Question

1. Suppose the relationship between Demand for good x (Qx) can be described by the following linear relationship (Py: price of good y, I = income):

Qx= 120 – 6Px + 5Py + 3 I

1. From the demand relationship above, you can conclude: Goods X and Y are substitute/complementary goods because_______________________, and a decrease in Py would cause quantity demanded/demand of Good X to increase/decrease.
2. Suppose Py = $5 per unit, and I = $10, and Px = $20. At these prices and income, and the income elasticity of demand is equal to _______ and cross price elasticity of demand is equal to _______.
3. Good X is a normal/inferior good. If income increases by 5%, the demand/quantity demanded for Good X will increase/decrease by ______. (Use your answer in (b) and show computations
4. Assume the prices and income as given in (b) above. The price elasticity of demand is equal to ____ and the demand for good X is elastic/inelastic?
5. Use the computed the elasticity in (d) to answer: How would a decrease in the price of X affect expenditure (revenu on good X, other things constant.

Answer 1

a) dQx/dPy = 5 > 0

So as Py rises , Qx rises, so two are Substitutes

Would cause demand of Good X to increase

b) Qx = 120-6*20+5*5+3*10

= 120-120+25+30

= 55

Income Elasticity of Demand = (I/Qx)*(dQx/dI)

= (10/55)*(3)

= 30/55

= .545

Cross price Elasticity of Demand = (Py/Qx)*(dQx/dPy)

= (5/55*(5)

= 5/11

C) good X is Normal good

as Income rises, Qx rises

If income rises by 5% , demand will increase by

2.72%

( 5*.54)%

D) price Elasticity of Demand: (Px/Qx)*(dQx/dPx)

= (20/55)*(-6)

= -2.18

As |e| > 1 , so Elastic

e) if Px falls, expenditure rises , bcoz demand is Elastic