Claudio Audio has $1000 which he can spend on either CD players or CDs. He cannot...

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?

Solutions

Expert Solution

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

Rahul Sunny answered 2 years ago

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