Inferior goods are those low quality goods whose demand generally decreases with increase in income of the consumer. For Example: Bajara, jaggery, etc.
Normal goods are those goods whose demand generally increases with increase in income of the consumer. For example: rice, when income of a consumer increases,he/she will demand more of rice.
It means that a rational consumer always prefers a combination having more of both the commodities as it offers him a higher level of satisfaction.
Or
A consumer’s preferences are called monotonic preferences when between any two bundles, he/she prefers the bundle which has more of at least one of the goods and no less of the other good compared to the other bundle.
In this situation, the budget set will remain the same because prices and income have changed in the same ratio.
Budget line is downward sloping because if a consumer wants to have more of one commodity he has to buy less of another commodity, given his limited income.
The budget set is a collection of all bundles of commodities that a consumer can purchase at market price with his income. A consumer has fixed income and he has to allocate his income to such bundle of commodities from which he can get the maximum satisfaction.
Since the expenditure on the good increases only by 2% in response of decrease in price of a good by 4%, the quantity demanded for the good will also increase by less than 4%, this implies it is a case of inelastic demand, 0< Ed< 1.
Here we are give price elasticity of demand Ed = -0.2. Since Ed is less than 1, it is the case of inelastic demand. If there is a 10 % increase in the price of the good, it will lead to less than 10% fall in the quantity demanded of the good; hence there will be rise in total expenditure.
Given
Price elasticity of demand, E_{d}= –0.2
Percentage change in price = 5%
By putting the given values in the formula we get,
⇒ % change in quantity demand = –0.5 × 5= | –1.0 |
⇒ % change in quantity demand = 1%
Therefore if there is a 5% increase in the price of the good, the demand for the good goes down by 1%.
Let Q = 10 – 3p
P = 5/3
Putting the value of P in Q we get
Q = 10 – 3 × 5/3
Q = 5
By differentiating Q with respect to P we get,
Now we know that elasticity of demand is calculated by the following formula
⇒ Ed = –3 × 5/3 × 1/5 = | –1 | = 1
⇒ Hence, the price elasticity of demand at price 5/3 is unity.
Given,
Q1 = 25, P1 = 4
Q2 = 20, P2 = 5
ΔQ = 5
ΔP = 1
The formula for calculating price elasticity of demand :
Pitting the value in the formula, we get,
Hence price elasticity of demand is less than unity.
Elasticity of demand represents the quantitative effect of change in price of the commodity on its quantity demanded. It is defined as the "degree of responsiveness of quantity demanded for the commodity to any change in price of the commodity". It can be estimated as the ratio of percentage or proportionate change in quantity demanded to the percentage or proportionate change in price of the commodity; i.e.
Where,
E_{d} = coefficient of price elasticity of demand
ΔP = change in price; ΔQ = change in quantity demanded; P = Original price and Q = Original quantity
Complements may be defined as the goods which are used together to satisfy a given want. The examples of goods which are complements of each other are pen and ink, car and petrol etc.
Substitutes refers to those goods which can be used in place of each other or in other words they are substitutes of each other. For example tea and coffee, gel pen and ball pen, etc.
p | d_{1} | d_{2} |
1 | 9 | 24 |
2 | 8 | 20 |
3 | 7 | 18 |
4 | 6 | 16 |
5 | 7 | 14 |
6 | 4 | 12 |
The market demand (dm) for the good at each price is calculated by adding up the demands of the two consumers at each price
p |
d_{1} |
d_{2} |
dm=d_{1} +d_{2} |
1 2 3 4 5 6 |
9 8 7 6 5 4 |
24 20 18 16 14 12 |
33 28 25 22 19 16 |
Given,
Number of consumers = 20
Identical demand function
d(p) = 10 – 3p ….. for P ≤ 10/3
d_{1}(p) = 0….. for P > 10/3
For price less than equal to 10/3 the market demand function is calculated by multiplying the demand function by 20
⇒ dm(p) = 20(10 – 3 p)
⇒ dm(p) = 200 – 60p
And for all prices above 10/3, the market demand function is written as:
⇒ dm = 0
No, if my friend is indifferent to the bundles (5, 6) and (6, 6), her preferences are not monotonic.
If a consumer has monotonic preference, she will always prefer the bundle which has more of at least one of the goods and no less of the other good compared to the other bundle.
