Malachi only consumes 2 goods: DVD rentals and coffee.

His utility function is:

U(R,C) = R^0.75C^0.25

Where R is the number of rentals and C in cups of coffee. Malachi has $16 in his pocket right now and he plans to spend it all 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 (Please develop your answer from utility maximization problem to solving for the demands and show all of your work).

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. (Show your work to develop the mathematical solution).

c.Develop the graphical solution for part b and relate your graph to the numeric solution that you found in a and b.

d.From your work, calculate the price and income elasticities of the two goods. Are is good a normal or inferior good?