Imagine that you consume only two goods: bagels and coffee. Our utility function is characterized by

U(Qc,Qb)=Qc^025*Qb^0.75

The price of bagels is $5 and the price of coffee is $2 and your income is $1,000

i. Find out our initial consumption bundle and the utility it provides.

ii. What share of your income do you spend on each good?

iii. One day you wake up to the horrible news that the price of coffee increased to $3. What is the new optimal consumption bundle?

iv. Your mom is concerned with your ability to focus and wants to give you enough money so you can afford your original level of consumption at the new prices. How much money should your mom give you?

v. Your dad is upset that your mom will give you too much money and instead he wants to give you enough money to preserve your utility. Finding the substitution bundle, find out how much money your dad will give you.

vi. Who do you love more?

vii. Graph this scenario. Make sure to include the 2 budget constraints that reflect the amounts received from each paren.