Consumer's Equilibrium - Basic
In order to get the fair idea about this topic we need to understand some basic things associated with this topic.
Marginal Utility of a good -: It is always diminishing. Law of diminishing MU will operate. This law states when a
consumer consumes more and more amount of a good, he derives less and less satisfaction from the consumption of
successive units.
Marginal Utility of Money -: This is assumed to be constant. If a consumer gets satisfaction worth 4 utils from one
rupee, he will get satisfaction worth 400 utils from Rs 100/-.
Marginal Utility of a good in terms of Money (MUx tm)-: This is the ratio of Marginal utility of a good to MU of
money. It is just conversion of Marginal utility of a good in to money. It means how much money is required to buy the
given utility.
Suppose Utility of one rupee = 4 utils
Suppose a consumer is consuming a chocolate and getting satisfaction equals to 100 utils. Then utility of how much
money is equal to 100 utils. off course rupees 25/MUxtm = MUx/MUm
= 100/4 = 25/Where MUx is marginal utility of a good x
MUm is marginal utility of money
MUxtm is marginal utility of a good in terms of money.
Utility per Ruppee -: It is the ratio of Marginal Utility of a good to price of that good.
Utility per rupee = MUx/ Px
Where MUx is marginal utility of a good x
Px is price of good x.
Posted by Arun sharma at 1:54 AM
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Labels: 5.Consumer's Equilibrium
Consumer's Equilibrium - Single Commodity Case
A consumer is said to be in equilibrium when he is maximising his satisfaction.
In case of single commodity the consumer is in equilibrium when marginal utility of a good in terms of money becomes
equal to the price of that good.
MUx= Px
..........................................
where MUx = MUx/MUm
Condition of equilibrium
Suppose MUm is 1 utils and price of commodity is Rs 4.
UNITS
MUx
MUm
MU in terms of
money
(MUx/MUm)
Price of good x
1
10
1
10
4
Gains
2
6
1
6
4
Gains
3
4
1
4
4
Eq
4
2
1
2
4
Loss
When a consumer is consuming one unit he is getting utility equals to 10 utils which is equal to 10 rupees. But he is
spending only 4 rupees. So the consumer is in gains. He will increase his consumption. when he is consuming
second unit he is getting satisfaction equals to rupees 6 but his expenditure on second unit is rupees 4 only. Again he
is in gains.He will increase his consumption.
At third unit his satisfaction is equal to rupees 4 and he is spending rupees 4 for this unit. He is in equilibrium.
At fourth unit he is in loss as price is more than the satisfaction he is getting from fourth unit. he will buy the fourth unit
only when the price of fourth unit is reduced to rupees 2.
So
MUxtm > Px Gains
MUxtm = Px Equilibrium
MUxtm < Px Loss
The condition in single commodity is
MUxtm = Px
or
MUx/MUm = Px
This can also be explained as
MUxtm = Px
or MUx/MUm = Px
(i)
or
MUx/Px = MUm
(ii)
The condition may also become -: when the utility per rupee of good x ( ratio of marginal utility of good x to its price)
becomes equal to utility of money for that consumer ,the consumer is said to be in equilibrium.
Q.1 Explain consumer's equilibrium in case of single commodity?
Q.2 Given the price of a commodity how does a consumer decide how many units of that good to buy?
Q. 3 Given the utility of money how does a consumer decide how many units of that good to buy?
Q.4 Explain the conditions of consumer's equilibrium in case of single commodity?
Hints 1. As explained above
2. by using MUxtm = Px
3. by using MUx/Px = MUm
4. by explaining
MUxtm > Px Gains
MUxtm = Px Equilibrium
MUxtm < Px Loss
Posted by Arun sharma at 1:24 AM
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Labels: 5.Consumer's Equilibrium
Consumer's Equilibrium - Two Commodity Case
The condition of Consumers Equilibrium in case of single commodity case is-: When marginal utility of a good in terms
of money becomes equal to price of that commodity.
Condition in case of good x -: MUxtm = Px
or
MUx/MUm= Px
Condition in case of good y-: : MUytm = Py
(i)
As we know MUxtm=MUx/MUm
or
MUy/MUm= Py
(ii)
Eq (i) can be written as MUx/Px = MUm and Eq (ii) can be written as MUy/Py = MUm
comparing both above
MUx/Px = MUy/Py = MUm
