Tina is very particular about her purchases: she only buys hot dogs and soda, an

Question

Tina is very particular about her purchases: she only buys hot dogs and soda, and every time she makes a purchase she buys exactly three hot dogs and soda. She would never buy three hot dogs without a soda, and would never buys a soda without three hot dogs.

1. Come up with at utility function that describes Tina's preferences

2. If a hot dog costs 2 dollars and a soda costs 3 dollars what is her optimal bundle of soda and hot dogs if she has an income of 63 dollars

3. Find her demand function for hot dogs and her demand function for sodas

Explanation / Answer

1. Let the number of hot dogs bought by Tina be x and number of sodas be y. Here, hot dogs and soda are perfect complements as Tina always consumes 3 hot dogs with 1 soda. The utility function for preferences is given as

u(x,y) = min{x, 3y}

As you can see. 3 goes goes in front of the number of sodas. This is because, intuitively speaking, each soda is thrice as valuable as a hot dog.

b. The budget constraint for sodas and hot dogs is given as,

pxx + pyy = m

Where,px is price of a hotdog and  py is price of a soda.

and m is the income.

now, x=3y, we know that Tina always consumes 3 hot dogs with 1 soda.

px =2 and py =3

m=63

Now, 2(3y)+3y=63

9y=63

y=7

x=21

3. The budget constraint is given as, px(3y) + pyy = m

y(3px +py)=m

so, demand function for y= m/(3px +py)

as we know, x=3y

demand function for x=3m/(3px +py)

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