Imagine a market for X composed of four individuals: Mr. Pauper (p), Ms. Broke (b), Mr. Average (a), and Ms. Rich (r). All four have the same demand function for X: it is a function of income (I), the price of X (Px) and the price of an important substitute (Py). The demand function is: IP X = 2PX (a) What is the market demand function for X? Assuming that Px = Py = 1 and I = I 16, la 25, and I = 100, what is the (market total) quantity demanded? = (b) If Px doubles (that is to say from 1 to 2), what would be the new market level of X demanded? If Mr. Pauper lost his job and his income fell by 50 percent, how would that affect the market demand for X? What if Ms. Rich's income were to drop by 50 percent? If the government were to impose a 100 percent tax on Y (that is to say, the price of Y increases from 1 to 2), how would that effect the demand for X? (c) For any one of the individuals (using the demand function above) derive the price elasticity of demand for X and the income elasticity of demand for X.