Question

Qs=20r + 100p

Qd= 4000 - 100p + 10i

Using the supply and demand equations above, explain in words how equilibrium quantity changes with an increase in income.

Answer 1

Answer

Equilibrium occurs at that level of price at which Quantity demand = quantity supplies i.e. Qs = Qd

Hence Qs = Qd

=> 20r + 100p = 4000 - 100p + 10i

=> p = 20 - 0.1r + 0.05i

Putting it in Qs we get

Q* =  20r + 100p =  20r + 100(20 - 0.1r + 0.05i)

=> Q* = 20r + 2000 - 10r + 5i

=> Q* = 10r + 2000 + 5i

$Hence, \frac{\partial Q^*}{\partial i} = 5$

So, When income increases Demand will shift to the right and as calculated above Equilibrium quantity will increase by 5 units if we increase income by 1 unit.