
Assume
Utility function is represented by U=ƒ(X, Y)
dU dU
Total differentiation of this function du= dy + dx
dY dx
We know that along an indifference curve there is no change in utility du=0
dU dU
du= dy + dx=0
dY dx
dU dy=−dU dx
dy dx
dU dU
÷ dx
dy dx
dy =−dx
dU dU
÷ dx
dy dx
−dx −dy
=
dy dx
dU
=MUy
dy
dU
=MUx
dx
MUy −dy
= =MRS
MUx dx
MAXIMIZATION OF UTILITY/SATISFACTION (ORDINAL THEORY)
- Consumer theory behaviour and demand are built on the assumption that an individual
makes choices so as to maximize utility.
-The consumer arranges his/her purchases so as to maximize utility subject to his money
income constrain.
32
, This means that we can easily determine one’s demand curve.
Limited Money Income
• Assuming that the consumer buys X1 of commodity X and Y1 of commodity Y at prices
Px and Py respectively. Assume that he has limited income which he can spend (B). This
B is acting as a constrain to consumer’s attempt to maximize his/her utility and is known
as the budget constrain/income constrain.
B ≥ PX + Py Y PxX + PyY < B
If we solve for Y we can represent income constrain graphically
B = PX + Py Y
PyY = B – Px X
B Px
Y= − X
Py Py
1 Px
B− X
Py Py
The budget line equation
Good Y
Budget line
Py Py
Good X
The slope of the budget line is the derivate of the budget line equation with respect to X.
Y= B – Px XB Px
−dy −Px
=
dx Py
It is the negative of the price ratio of the two commodities.
Example
If the price of X is 20sh and price of Y is 10sh and income available for the expenditure of two
commodities is 100 sh.
33
, Required:
1. Write the budget constrain
2. Find the budget equation
3. Draw the budget line and the slope
Solution
1. B≥P xX +PyY
1000=20x+10y budget constraint
2. 1000- 20X = 10y
10y = 1000 - 20x
(Y =1000 − 20 X)
10 10
y = 100 - 2x budget lines equations
We know along the indifference curve there is no change in utility
3. If X= 0 Y=100
If Y =0 X=50
100
Budget line
(Y=100- 2X)
50
Y = 100 – 2x
dy
=−2 = (differentiation)
dx
Px 20
= =−2
Py 10
THE BUDGET LINE
It is a locus of points of commodity combination that can be bought if the entire income of the
consumer is spent.
Budget Space
Is asset of all commodity combination that may be purchased by spending some or all of a given
money income.
Good Y
Budget line
Budget
Space 34
Downloaded by Kawa Products (kawahproduGco
t so
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X ail.com)
• MRS is the number of units of good Y that must be given up in exchange for an extra unit
X so that consumer can maintain the same level of satisfaction.
The value of marginal rate of substitution diminishes as X increase.
Assume
Utility function is represented by U=ƒ(X, Y)
dU dU
Total differentiation of this function du= dy + dx
dY dx
We know that along an indifference curve there is no change in utility du=0
dU dU
du= dy + dx=0
dY dx
dU dy=−dU dx
dy dx
dU dU
÷ dx
dy dx
dy =−dx
dU dU
÷ dx
dy dx
−dx −dy
=
dy dx
dU
=MUy
dy
dU
=MUx
dx
MUy −dy
= =MRS
MUx dx
MAXIMIZATION OF UTILITY/SATISFACTION (ORDINAL THEORY)
- Consumer theory behaviour and demand are built on the assumption that an individual
makes choices so as to maximize utility.
-The consumer arranges his/her purchases so as to maximize utility subject to his money
income constrain.
32
, This means that we can easily determine one’s demand curve.
Limited Money Income
• Assuming that the consumer buys X1 of commodity X and Y1 of commodity Y at prices
Px and Py respectively. Assume that he has limited income which he can spend (B). This
B is acting as a constrain to consumer’s attempt to maximize his/her utility and is known
as the budget constrain/income constrain.
B ≥ PX + Py Y PxX + PyY < B
If we solve for Y we can represent income constrain graphically
B = PX + Py Y
PyY = B – Px X
B Px
Y= − X
Py Py
1 Px
B− X
Py Py
The budget line equation
Good Y
Budget line
Py Py
Good X
The slope of the budget line is the derivate of the budget line equation with respect to X.
Y= B – Px XB Px
−dy −Px
=
dx Py
It is the negative of the price ratio of the two commodities.
Example
If the price of X is 20sh and price of Y is 10sh and income available for the expenditure of two
commodities is 100 sh.
33
, Required:
1. Write the budget constrain
2. Find the budget equation
3. Draw the budget line and the slope
Solution
1. B≥P xX +PyY
1000=20x+10y budget constraint
2. 1000- 20X = 10y
10y = 1000 - 20x
(Y =1000 − 20 X)
10 10
y = 100 - 2x budget lines equations
We know along the indifference curve there is no change in utility
3. If X= 0 Y=100
If Y =0 X=50
100
Budget line
(Y=100- 2X)
50
Y = 100 – 2x
dy
=−2 = (differentiation)
dx
Px 20
= =−2
Py 10
THE BUDGET LINE
It is a locus of points of commodity combination that can be bought if the entire income of the
consumer is spent.
Budget Space
Is asset of all commodity combination that may be purchased by spending some or all of a given
money income.
Good Y
Budget line
Budget
Space 34
Downloaded by Kawa Products (kawahproduGco
t so
@dgm
X ail.com)
