Consider the following utility data for some hypothetical consumer QTUApples TUOranges 0 20 0 1 2 3 4 56 7 88NGS99 36 50 62 72 80 86 0 48 88 124 156 180 192 200 A Use this data to assist you in answering the following questions a Derive a linear equation which approximates the income expansion path between M 5 and M 14 Assume PA 1 and Po 2 6 pts b Using the midpoint method compute income elasticity of demand for apples and oranges between M 5 and M 14 Are these goods normal inferior Assume P 1 and Po 2 How do you know Explain 6 pts c Suppose that the price of oranges falls to 1 assume that the price of apples remains unchanged Adjust your budget constraint and point out the new optimal consumption bundle Assume this individual s income 5 6 pts d Using the midpoint method and the aforementioned change in the price of oranges calculate the price elasticity of demand for oranges and the cross price elasticity of demand for apples Are oranges price elastic Are apples and oranges substitutes or complements Show all work and explain 6 pts e Derive a linear approximation of this individual s demand curve for oranges 6 pts