Suppose a person has $20 to spend on music and likes both rap music (R) and country music (C) with a set of preferences so that U=C^1/2R^1/2. Suppose that the iTunes price of a rap music song is PR=2 and the price of a country music song is PC=1.
A. Write down the budget constraint equation for him.
B. Show his optimal consumption choice in a graph. Use the horizontal axis for number of rap music songs (R) and vertical axis for country music (C). Draw the budget constraint, indifference curves, the optimal choice (a point) in the graph. Be as accurate as possible, and label some key points with numbers (their values).
C. Solve for the optimal choice for him using calculus. Find the value for R, C, and his utility.