Question

Initially the price of good X is $4 and the price of good Y is $8. Income is $200 per unit of time. Income decreases from $200 per unit of time to $100 per unit of time. X is an inferior good.

a. What happens to the slope of the budget line?
b. Is there a substitution effect? If so, how is the utility maximizing quantity of good X affected?
c. What happens to the X-intercept of the budget line? (Be specific)
d. What happens to the Y-intercept of the budget line? (Be specific)
e. Is there an income effect? If so, how is the utility maximizing quantity of good X affected?
f. Accounting for both the income and substitution effects, how is the utility maximizing quantity of X affected?

Answer 1

Step-by-step explanation:

a. The slope of the budget line is determined by the relative prices of goods X and Y. Since the price of good X remains unchanged at $4, while the price of good Y remains unchanged at $8, the slope of the budget line remains constant.

b. Yes, there is a substitution effect. When the income decreases, consumers tend to substitute away from relatively more expensive goods towards relatively cheaper goods. In this case, since X is an inferior good, its demand decreases as income decreases. The utility-maximizing quantity of good X will be affected by the substitution effect, and it will decrease.

c. The X-intercept of the budget line represents the quantity of good X that can be purchased when all income is spent on good X, assuming its price remains constant. In this case, since the price of good X remains unchanged at $4 and the income decreases from $200 to $100, the X-intercept of the budget line will be halved. It will go from 50 units of good X (calculated as $200/$4) to 25 units of good X (calculated as $100/$4).

d. The Y-intercept of the budget line represents the quantity of good Y that can be purchased when all income is spent on good Y, assuming its price remains constant. Since the price of good Y remains unchanged at $8 and the income decreases from $200 to $100, the Y-intercept of the budget line will also be halved. It will go from 25 units of good Y (calculated as $200/$8) to 12.5 units of good Y (calculated as $100/$8).

e. Yes, there is an income effect. When income decreases, it affects the purchasing power of the consumer. In this case, the decrease in income from $200 to $100 will result in a negative income effect for an inferior good like X. The utility-maximizing quantity of good X will decrease due to the income effect.

f. Taking into account both the income and substitution effects, the utility-maximizing quantity of good X will decrease. The substitution effect leads to a decrease in the quantity of good X, as consumers substitute away from relatively more expensive goods. The income effect for an inferior good like X further decreases the quantity of good X as income decreases. Therefore, the utility-maximizing quantity of good X will be lower after considering both effects.