Assume that Professor Forehead\'s preferences for jars of peanut butter (good x1

Question

Assume that Professor Forehead's preferences for jars of peanut butter (good x1) and jars of jelly (good x2) are represented by u(x1, x2) = min{2x1, x2} Assume further that p1 =1.4, p2=0.3, m=$26. What is his optimal consumption plan? Suppose now that p1 decreases to 1. Find his new optimal bundle. What the size of the substitution effect on jars of peanut butter, when p1 decreases from $1.4 to $1? What is the size of the income effect on peanut butter? What is the size of the substitution effect on jars of jelly, when p1 decreases from $1.4 to $1? What is the size of the income effect on jelly?

Explanation / Answer

u = Min {2x1, x2}

Budget line equation: M = x1 Px1 + x2 Px2

26 = 1.4x1 + 0.3x2

(a)

Here, the goods are perfect complements and therefore the optimal condition, MRS = p1 / p2 does not hold.

Optimal consumption bundle is when 2x1 = x2

Substituting in budget line,

26 = 1.4x1 + 0.3x2

26 = 1.4x1 + 0.3 x 2x1 = 2x1

x1 = 13

x2 = 2x1 = 26

(b) now, p1 = 1

substituting in budget line:

26 = x1 + 0.3x2

26 = x1 + 0.3 x (2x1) = 1.6x1

x1 = 26 / 1.6 = 16.25

x2 = 2x1 = 32.5

(c)

When p1 decreased from 1.4 to 1, x1 increased from 13 to 16.25.

Substitution effect when two goods are perfect complements, is zero because the goods are always consumed in conjunction.

For good x1 (peanut butter):

Total effect (x1) = 16.25 – 13 = 3.25

Income effect = Total effect – Substitution effect = 3.25 – 0 = 3.25

(d) As seen in previous parts, when p1 decreases from 1.4 to 1, x2 increases from 26 to 32.5.

So, for good x2 (jelly):

Total effect = 32.5 - 26 = 6.5

Substitution effect = 0 (since x1, x2 are perfect complements)

Income effect = Total effect – Substitution effect = 6.5 – 0 = 6.5

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