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Problem 1 A consumer has set a budget of $300 for the consumption of good X and Y. The price of Good X is $20, and the price of good Y is $10, The consumer has a Utility function given by U(X,Y) - xyl a) Find the optimal consumption choice of the individual and the utility obtained. b) Briefly express in writing the process that you used to find the solution. c) Discuss some of the possible limitations of the Consumer Choice Model when it comes to predicting the behaviour of consumers. Problem 2 A consumer has set a budget of $500 for the consumption of good X and Y. The price of Good X is $10, and the price of good Y is $10. The consumer has a Utility function given by U(X, Y)-xy. a) Find the optimal solution using a method that does not involve equations and illustrate the solution. b) Calculate an equation that represents the demand for good X. Solve for X and leave Px as a parameter or unknown Problem 3 a) Illustrate the consumption choice t dividual when two goods are considered "perfect substitutes" in consumption b) Illustrate the consumption choice for an individual when two goods are considered "perfect complements" in consumption c) Illustrate the consumption choice for an individual when the horizontal axis illustrates a bad and the vertical axis illustrates and good. Identify the preferred indifference curvesin dy Illustrate the consumption choice for an individual when the horizontal axis illustrates a good and the vertical axis illustrates a USELESS. Identify the preferred indifference curves. c) Illustrate the consumption choice for an individual when the both goods are considered bads and the consumer has to spend the budg