A consumer has a demand function for good 1: Where p_1 and p_2 are respective pr

Question

A consumer has a demand function for good 1: Where p_1 and p_2 are respective prices of goodl and good2 and m is the income, Show whether good 1 is a (gross) substitute or a (gross) compement for good 2.The initial values of variables are: m = 100, p_1 = 4,p_2 = 5. What is the original optimal consumption? The price of good one increases to p'_1= 5 What is the income that would make the original consumption of both go new the prices? What is the Slutsky substitution effect of the price change? What is the Slutsky income effect of the price change? show that the Slutsky equation holds.

Explanation / Answer

Multiple questions asked.

First 4 subparts are answered below.

a)

As it can be seen from the demand equation, an increase in p2 will increase x1.

That is, when price of good 2 increases, demand for good 1 increases. This implies that the goods are substitutes.

b)

Plug in the given values in demand equation to find the current consumption bundle x1

Original consumption: 10 + (m/2p1) + 2p2

X1 = 10 + (100/8) + 2(5)

x1* = 32.5 units

c)

First we will find p2x2 which = m-p1x1 = 100-(32.5×4) = -30

In order to find the new income (M’), the original bundle should be affordable, at new price. That is,

x1p1’+x2p2=m’

(32.50×5)+(-30)=m’

M’ = 132.50 (new income)

d)

New consumption bundle after price change: X1’ = 10 + (132.50/10) + 2(5) = 23.25 units

Thus, slutsky substitution of price change = x1* - x1’ = 32.5 – 23.25 = 9.25 units.

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