A consumer wishes to purchase commodities. Price of good 1 Rs.2 and th...
**Budget Line Equations:**
The budget line equations represent the different combinations of goods that a consumer can afford to purchase given their income and the prices of the goods. In this case, the consumer wants to purchase two goods, good 1 and good 2, with prices of Rs. 2 and Rs. 4 respectively.
Let's assume the consumer's income is denoted by Y and the quantities of good 1 and good 2 are denoted by Q1 and Q2 respectively.
The budget line equation can be written as:
**Q1 * P1 + Q2 * P2 = Y**
Substituting the values:
**Q1 * 2 + Q2 * 4 = 20**
**Slope of the Budget Line:**
The slope of the budget line represents the rate at which the consumer can trade one good for another while staying within their budget constraint. The slope is calculated as the ratio of the prices of the two goods.
In this case, the slope of the budget line can be calculated as:
**Slope = -P1 / P2 = -2 / 4 = -0.5**
The negative sign indicates that as the consumer increases the quantity of good 1, they will have to reduce the quantity of good 2 to stay within their budget constraint.
**Budget Set:**
The budget set represents the set of all feasible combinations of goods that the consumer can purchase given their budget constraint. In this case, the budget set will depend on the consumer's income and the prices of the goods.
To determine the budget set, we can rearrange the budget line equation to solve for Q2:
**Q2 = (Y - Q1 * P1) / P2**
Substituting the values:
**Q2 = (20 - 2Q1) / 4**
The budget set will be the range of values for Q1 and Q2 that satisfy the budget line equation and are non-negative.
**Drawing the Budget Line:**
To draw the budget line, we can plot the quantities of good 1 on the x-axis and the quantities of good 2 on the y-axis. The intercepts on the x and y-axis can be determined by setting Q1 or Q2 equal to zero in the budget line equation.
When Q1 = 0, the budget line equation becomes:
**Q2 * P2 = Y**
**Q2 = Y / P2 = 20 / 4 = 5**
When Q2 = 0, the budget line equation becomes:
**Q1 * P1 = Y**
**Q1 = Y / P1 = 20 / 2 = 10**
Plotting these intercepts and connecting them with a straight line gives us the budget line.
**Effect of Increased Income:**
If the income of the consumer increases from Rs. 20 to Rs. 40, the budget line will shift outward parallel to the original budget line. This is because the consumer now has more purchasing power and can afford higher quantities of both goods.
The new budget line equation becomes:
**2Q1 + 4Q2 = 40**
The slope of the new budget line remains the same (-0.5), but the intercepts on the x and y-axis increase. This means that the consumer can now afford a greater range of combinations of goods.
The budget set will expand, allowing the consumer to choose from a
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