Answer to Question #221185 in Microeconomics for Vickie

Question

Suppose that the consumer has a demand function of the milk from X1=10+(m/10p1) originally his income was 120 per week and the price of milk was 3 per unit
What is the demand of the milk per week suppose that the price of milk falls 22 pioneer what is the demand at his new price of milk per week what is the total change in demand in a week
Calculate the substitution effect and income effect after this change in price

Answer 1

Evaluating the Substitution Effect.

m = $120,

p1 = $3 per unit

Demand

$x1 = 10 + m/10p1 .$

The demand for milk is (10 + 120/(10*3) = 14 units per week

If the prices falls to p2 = $2 per unit. The demand for milk is;

10 + 120/(10*2) = 16 units per week

Substitution Effect = Incomes required to keep the purchasing power consistent.

$m' =m+Δm = m +x1 Δp1=120+14*(2-3) =106$

The substitution effect is therefore;

$Δx1s=x1(p1',m')-x1(p1,m)$

$x1(2,106)-x1(3,120) = 1.3$

Income Effect.

This refers to the change demand caused by a shift.

Constant prices (p1',m')

$Δx1n = x1(p1',m)-x1(p1',m)$

The income effect is therefore negative for normal goods and positive for inferior goods. In a nutshell, the rise in prices reduces the income which in turn reduces the demand for the commodities.