Question

2. Suppose that Bob has $200 budget to spend on hotdogs and soda. Hotdogs are $4 each and soda are $2 each. If Bob’s utility function is u= 5h^.4 x s^.6 then calculate the quantity of hotdogs and soda that Bob needs to buy in order maximize his utility.

Answer 1

Maximise Utility : 5h^0.4s^0.6, subject to constraint 4h + 2s <= 200

For maximisation of utility , we know

=   =

=> 4s = 12h

=> s=3h

Also, since both the goods are normal goods, therefore the budget constraint with hold with equality in equilibrium. Therefore, 4h + 2s = 200 in equilibrium and since s=2h

• 4h + 2*3h = 200
• 10h=200
• h=20 and hence s=60