If she had monotonic preference, she would have preferred bundle (6, 6) to the bundle (5, 6).
If a consumer has monotonic preference, she will always prefer the bundle which has more of at least one of the goods and no less of the other good compared to the other bundle.
Accordingly her ranking for the given bundles is as follows:
1^{st} Rank = (10, 10)
2^{nd} Rank = (10, 9)
3^{rd} Rank = (9, 9)
Bundle (10, 10) is monotonically preferred over bundles (10, 9) and (9, 9) and bundle (10, 9) is monotonically preferred to the bundle (9, 9).
No, if a consumer has monotonic preference,she can never be indifferent between two bundles (10,8) and (8,6). She will always prefer the bundle which has more of at least one of the goods and no less of the other good compared to the other bundle. In this case that bundle is (10, 8),she will prefer it over the bundle (8, 6) as it has more of both the goods as compared to the other bundle.
(i) Let good 1 be X and good 2 be Y and Consumer’s income be M
Give P_{X} = P_{Y} = ₹ 10
Consumer’s income, M = ₹ 40
Bundles available to consumers are:
(0,4), (4,0), (1,3),(3,1), (2,2),(0,0), (0,1), (0,2), (0,3), (1,0), (2,0), (3,0), (1,1), (1,2), (2,1).
(ii) Among the bundles that are available to the consumer those which cost her exactly ₹ 40 are:
(0,4), (4,0), (1,3),(3,1), (2,2)
Let good 1 be X and good 2 be Y and Consumer’s income be M
Given,
Px = 6
Py = 8
Equation of budget line is written as:
P_{X} . X + P_{Y} . Y = M
Putting the values in equation we get,
⇒ 6 × 6 + 8 × 8 = M
⇒ M = 36 + 64 = 100
Hence consumer’s income is ₹100.
If price of good 2 decreases by a rupee but the price of good 1 and the consumer’s income remain unchanged, consumer can buy more of good 2. The new budget line equation will become:
4X + 4Y = 20.
In this case the budget line AB will pivot at point B and rotates upward to A_{1}B.
If consumer’s income increases to ₹ 40 with no change in prices, the consumer can consume more of both goods.
In this case the budget line AB will shift parallel to the right to A_{1}B_{1}.
Equation of new budget line is written as:
P_{X} . X + P_{Y} . Y = M2
Or
4X + 5Y = 40.
The budget line represents all the commodities which a consumer can purchase with his entire income. Let us have two commodities X and Y. Their respective prices are P_{X} and P_{Y}. The entire income of the consumer is ₹100. The budget line can be written as follows:
P_{1}x + P_{2}Y =100
d_{1}(p) = 20 – p …… for p ≤ 20………….(let it be eq 1)
d_{1}(p) = 0 ………….. for p > 20
d_{2}(p) = 30 – 2p …… for p ≤ 15………….(let it be eq 2)
d_{2}(p) = 0 ………….. for p > 15
For price less than equal to 15 the market demand function is calculated by adding eq 1 and eq2
⇒ dm(p) = 50 – 3 p
For price greater than 15 but less than or equal to 20, the market demand function is written as:
⇒ dm(p) = 20 – p
And for all prices above 20 ,the market demand function is written as:
⇒ dm = 0
(i) Let the two goods be X and Y
Given,
Price of good X, P_{X} = ₹ 4
Price of good Y, P_{Y} = ₹ 5
Consumer’s income, M = ₹ 20
Equation of budget line is written as:
P_{X}. X + P_{Y}. Y = M
Or
4X + 5Y = 20.
(ii) If the consumer spends his entire income of good 1 i.e. good X, it means quantity demanded of good Y = 0
New budget equation: 4X + 5 × Zero = M
⇒ 4X + 5 × 0 = 20
⇒ 4X = 20
⇒ X = 20/4
⇒ X = 5 units
This implies,if the consumer spends his entire income of good X he can consume 5 units of that good.
(iii) If the consumer spends his entire income of good 2 i.e. good Y, it means quantity demanded of good X = 0
New budget equation: 4 x Zero + 5Y = M
⇒ 5Y=20
⇒ Y= 20/5
⇒ Y= 4 units
This implies,if the consumer spends his entire income of good Y he can consume 4 units of that good.
(iv) Slope of budget line = P_{X}/P_{Y}
= 4/5 = 0.8.
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