1. (35 points) Assume a farmer derives utility from Income in the following manner

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1 Exam 3 AGEC 421 Advanced Agricultural Marketing Spring 2012 Instructor: Eric Belasco Name Belasco Key 1. (35 points) Assume a farmer derives utility from Income in the following manner where is income (in thousands). For this particular farmer, 2 and This farmer is deciding between two strategies: (1) continue working on the farm or (2) taking a job in town. Under strategy 1, there is an 80% chance of a net income equal to $70,000 and a 20% chance of a net income equal to $20,000. Alternatively, working in town provides a guaranteed income of $55,000. a. (5 points) Compute the first and second derivatives for the utility function above... b. (5 points) Based on your answer in part (a), determine whether this individual is risk averse or not. Explain what is meant by risk averse. If an individual has a utility function such that and, then the individual is said to be risk averse. This implies their utility function is increasing at a decreasing rate, with respect to income. This individual is willing to pay a fair premium in order to offset risk associated with a fair bet. 1

2 c. (5 points) Compute the expected utility associated with each strategy and determine which strategy this individual is likely to accept. Strategy 1:.... Strategy 2:.. Strategy 1 is preferred since the expected utility is higher. d. (10 points) Now assume this individual decides to work on the farm and can purchase insurance which essentially guarantees a net income of $59,000 (this income includes the cost of insurance) i. Show whether the guaranteed net income from purchasing insurance is above or below the expected income derived from this individual working on the farm?.. Expected income is higher under the riskier scenario. ii. Show whether this individual maximizes their expected utility through buying insurance, relative to strategy 1 above? Strategy 3:.. Even though the insurance strategy has lower expected wealth, it is expected utility maximizing relative to strategy 1. 2

3 e. (10 points) Now assume the individual above changes their outlook with regard to risk. More specifically, their utility function above changes to include the following parameters where 1 and 0. i. Show whether this individual would accept the insurance product that guarantees a net income of $59,000 or accept the risk in strategy 1. This risk neutral individual would prefer the no insurance option since expected utility is higher. ii. Explain how this individual s perception of risk has changed. Be specific. This individual is risk neutral since, meaning Income is linearly related to utility. Maximizing expected income is the same as maximizing expected utility since this individual is not risk averse or risk loving. 3

4 2. (30 points) Assume you are hired as an analyst to evaluate feeder cattle prices. You are given monthly data starting in November The figure below is a plot of the monthly price series. 160 Feeder Cattle Nearby Futures Price Nov 89 Oct 90 Sep 91 Aug 92 Jul 93 Jun 94 May 95 Apr 96 Mar 97 Feb 98 Jan 99 Dec 99 Nov 00 Oct 01 Sep 02 Aug 03 Jul 04 Jun 05 May 06 Apr 07 Mar 08 Feb 09 Jan 10 Dec 10 Nov 11 In an effort to characterize and predict feeder cattle prices, you run the following three models (1) (2) (3) where is the feeder cattle price in month t, such that 0,1,2,,268 and. For example, in Nov and on the last observation (March 2012), 268. Results are shown below. Model 1: Dependent variable Yt Coefficients Standard Error t Stat Lower 95% Upper 95% Intercept T Model 2: Dependent variable Yt Coefficients Standard Error t Stat Lower 95% Upper 95% Intercept Lag (Y t 1) Model 3: Dependent variable dyt Coefficients Standard Error t Stat Lower 95% Upper 95% Intercept dy t

5 a. (5 points) Based on the results from model 1, does there appear to be a time trend? Characterize this time trend using the parameter estimates. Yes, each month prices increase by about $0.175, which is shown to be statistically different from zero. b. (5 points) Use model 1 to predict April 2012 cattle prices. (Hint: T=269) Explain why this prediction does or does not seem reasonable.... This doesn t seem reasonable given prices are nearly $160 in March There is a clear autocorrelation component in this series. c. (5 points) Based on the results above, do feeder cattle prices appear to be stationary or nonstationary? Explain how you came to this conclusion. Using model 2 we can test to see whether prices are stationary by inspecting whether the 95% confidence interval for contains 1. Since 1 is contained within the interval (0.9865, ), we fail to reject that hypothesis that the series is nonstationary. This test is called the Dickey Fuller test. 5

6 d. (5 points) Explain in words, the difference between a series that is stationary and a series that is nonstationary. A stationary series has a stable expected or conditional mean while a nonstationary has a changing expected or conditional mean. If a series is stationary, then the past series informs the future, while in a nonstationary series our best estimate for tomorrow is based almost entirely on prices today. e. (5 points) Would you suggest using model 2 or 3 in order to predict feeder cattle prices for April 2012? Justify your answer. I would suggest using model 3, since model 2 is nonstationary and would result in inconsistent results. f. (5 points) Use the model you suggested in part (iv) to forecast feeder cattle prices for April 2012 given that the prices in February and March 2012 were and , respectively