So in case of two commodities the consumer is said to be in equilibrium when the ratio of marginal utilities of both the
goods to their respective prices becomes equal to utility of a rupee.
MUx/Px denotes utility per rupee while consuming good x
MUy/Py denotes utility per rupee while consuming good y
We can also say that when utility per rupee from the last rupee spent on each good becomes equal the consumer
attains equilibrium.
If
MUx/Px > MUy/Py it means utility per rupee from consumption of good x is greater than utility per rupee from
consumption of good y.
The consumer should increase the consumption of good x and reduce the consumption of good y. By doing so the
utility per rupee from good x will decrease and utility per rupee from good y will increase and ultimately both become
equal. The consumer will attain equilibrium.
If
MUx/Px < MUy/Py it means utility per rupee from consumption of good x is less than utility per rupee from
consumption of good y.
The consumer should increase the consumption of good y and reduce the consumption of good x. By doing so the
utility per rupee from good y will decrease and utility per rupee from good x will increase and ultimately both become
equal. The consumer will attain equilibrium.
Hence in case of two commodities the consumer attains equilibrium when
MUx/Px = MUy/Py = MUm
Q.1 Explain consumer's equilibrium in case of two commodities using utility analysis.?
Q.2 Explain the conditions of consumers equilibrium in case of two commodities using utility analysis?
Q3. A consumer is consuming two goods and he is in equilibrium. Suppose the price of good y increases. How does
this affcet his consumption of both the goods. Explain?
Hints
1. Explained as above
2. Explained as above
3. when price will increase (means denominator will increase so the value of fraction will decrease) utility per rupee
will fall.
at Equilibrium MUx/Px = MUy/Py
but when price of y increases then MUx/Px > MUy/Py ( as utility per rupee of good y will fall).
Posted by Arun sharma at 12:37 AM
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Labels: 5.Consumer's Equilibrium
Sunday, May 31, 2015
Budget Set/ Budget Line Indifference curve Analysis
THERE ARE TWO GOODS GOOD 1 AND GOOD 2
PRICES OF TWO GOODS ARE P1 AND P2
QUANTITIES OF TWO GOODS CAN BE REPRESENTED BY X1 AND X2
INCOME OF THE CONSUMER IS M
ANY COMBINATION OF GOOD 1 AND GOOD 2 IS KNOWN AS BUNDLE.
(GOOD 1,GOOD 2) IN THE SAME WAY (1,2) (3,4) (5,4) (7,8) (4,3) ARE KNOWN AS BUNDLES.
BUDGET SET
IT COMPRISES OF SETS OF BUNDLES WHICH A CONSUMER CAN PURCHASE FROM HIS INCOME.
EQUATION FOR BUDGET SET
P1 X1 + P2 X2 <= M
BUDGET LINE
IT COMPRISES OF ALL THOSE BUNDLES WHICH COST THE CONSUMERS EXACTLY EQUAL TO HIS INCOME.
EQUATION FOR BUDGET LINE
P1 X1 + P2 X2 = M
IT CAN BE DRAWN WITH THE HELP OF HORIZONTAL INTERCEPT AND VERTICAL INTERCEPT.
HOROZONTAL INTERCEPT -: WHEN A CONSUMER SPENDS HIS ENTIRE INCOME ON THE PURCHASE OF GOOD
I.
M/ P1
VERTICAL INTERCEPT -: WHEN THE CONSUMER SPENDS HIS ENTIRE INCOME ON THE PURCHASE OF GOOD 2.
M/P2
•
SLOPE OF BUDGET LINE
BUDGET LINE IS DOWNWARD SLOPPING MEANS IN ORDER TO HAVE MORE OF ONE GOOD A CONSUMER HAS
TO GIVE UP SOME UNITS OF OTHER GOOD .
SLOPE OF BUDGET LINE DETERMINES BY HOW MUCH AMOUNT GOOD2 IS GIVEN UP IN ORDER TO HAVE ONE
MORE UNIT OF GOOD1.
SUPPOSE WE WANT TO INCREASE THE CONSUMPTION OF GOOD 1 BY ONE UNIT WE HAVE TO SPEND P1 AMOUNT MORE
AND SO , WE HAVE TO REDUCE CONSUMPTION ON GOOD 2 BY THIS P1 AMOUNT.
NOW HOW MANY UNITS OF GOOD 2 WE CAN PURCHASE FROM P1 ?
WE CAN PURCHASE
P1
UNITS FROM P1.
P2
NOW SUPPOSE PRICE (P1) OF GOOD 1 =RS 50
PRICE (P2) OF GOOD 2 =RS 20
MONOTONIC PREFERENCES
OUT OF GIVEN TWO BUNDLES A CONSUMER WILL ALWAYS PREFER THE BUNDLE WHICH HAS MORE OF AT
LEAST ONE GOOD AND THE OTHER GOOD MUST NOT BE DIMINISHING.
FOR EXAMPLE
(4,5)
&
(5,5)
(4,5)
&
(5,6)
BUT IN THIS CASE -:
(4,5)
&
(5,4) NO ?
MARGINAL RATE OF SUBSTITUTION
IN ORDER TO INCREASE THE CONSUMPTION OF GOOD1 BY ONE UNIT A CONSUMER HAS TO GIVE UP CERTAIN
UNITS OF GOOD2 .
OR
THE RATE AT WHICH CONSUMER SUBSTITUTE GOOD1 FOR GOOD2 IS KNOWN AS MARGINAL RATE OF
SUBSTITUTION.
DIMINISHING MARGINAL RATE OF SUBSTITUTION
THR RATE AT WHICH CONSUMER SUBSTITUTE ONE UNIT OF GOOD1 WITH GOOD2 DIMINISHES AS HE
INCRESES THE CONSUMPTION OF GOOD1.
 GOOD1
GOOD2
MRS

