Question

You have an income of $40 to spend on two goods. Good 1 costs $10 per unit, and Good 2 costs $5 per unit.

1. Write down your budget equation

2. If you spent all your income on good 1, how much could you buy?

3. If you spent all your income on good 2, how much could you buy?

4. Draw a budget line in a graph, with good 1 on the x-axis and good 2 on the y-axis.

5. Suppose the price of good 1 falls to $5 while everything else stays the same. Write down your new budget equation. On the graph above, draw your new budget line.

6. Suppose the amount you are allowed to spend falls to $30, while the prices of both goods remain at $5. Write down your budget equation. Draw this budget line on the same graph. Label each line.

7. On your diagram, shade in the area representing good bundles that you can afford with the budget in part 6), but could not afford in part 1). Use another color of ink to shade the area that you could afford with budget in part 1) bud cannot afford with budget in part 6). Label the area properly

Answer 1

Given - income (I) is $40, price of good1 () is $10 and price of good 2 () is $5, for x represents good1 and its quantity and y represents good2 and its quantity.

1. The budget constraint equation can be written as , as for is amount of income spent to purchase x units of good1 and is amount of income spent to purchase y units of good2, and both are summed up and equated to income I, showing that all the purchases in total, exhaust the income. In this case, the budget equation is .

Note: If assume that the income is not 'necessarily' exhausted, the budget equation can be written as , shouwing that all the purchase of the goods are within the income, and some income might be left after the purchase.

2. Price of good1 is dollar, and income is $40. The maximum number of good1 that can be purchased is , if all income is used to spent good1.

3. Price of good2 is dollar, and income is $40. The maximum number of good2 that can be purchased is , if all income is used to spent good2.

4.

As can bee seen, the budget line connects the maximum amount of respective goods that can be bought with given income.

5. If the new is $5 instead of $10, the maximum amount of good1 that can be bought is . Hence, the budget line would connect that point. The new budget equation is hence .

6. Suppose I falls to $30, instead of being $40. The new budget equation is hence .

BL1 is budget line as part 1, while BL2 is budget line as price of good1 falls in part 5, and BL3 is the budget line with fall in income in this part.

7. The shaded diagram is as below.

The BL1, BL2 and BL3 are as mentioned in part 6.

The green area represents the bundles that could be purchased in part 1's BL1 but not in part 6's BL3. The yellow area represents the bundles that could be purchased in part 6's BL3 but not in part 1's BL1.