Question

4. Malachi only consumes 2 goods: DVD rentals and coffee. His utility function is U(R,C)=R0.4C0.6 where R is the number of DVD rentals and C is cups of coffee. Malachi has $30 in his pocket right now, and he plans to spend all of the money on rentals and coffee today. a. The price of one rental is $3 and the price of one cup of coffee is $2 per cup. Solve for the optimal bundle. b. Suppose that Malachi signs up for a membership that reduces the price of a rental to $2, while leaving his income unchanged. Find the substitution effect, the income effect and the total effect of the change in rental price on Malachi's consumption of coffee and rentals. Based on the answer above, are DVD rentals and coffee normal goods or inferior goods 10 Malachi?

Answer 1

A-4) UIR, c) = (R) x (cor R- DVD Rental M2 $30. - Coffee. a PR2 & 3, le 2 &2. Budget : Rx Pe + cx fc 2 M constraint straint 3R + 20 = 30. This is the case of Cobb Douglas production function, thus, x M = 0.4 x 30 = 0.4x300 - 4 write 0.6to.4 3 cda = 0.6 x 30 = 0.6x15= 9 units. Leß orto.4 2 2 B New Rdz 0.4 x 30 - 0.4x301 6 unite. I Thus, Total effect = 6-42 2 unit. Oma 4x el-pe) = 4X(2-3) = -4 ure m'e M - 4= 30-42 $26. Rd" = 0.4x 26 = 5.2 write (Demand at new income and new Thus, price level) substitution effect = 5.2-4 = 1.2 units. Freome effect = 6-5.22 0.8 units since the demand for both DVD Rentals and coffee is to related positively Goods are income end, thus, both Normal goods.