Income and Substitution Effects

Pat consumes only playing cards ((3) and Videotapes (v) . His preferences can be represented by the following utility function: u(c, v) = 2 - ln(c) + v The price of a unit of playing cards is pc, the price of videotapes is 10v7 and Pat has an income of Y dollars. Pat can consume fractional, but not negative, amounts of cards and Videotapes. 1. (6 points) Suppose that prices are pC = 1, p1, = 10 and income Y = 50. Calculate numerically his demand. 2. (6 points) Now suppose that the price of Videotapes increases to pv = 30. How many cards and Videotapes will he buy now? 3. (12 points) How much of the drop in demand for videotapes is due to the substitution effect and how much is due to the income effect? Calculate this numerically and graphically show the income and substitution effects using budget constraints and indifference curves