Exercise 2 Income Changes (Quasilinear) Chocolate is definitely not considered an essential good, and being a small portion of overall income, its consumption does not particularly affect your overall budget It definitely has diminishing marginal utility, as the intake of the tenth chocolate bar is less appetizing than the first you eat You have a quasilinear utility, u x 1 x 2 , where x 1 is consumption of chocolate and x 2 is consumption of everything else a)A unit of chocolate costs 50 cents (p 1 0 5) and the price of everything else is normalized to 1 (p 2 1) Given your budget constraint, m x 1 p 1 x 2 p 2 , derive the demand function for chocolate and for everything else (income, m, is a variable) b)Draw the budget constraints and optimal indifference curves for m 100, m' 200 and m'' 300 Draw the income offer curve c)In two separate graphs illustrate the two Engel curves given the three income levels in part b d)Take the derivative with respect to m of both demand curves x 1 (m) m and x 2 (m) m Are the derivatives positive or negative Are x 1 and x 2 inferior or normal goods e)What is the share of expenditure in goods (p 1 x 1 m), and the share of expenditure in services (p 2 x 2 m) How does it vary with the increase in m Are these luxury or necessary goods

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Exercise 2. Income Changes (Quasilinear) Chocolate is definitely not considered an essential good, and being a small portion of overall income, its consumption does not

Exercise 2. Income Changes (Quasilinear)

Chocolate is definitely not considered an essential good, and being a small portion of overall income, its consumption does not particularly affect your overall budget. It definitely has diminishing marginal utility, as the intake of the tenth chocolate bar is less appetizing than the first you eat. You have a quasilinear utility, u = x₁ + x₂, where x₁ is consumption of chocolate and x₂ is consumption of everything else.

a)A unit of chocolate costs 50 cents (p₁=0.5) and the price of everything else is normalized to 1 (p₂=1). Given your budget constraint, m = x₁p₁ + x₂p₂, derive the demand function for chocolate and for everything else (income, m, is a variable).

b)Draw the budget constraints and optimal indifference curves for m=100, m'=200 and m''=300. Draw the income offer curve.

c)In two separate graphs illustrate the two Engel curves given the three income levels in part b.

d)Take the derivative with respect to m of both demand curves: x₁(m)/m and x₂(m)/m. Are the derivatives positive or negative? Are x₁ and x₂ inferior or normal goods?

e)What is the share of expenditure in goods (p₁x₁/m), and the share of expenditure in services (p₂x₂/m)? How does it vary with the increase in m? Are these luxury or necessary goods?