Question

Initially the price of good Xis $2 and the price of good Yis $1.  Income is $100 per unit of time.  Income decreases from $100 per unit of time to $50 per unit of time.  Yis 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 Xaffected?

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 Yaffected?

f.  Accounting for both the income and substitution effects, how is the utility maximizing quantity of Xaffected?

Answer 1

a. Slope of the budget line = -Price of good X/Price of good Y = -2/1 = -2. So, it remains same with change in income.

b. No, there is no substitution effect as substitution effect shows change in quantity demanded due to change in relative prices. Relative prices remains same as only income is changing so the utility maximizing quantity of good X ix not affected due to the substitution effect.

c. X intercept of the budget line = Income/Price of good X
When income = $100, X intercept = 100/2 = 50
When income = $50, X intercept = 50/2 = 25
So, X intercept decreases from 50 to 25 with decrease in income.

d. Y intercept of the budget line = Income/Price of good Y
When income = $100, Y intercept = 100/1 = 100
When income = $50, Y intercept = 50/1 = 50
So, Y intercept decreases from 100 to 5o with decrease in income.

e. Income effect is change in consumption due to change in real income. So, as income decreases, real income decline and thus the utility maximizing quantity of good Y increases because quantity demanded of inferior good increases with decrease in income.

f. The utility maximizing quantity of X decreases because of income effect because X is a normal good so its quantity demanded decreases with decrease in real income and it does not change because of substitution effect. Thus, the utility maximizing quantity of X decline.