Chapter 2 Consumer Equilibrium Solutions
Question - 1 : - What do you mean by the budget set of a consumer?
Answer - 1 : -
It refers to the set of consumption bundles that are available to or affordable by the consumer; while being aware of his/her income-level and the existing market prices.
Question - 2 : - What is a budget line?
Answer - 2 : -
A budget line represents the different combinations of two goods that are affordable and are available to a consumer; while being aware of his/her income-level and market prices of both the goods.
Let x1 be the amount of good 1.
x2 be the amount of good 2.
P1 be the price of good 1.
P2 be the price of good 2.
P1x1 = Total money spent on good 1
P1x2 = Total money spent on good 2
Then, the budget line will be:
P1x1 + P2x2 = M
All the consumption bundles on the budget line cost the consumer exactly the equivalent of hi/her income.
Question - 3 : - Explain why the budget line is downward sloping.
Answer - 3 : -
The budget line is a negatively downward sloping line. The slope of a budget line measures the amount of good 2 that must be sacrificed in order to get an additional unit of good 1, as the consumer’s income (M) is fixed. The budget line is downward sloping because, in order to increase the consumption of one good, the consumption of the other good must be reduced, with constant M.
The slope of the budget line is
, which implies the rate of exchange or the rate at which good 2 can be substituted for good 1.
Question - 4 : - A consumer wants to consume two goods. The prices of the two goods are Rs 4 and Rs 5 respectively. The consumer’s income is Rs 20.
Answer - 4 : -
(i) Write down the equation of the budget line.
(ii) How much of good 1 can the consumer consume if he/she spends his/her entire income on that good?
(iii) How much of good 2 can be consumed if he/she spends his/her entire income on that good?
(iv) What is the slope of the budget line?
Answer
(i) P1 =Rs 4
P2 = Rs 5
M = Rs 20
Equation of the budget line = P1x1 + P2x2 = M
4x1 + 5x2=20
(ii) If Rs 20 is entirely spent on good 1, then the amountof good 2 demanded will be zero i.e., x2 =0 as the consumer has no income left to spend on good 2.
4x1 + 5 (0) = 20
4x1 = 20
Amount of good 1 consumed = 5 units
(iii) If Rs 20 is entirely spent on good 2, then x1 = 0, as the consumer has no income left to spend ongood 1.
4(0) + 5(x2) = 20
5(x2) = 20
Amount of good 2 consumed = 4 units
(iv) Slope of the budget line = 
How does the budget line change if the consumer’s income increases to Rs 40 but the prices remain unchanged?
Answer - 5 : -
M2 = Rs40
P1 = Rs 4
P2 = Rs 5
Initial equation of the budget line:
4x1 + 5x2 = 20
New equation of the budget line:
4x1 + 5x2 = 40
As M hasincreased, the consumer can now purchase more of both the goods and the budgetline will shift parallelly outwards to A’B’ from AB.
Horizontal intercept will be 
Vertical intercept will be 
The slope of the new budget line will be the same as thatof the old budget line.
Question - 6 : - How does the budget line change if the price of good 2 decreases by a rupee but the price of good 1 and the consumer’s income remain unchanged?
Answer - 6 : -
P1 = Rs4
P2 = Rs 5
M = Rs20
Since the income and the price of good 1 areunchanged, the decrease in the price of good 2 will increase the verticalintercept of the budget line. The new budget line will also pivot outwardsaround the same horizontal intercept.
Horizontal intercept
Vertical intercept
Slope 
The slope of the new budget line will be more and the newbudget line will be steeper than the original one.
Question - 7 : - What happens to the budget set if the prices as well as the income double?
Answer - 7 : -
Ifthe prices and the income are doubled, then the budget line will remainunchanged.
| M1 = Rs 20 |
| P1 = Rs 4 |
| P2 = Rs 5
| M2 = Rs 40 |  = Rs 8
|  = Rs 10
Horizontal intercept Vertical intercept Slope  Hence,the vertical intercept, the horizontal intercept and the slope of the budgetline will remain the same. The new budget line will be the same as the oldbudget line but associated with higher income and higher prices of both thegoods. | |
Question - 8 : - Suppose a consumer can afford to buy 6 units of good 1 and 8 units of good 2 if he/she spends her entire income. The prices of two goods are Rs 6 and Rs 8. How much is the consumer’s income?
Answer - 8 : -
P1 = Rs6 P2 = Rs 8
x1 = 6 x2 = 8
Budget line = M = P1x1 + P2x2
M = 6 × 6 + 8 × 8
M = 36 + 64
M = 100
Thus, the consumer’s income is Rs 100.
Question - 9 : - Suppose a consumer wants to consume two goods that are available only in integer units. The two goods are equally priced at Rs 10 and the consumer’s income is Rs 40.
Answer - 9 : -
(i) Write down all the bundles that are available to the consumer.
(ii) Among the bundles that are available to a consumer, identify those that cost will him/her exactly Rs 40.
Answer
(i) P1 = Rs 10
P2 = Rs 10
M = Rs 40
Budget set ⇒ P1x1 + P2x2 ≤ M
10x1 + 10x2 ≤ 40
The bundles that areavailable to the consumer should cost less than or equal to Rs 40.
Horizontal intercept 
Vertical intercept
Slope 
The bundles in the shadedregion (ΔAOB) are all available to the consumer, including the bundles lying onthe line AB.
| (0, 0) | (0, 1) | (0, 2) | (0, 3) | (0, 4) |
| (1, 0) | (1, 1) | (1, 2) | (1, 3) | (1, 4) |
| (2, 0) | (2, 1) | (2, 2) | (2, 3) | (2, 4) |
| (3, 0) | (3, 1) | (3, 2) | (3, 3) | (3, 4) |
| (4, 0) | (4, 1) | (4, 2) | (4, 3) | (4, 4) |
(ii) The coordinates thatlie on the line AB cost exactly the same as the income of the consumer. Thebundles are as follows:
(0,4), (1, 3), (2, 2), (3, 1), (4, 0)
Question - 10 : - What do you mean by monotonic preferences?
Answer - 10 : -
It means that the consumer prefers a particular bundle over the other bundle if the former consists of at least more of one good and no less of the other good.
Example:
If bundle A(3, 5) and bundle B(3, 2) are available to the consumer, then he/she will prefer bundle A over bundle B as bundle A consists of more units of good 2 than bundle B.