Malachi only consumes 2 goods: DVD rentals and coffee. His utility function is
U(R,C) = R0.75C0.25
where R is the number of rentals and C is cups of coffee. Malachi has $16 in his pocket right now, and he plans to spend all of the $16 on DVD rentals and coffee today.
a. The price of one rental is $4 and the price of coffee is $2 per cup. Solve for Malachi's 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 decrease in the price of video rentals on Malachi's consumption of rentals and coffee.
c. From your answer to part (b), are DVD rentals and coffee normal or inferior goods for Malachi? Explain.