In: Economics
Claudio Audio has $1000 which he can spend on either CD players
or CDs. He
cannot play his CDs without the CD player, but additional CD
players don't make him any
happier, since he can listen to only one at a time. CD players cost
$400 each; and CDs cost $10
each.
a. Write down the equation for Claudio's budget line.
b. Describe in words and math Claudio’s consumer problem.
c. Sketch in Claudio's indifference curves, with CD players on the
horizontal axis.
d. Can you figure out from the information given what the
equilibrium will be?
a) Income is 1000. Prices are PCDP = 400 and PCD = 10
Budget line is M = CDP*PCDP + PCD*CD
1000 = 400CDP + 10CD
b) Claudio is willing to maximize his utility given the budget constraint
In mathematical terms this implies
Max U = min (CDP, CD) s.t 1000 = 400CDP + 10CD
c) Indifference curves are L-shaped with kink occurring at CD = CDP
d) Note that 1000 = 400CDP + 10CD
1000 = 400*CDP + 10CDP
CDP = CD = 1000/410 or 100/41
Hence CDP and CD both are 100/41