Question #63291

Using two goods X1 and X2 with their respective prices and , where both goods are normal goods. If the price of good X1 decreased from to , Using a clearly labeled diagram, explain and identify using either Hicksain approach or Slutsky approach the:-
i. Total change in demand for X
ii. Substitution effect
iii. Income effect

Expert's answer

If The demand function face by the consumer for good X is given by X = 25 + MP^(-1)/10, then:

X(P,M) = X(20, 6400) = 25 + (6400 * 1/20)/10 = 57 units per day,

X(P,M) = X(40, 6400) = 25 + (6400 * 1/40)/10 = 47 units per day,

Total change = reduced 10 units of good X per day

∆M = X1∆P1 =57(40 - 20) = 1140

M’ = M + ∆M

6400 + 1140 = 7540

X(P’1M’) = X(40, 7540) = 25 + (7540 * 1/40)/10 = 43.85 - Substitution effect.

∆Xs1 = X(P’1M’) – X(P1M)

Income efect:

X(P’1M) = X(40,6400) = 47,

X(P1M) = X(40,7540) = 43.85

Thus: Total effect ∆Xn1 = X1(40,6400) – X1(40,7540) = 47 – 43.85 = 3.15

X(P,M) = X(20, 6400) = 25 + (6400 * 1/20)/10 = 57 units per day,

X(P,M) = X(40, 6400) = 25 + (6400 * 1/40)/10 = 47 units per day,

Total change = reduced 10 units of good X per day

∆M = X1∆P1 =57(40 - 20) = 1140

M’ = M + ∆M

6400 + 1140 = 7540

X(P’1M’) = X(40, 7540) = 25 + (7540 * 1/40)/10 = 43.85 - Substitution effect.

∆Xs1 = X(P’1M’) – X(P1M)

Income efect:

X(P’1M) = X(40,6400) = 47,

X(P1M) = X(40,7540) = 43.85

Thus: Total effect ∆Xn1 = X1(40,6400) – X1(40,7540) = 47 – 43.85 = 3.15

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