Question

Jaydon’s utility is estimated to be U(q1,q2)=20q1^0.5q2^0.5. Jaydon has an income of 500, p₁ = 10, and p₂ = 20. Suppose the price of good 2 decreased to 10, while p₁ and income remain the same. Find the values of the total effect, the substitution effect, and the income effect of the change in p₂ on the demand of good 1 and good 2.

Answer 1

Using marshellian std demand fn

q1 = a/a+b *m/p1

q2=b/a+b *m/p2

where a and b are powers attached to q1 and q2

q1 = 0.5/0.5+0.5 * m/p1 = 0.5* 500/10 = 25

q2 = 0.5/0.5+0.5 *m/p2 = 0.5* 500/20 = 12.5

now we we calculate m' ( orginal bundles with new prices)

m' = 25*10 + 12.5*10 = 375

now using above formulas for q1 and q2 at m' at new prices

q2'' = 0.5 *375/10 = 18.75

now finally calculating q2 at m and new price

q2' = 0.5* 500/10 = 25

T.e = q2' - q2 = 25 - 12.5 = 12.5

s.e = q2'' - q2 = 18.75 - 12.5 = 6.25

i.e = t.e - s.e = 12.5 - 6.25 = 6.25