# Analyzing the given demand functions

1. Using the following equation, what is the demand equation as a function of Ps if the price of other pastas (Po) is $2, the individual's income (Y) in thousands is $25, and tastes (Z) are represented by 20? What happens if the individual's income increases to $30?

Qd= 500 - 10Ps + 5Po + 20Y +40Z

2. Given the regression estimate of the demand equation of

Qx = 1,000 - 3.3Px + 0.001Y

where Y is income, what is the change in demand if price rises by $1, holding income constant? What is the percentage change in demand if price rises by $1 from an initial price of Px = $200 given Y = 10,000? What is the effect on demand of a $1 increase in income, holding price constant?

3. Consider the estimate demand equation of

Qx = 1,000 -3.3Px -0.2Pz + 0.001Y

(3.5) (2.1) (0.5)

with t values in parenthesis, where Pz is the price of another good Z, and Y is income. Is good Z a substitute or a complement? Can we say confidently whether good X is a normal good or an inferior good?

#### Solution Preview

1. Using the following equation, what is the demand equation as a function of Ps if the price of other pastas (Po) is $2, the individual's income (Y) in thousands is $25, and tastes (Z) are represented by 20? What happens if the individual's income increases to $30?

Qd= 500 - 10Ps + 5Po + 20Y +40Z

Put Po=$2, Y=$25, Z=20

Qd=500-10Ps+5*2+20*25+40*20=1810-10Ps

In the first case, demand equation will be given by

Qd=1810-10Ps

Now let us assume that individual income rises to $30 thousands. Then

Qd=500-10Ps+5*2+20*30+40*20=1910-10Ps

Demand equation will change to

Qd=1910-10Ps

Change in demand=(1910-10Ps)-(1810-10Ps)=100 ...

#### Solution Summary

Solutions study the variations in demand due to changes in income.