Suppose an individual has an income of $200 per time period, the price of good X is $2 and the price of good Y is $1. 4.1. Graphically illustrate a set of indifference curves that correspond to the budget constraint given above. (4 marks) 4.2. According to Utility Theory, state the condition necessary for Utility Maximization. (2 marks) 4.3. Now suppose, Good X is an inferior good. Using a neat, carefully drawn and labeled diagram, show the substitution and income effects resulting from a decrease in PX to $1, while M and PY remain constant. (4 marks) 4.4. Draw a diagram showing the positions of a competitive firm and of the industry in the long-run equilibrium. Suppose this is the cotton industry. The development of artificial fibers reduces the demand for cotton. Show what happens in the short run and in the long run if all farmers face a decreasing cost industry. Hence, derive graphically, the long-run industry supply curve