问题 16 2分 In the Two Period Consumer model, the Net Effect from a decrease in the interest rate for a net borrower is: C1↑; C2?: Savings ↑ C1↑; C2?: Savings ↓ C1↑; C2↓: Savings ↓ C1?; C2↓: Savings ? C1?; C2↑: Savings ? 问题17 2分
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A net borrower is someone who borrows in the first period and repays in the second. Show more…
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Consider a two-period model in which the consumer chooses consumption today (c), consumption tomorrow (c') and savings (s > 0) or borrowing (s < 0) to solve the problem below. maxU(c,c') subject to: c + s = y and c' = y' + (1+r)*s Let y = 5.1 and y' = 7.8. Let the net interest rate be r = 4 percent. Keeping in mind that the slope of the budget constraint is negative, answer the questions in parts a) and b). For part a) report 2 decimal places. a). The slope of the lifetime budget constraint of the consumer is b). If the net interest rate increases, the budget constraint A. becomes flatter B. becomes steeper C. remains unchanged
Akash M.
Consider a household whose utility is determined by its consumption in periods 0 and 1. Let c0 and c1 denote the consumption in periods 0 and 1, respectively. The utility of this household can be represented by a utility function: U(c0, c1) = u(c0) + βu(c1). Assume further that the per-period utility u(c) is given by u(c) = log(c), and the discount factor β is given by β = 9/10. In periods 0 and 1, this household is endowed with incomes y0 = 190 and y1 = 380, respectively. Importantly, this household can save or borrow in period 0 at the interest rate r = 1/9. (a) Check if the per-period utility function u(c) satisfies i) u'(c) > 0 and ii) u''(c) < 0, where u'(c) denotes du/dc and u''(c) denotes d^2u/dc^2. Describe the economic meaning of these conditions. Show that when the per-period utility function u(c) satisfies the two conditions above, households' total utility U(c0, c1) satisfies i) Uc0 > 0, Uc1 > 0 and ii) Uc0,c0 < 0, Uc1,c1 < 0, where Uc0 and Uc1 denote ∂U/∂c0 and ∂U/∂c1, respectively, and Uc0,c0 and Uc1,c1 denote ∂^2U/∂c^20 and ∂^2U/∂c^21, respectively. (b) Write down this household's intertemporal optimization problem using sequential budget constraints. Indicate which term captures the saving or borrowing of this household in the sequential budget constraints. Using this term, describe when this household saves and when it borrows. (c) Derive the intertemporal budget constraint and explain its economic meaning (using the concept of the present discounted value). (d) Rewrite this household's intertemporal optimization problem using the intertemporal budget constraint. Explain why the gross interest rate (1 + r) can be interpreted as a relative price between current and future consumption. (e) Set up a Lagrangian equation and derive the optimal conditions. (f) Derive the Euler equation and provide an economic reason why this equation has to hold at the optimum.
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A student has current income y1 and expects future income y2. She plans current consumption c1 and future consumption c2 in order to maximise utility U = 2∑c1 + 2̢∑c2, c1, c2 > 0 where ̢ > 0 is her discount factor. If she borrows now, c1 > y1, then future consumption, after repaying the loan c1 - y1 with interest r, will be c2 = y2 - (1+r)(c1 - y1). Alternatively, if she saves now, c1 < y1, future consumption will be c2 = y2 + (1+r)(y1 - c1) after receiving interest r on her savings. The student takes the interest rate r as given. Answer the following questions: (a) [5 marks] State carefully the maximisation decision of the student. (b) [8 marks] Find the optimal plan (c1*, c2*). Show your workings and interpret your results. (c) [7 marks] Show how an increase in the interest rate affects the level of borrowing or saving. Show your workings.
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