Suppose that Kalie lives off from beef sticks (q1) and Gatorade (q2) and has the following utility function, U=q1^(2/3)q2^(1/3). The price of a pack of beef sticks (p1) is $10 and the price of a 32oz Gatorade (p2) is $2.50. Kalie has $50 to spend on the two things that she loves.

a. Graph Kalie's budget line. b. What is Kalie's MRT? Explain what this number means. c. What is Kalie's MRS? Explain what the MRS means. d. What are the conditions for utility maximization? Draw a graph depicting the conditions for utility maximization and explain what they mean. e. Solve for Kalie's demand function for beef sticks. Show your work. f. Solve for Kalie's demand function for Gatorade. Show your work. g. At current prices, how many packs of beef sticks will Kalie buy? h. At current prices, how many Gatorade's will Kalie buy? i. What is her current utility? j. How do you solve for Kalie's expenditure function? It is U=1.89q1^(2/3)q2^(1/3). Suppose the government imposed a $2 tax on beef sticks. (Assume the long-run elasticity of supply is perfectly elastic so that the incidence of tax falls entirely on the consumer). i. How many packs of beef sticks will Kalie buy? ii. How much tax revenue will the government collect from Kalie? iii. What will her utility be? iv. How much money does the government have to give Kalie to compensate her for the effect of the tax? v. Illustrate this part (k) of the problem with a graph. l. Suppose that Kalie is consuming beef sticks and Gatorade so that |MRS|>|MRT|. i. What adjustments would you suggest that Kalie make to her consumption? Explain why. ii. Illustrate this part (l) of the problem with a graph