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3. Suppose there are only two periods and in period 1 an individual is endowed with 1 vegetable. The individual decides how much of the vegetable to eat and how much to plant in period 1 (there are no refrigerators so the vegetable cannot be stored). If a fraction s of the vegetable is planted, then As, where A > 0, vegetables will grow for second-period consumption this is the only consumption available for period 2). The portion planted cannot be eaten (this is equivalent to 100% depreciation). Utility for the individual is given by: U(@,cy) = ln(q) + 0.8 In(ca), where and Care is consumption is period 1 and 2, respectively. (a) State the individual's period 1 and period 2 budget constraints and derive the two-period budget constraint. (b) State the individual's maximization problem. (c) For A = 0.5, derive the first order conditions and solve for the equilibrium values of ci and s (d) Does s (fraction planted) increase or decrease with increase in A? Explain in words. 3. Suppose there are only two periods and in period 1 an individual is endowed with 1 vegetable. The individual decides how much of the vegetable to eat and how much to plant in period 1 (there are no refrigerators so the vegetable cannot be stored). If a fraction s of the vegetable is planted, then As, where A > 0, vegetables will grow for second-period consumption this is the only consumption available for period 2). The portion planted cannot be eaten (this is equivalent to 100% depreciation). Utility for the individual is given by: U(@,cy) = ln(q) + 0.8 In(ca), where and Care is consumption is period 1 and 2, respectively. (a) State the individual's period 1 and period 2 budget constraints and derive the two-period budget constraint. (b) State the individual's maximization problem. (c) For A = 0.5, derive the first order conditions and solve for the equilibrium values of ci and s (d) Does s (fraction planted) increase or decrease with increase in A? Explain in words