CBSE Class 12 Economics Chapter 2: Consumer Equilibrium NCERT Solutions

The budget set represents all the possible combinations or bundles of goods that a consumer can afford to purchase given their available income and the prevailing market prices of those goods. It includes all bundles whose total expenditure is less than or equal to the consumer's income.

A budget line is a graphical representation that illustrates all the possible combinations of two goods that a consumer can purchase by spending their entire income at the given market prices. It is also referred to as the consumption possibility line.

The budget line is downward sloping because it represents the trade-off between two goods. If a consumer wishes to purchase more units of one good, they must reduce their consumption of the other good to stay within their budget constraint (i.e., spend their entire income). This inverse relationship between the quantities of the two goods is depicted by the negative slope.

Let the quantity of good 1 be X and the quantity of good 2 be Y. The price of good 1 (Px) is Rs 4, the price of good 2 (Py) is Rs 5, and the consumer's income (M) is Rs 20.

1. The equation of the budget line is given by $Px\; \backslash cdot\; X\; +\; Py\; \backslash cdot\; Y\; =\; M$. Substituting the given values, the equation is $4X\; +\; 5Y\; =\; 20$.
2. If the consumer spends her entire income on good 1, the quantity of good 2 consumed (Y) will be 0. The equation becomes $4X\; +\; 5(0)\; =\; 20$, which simplifies to $4X\; =\; 20$. Solving for X, we get $X\; =\; \backslash frac\{20\}\{4\}\; =\; 5$ units.
3. If the consumer spends her entire income on good 2, the quantity of good 1 consumed (X) will be 0. The equation becomes $4(0)\; +\; 5Y\; =\; 20$, which simplifies to $5Y\; =\; 20$. Solving for Y, we get $Y\; =\; \backslash frac\{20\}\{5\}\; =\; 4$ units.
4. The slope of the budget line is the ratio of the price of good 1 to the price of good 2, which is $\backslash frac\{Px\}\{Py\}$. Substituting the given prices, the slope is $\backslash frac\{4\}\{5\}\; =\; 0.8$.

If the consumer's income increases to Rs 40 while the prices of both goods (Px = Rs 4, Py = Rs 5) remain unchanged, the consumer can now afford to buy more of both goods. The budget line will shift parallel outwards from the original line. For example, the maximum quantity of good 1 she can buy becomes $\backslash frac\{40\}\{4\}\; =\; 10$ units, and the maximum quantity of good 2 becomes $\backslash frac\{40\}\{5\}\; =\; 8$ units. The new budget line equation is $4X\; +\; 5Y\; =\; 40$.

The original price of good 2 (Py) was Rs 5. If it decreases by a rupee, the new price becomes Rs 4. The price of good 1 (Px = Rs 4) and income (M = Rs 20) remain unchanged. The original budget line had intercepts at X=5 and Y=4. With the new price of good 2, the intercept on the Y-axis (quantity of good 2) becomes $\backslash frac\{M\}\{Py\_\{new\}\}\; =\; \backslash frac\{20\}\{4\}\; =\; 5$ units. The intercept on the X-axis (quantity of good 1) remains $\backslash frac\{M\}\{Px\}\; =\; \backslash frac\{20\}\{4\}\; =\; 5$ units. Therefore, the budget line AB will pivot upwards around point B (the x-intercept), rotating to a new line A1B, indicating that the consumer can now afford more of good 2.

If both the prices of the goods and the consumer's income double, the budget set and the budget line remain unchanged. Let's illustrate with the given example: Original prices Px = Rs 4, Py = Rs 5, and Income M = Rs 20. If prices and income double, the new prices become Px' = Rs 8, Py' = Rs 10, and the new income M' = Rs 40. The equation of the new budget line is $8X\; +\; 10Y\; =\; 40$. Dividing the entire equation by 2, we get $4X\; +\; 5Y\; =\; 20$, which is the same as the original budget line equation. The intercepts on both axes remain the same ($X\; =\; \backslash frac\{40\}\{8\}\; =\; 5$ and $Y\; =\; \backslash frac\{40\}\{10\}\; =\; 4$), and the slope ($\backslash frac\{Px\}\{Py\}\; =\; \backslash frac\{8\}\{10\}\; =\; \backslash frac\{4\}\{5\}$) also remains the same. Thus, the budget set and budget line do not change.

Let good 1 be represented by X and good 2 by Y. We are given that the consumer can afford to buy X = 6 units and Y = 8 units. The price of good 1 (Px) is Rs 6, and the price of good 2 (Py) is Rs 8. The budget line equation is $Px\; \backslash cdot\; X\; +\; Py\; \backslash cdot\; Y\; =\; M$. Substituting the given values: $$(6)\; \backslash cdot\; (6)\; +\; (8)\; \backslash cdot\; (8)\; =\; M$$ $$36\; +\; 64\; =\; M$$ $$100\; =\; M$$ Therefore, the consumer's income is Rs 100.