1
20
-

2
14
6

3
9
5

4
5
4

5
2
3
AMONG THESE BUNDLES (1,20) (2,14) (3,9) (4,5) AND (5,2)
THE CONSUMER WILL BE INDIFFERENT AS ONE GOOD IS INCREASING BUT OTHER IS DIMINISHING.ALL {EACH
OF} THESE BUNDLES (1,20) (2,14) (3,9) (4,5) AND (5,2) GIVES CONSUMER THE SAME LEVEL OF
SATISFACTION.
INDIFFERENCE CURVE REPRESENTS ALL THOSE BUNDLES AMONG WHICH A CONSUMER REMAINS
INDIFFERENT AND GETS THE SAME LEVEL OF SATISFACTION.
CONSUMER'S EQUILIBRIUM
A CONSUMER IS IN EQUILIBRIUM WHERE THE BUDGET LINE IS TANGENT TO THE INDIFFERENCE CURVE. IT
MEANS THE PREFERENCES OF CONSUMER MATCH WITH HIS PURCHASING POWER.
WHY SO ?
WHY NOT AT THE POINTS WHERE THE INDIFFERENCE CURVE INTERSECTS THE BUDGET LINE.
POINTS A,B & C LIES ON THE SAME INDIFFERENCE CURVE.THIS MEANS ALL THESE POINTS GIVES SAME
SATISFACTION TO CONSUMERS.THE EXPENDITURE ON BUNDLE A AND B IS EQUAL TO THE INCOME AS
THEY LIE ON BUDGET LINE. THE EXPENDITURE ON BUNDLE C COSTS LESS THAN INCOME AS THIS POINT
LIES BELOW THE BUDGET LINE.
NOW OUT OF A ,B &C WHAT THE CONSUMER WILL PREFER TO PURCHASE ?
OFF COURSE C AS IT COSTS LESS THAN A OR B.
BUT THE CONSUMERS WANTS TO SPEND HIS ENTIRE INCOME. SO THE CONSUMER WILL SHIFT TO
HIGHER INDIFFERENCE CURVE.
POINT D LIES ON HIGHER INDIFFERENCE CURVE AND IT ALSO COST EQUAL TO INCOME AS IT LIES ON
BUDGET LINE .
WHEN COMPARED WITH A AND B CONSUMER WILL PREFER D AS IT LIES ON
HIGHER INDIFFERENCE CURVE.
BUDGET LINE TANGENT TO IC CURVE
SLOPE OF INDIFFERENCE CURVE = SLOPE OF BUDGET LINE
MRSXY = PX/PY
SO WE CAN SAY THAT THE CONSUMER IS IN EQUILIBRIUM WHEN MARGINAL RATE OF SUBSTITUTION BETWEEN TWO GOODS
BECOME EQUAL TO PRICE RATIO OF THOSE TWO GOODS.
Posted by Arun sharma at 11:23 AM
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Labels: 18 Indifference curve, 5.Consumer's Equilibrium
Thursday, April 9, 2015
Utility analysis
Want satisfying power of a commodity is called Utility.
When you consume some thing it means you are getting some utility out of it.
To make understanding of the concept' utility is assumed to be measured in terms of numbers.The units of utility is
taken as utils. Utility can be measured cardinally.
So if somebody says to you that he has got 80 utils of satisfaction after watching a movie you should understand that
he is not joking.
Total Utility is the total psychological satisfaction a consumer obtains after consuming a particular amount of a good.
Marginal utility is net addition to total utility by consuming one more unit of the good.or Utility derived from the
consumption of successive units.
Units Total utility Marginal utility
1 ----------- 50 ---------------- 50
2 ----------- 96 ---------------- 46
or
Units Total utility Marginal utility
5 ------------- 120 ----------------- 6 ------------- 145 ----------------- 25