Question

Klaus cares only about how much he can write. Because a pen will write 7 miles of text and a pencil will write 35 miles of text, Klaus considers them perfect 5-to-1 substitutes. The price of pens is given by P_pen, and the price of pencils is given by P_pencil, and if Klaus's income is given by Y, use indifference curve analysis to derive the demand curve for pencils.

Answer 1

Klaus cares only about how much he can write so that. pen that write 7 miles of text and a pencil that write 35 miles of text, are perfect substitutes so that MUPencil = 5 x MUPen. This also implies that MUPencil/MUPen = 5.

At the optimal choice for perfect substitutes we know that

• If MUPencil/MUPen > Ppencil/Ppen, only Pencil is consumed. This implies when Ppencil/Ppen < 5 or Ppencil < 5Pen, QPencil = M/Ppencil where Y is the income.
• If MUPencil/MUPen < Ppencil/Ppen, only Pen is consumed. This implies when Ppencil/Ppen > 5 or Ppencil > 5Pen, QPencil = 0
• If MUPencil/MUPen = Ppencil/Ppen, Consumer is indifferent between Pens and Pencil. This implies when Ppencil/Ppen = 5 or Ppencil = 5Pen, QPencil = infinite.