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2. Asset Prices This question relates to the dividend-discount model. (a) Starting from the denition of the rate of return on stocks, show that stock prices obey the following rstorder difference equation D: Pt+1 P=+ t (1+Tt+1) (1+Tt+1) where D: represents dividends and n is the rate of return on stocks. (b) Now assume that agents have rational expectations and that expected future stock returns are constant and equal to 1'. Show that this difference equation implies the following representation for stock prices i 1 k+1 P: = ( ) EtDt+k k=0 1 + 1-" Discuss any assumptions that you make in deriving this equation. (c) Suppose dividend payments are expected to grow at rate 9 forever. What does the dividend- discount model (is. the model derived in part (b) above) imply for the current level of stock prices? (d) Now suppose that instead of growing at rate 9 each period, dividends can be expressed as the sum of two componentsa trend component that grows at rate 9 each period and a cyclical component it; that follows an AR(1) process at = pie1 + E: where 0