It’s the 4th of July, and you need to decide how much money to spend on beer (b)
ID: 1137430 • Letter: I
Question
It’s the 4th of July, and you need to decide how much money to spend on beer (b) and how much to spend on fireworks (f). Beer and fireworks each have a unit price of $1, that is, $1 gets you one unit of either good. You have $50 to spend, and your utility function is u(f, b) = 10 sqrt(f) + b
Recall that for any constants C and D, the derivative of C sqrt(D + x) is C / (2 sqrt(D + x)).
Suppose you are spending the holiday alone.
(i) How much money will you choose to spend on fireworks, and how much on beer? (Since more of everything is better, your budget constraint will hold with equality, or f + b = 50; one way to solve this, then, is to plug in 50 – f for b, and find the value of f that maximizes u(f, 50 – f).)
(ii) What is the efficient amount for you to spend on fireworks, and the efficient amount for you to spend on beer?
Explanation / Answer
i) max 10F^(1/2)+B
max 10F^(1/2)+50-F
Derive- 5(F^1/2)+1
5*F^(1/2)=1
F=$25
One will spend $25 on fireworks and $25 on beer
ii) The efficient amount to spend on fireworks and beer is also $25 to $25 because only one person is involved and there is no externality so that private benefits and cost are same as social benefits and cost.
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