Question

Suppose the supply curve for a product is given by the equation QS = 1000 + P, where price P is measured in dollars and quantity Q is measured in number of units.

1. Now suppose that the demand curve is given by the equation QD = 9000 - P - 0.05I, where I is income measured in dollars. If income is $100,000, what is the current equilibrium price and quantity?

2. Suppose that income falls from $100,000 to $80,000. Now what would be the equation for the demand?

3. What will be the new equilibrium price and quantity after the income decrease?

4. Explain what type of good is the product given the change in consumption after a change in income, use a partial derivative to answer the question.

Answer 1

QS = 1000 + P

QD = 9000 - P - 0.05I

If I = $100,000

QD = 4000-P

1. Equiliribrium occurs when quantity supplied equals quantity demanded

4000-P =1000+P

or, P =3000/2 ;

Therefore equilirium prices and quantities are:

P_e= 1500 , Q_e = 2500

2. If I becomes $ 80000

QD' = 9000 - P- 0.05*80000

= 5000- P

3. New equilibrium QD'=QS

5000 - P = 1000+P

or P_e' = 3000 ; Q_e' = 3000+1000 = 4000

4.

The product mentioned here is an inferior good because its consumption goes up when income falls.