Every month Karen chooses to spend 80$ of her monthly income on two goods: Movies (X) and Popcorn (Y). Her preferences over these two goods can be represented by the following utility function: U(X, Y) = X0.5Y0.5. a. What is Karen's marginal utility from consuming movies (MUX) and popcorn (MUY)? b. Find Karen's marginal rate of substitution (MRS) of movies for popcorn. c. Suppose that the average price for a movie ticket (PX) is $8 and that the average price for a small bag of popcorn (PY) is $2. Write an expression for Karen's budget line and find the marginal cost of both movies (in terms of popcorn) and popcorn (in terms of movies). d. Given the information about prices in part 'c' above, what is Karen's optimal consumption bundle? What is her level of satisfaction (in terms of 'utils')? Sketch your solution with movies on the x-axis. e. Assume now that a decrease in the supply of corn, due to the recent unusual wet weather, led to a 100% increase in the price of popcorn (PY). Draw Karen's new budget line. What can you say about her purchasing power? f. Given this new information in part 'e' above, what