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Let’s consider an alternative version of the social planner’s problem in which the planner also chooses Mt, in addition to Ct,Ct+1, and Kt+1. subject to max U = u(Ct) + v(Mt ) + βu(Ct+1) Ct ,Ct+1 ,Kt+1 ,Mt Pt Ct +Kt+1 −(1−δ)Kt +Gt =AtF(Kt) Ct+1 − (1 − δ)Kt+1 + Gt+1 = At+1F (Kt+1) (a) What is the optimality condition with respect to Mt? (b) Does the planner’s optimal allocation of money coincide with the allocation of money at the equilibrium of the Neoclassical model? (c) Is there a nominal interest rate at which the planner’s solution coincides with the equilibrium allocation?

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07:42 ? Ims.dut.udn.vn/mc $ + $ 43 Th?i gian còn l?i 0:16:34 Câu h?i 11 Ch?a trá l? ??t ?i?m 1,00 P ??t c? Find the Maclaurin series for $ f(x)=x \cos (4 x) $. Select the correct answer. a. $ \sum_{n=0}^{\infty} \frac{(-1)^{n} 4^{2 n} x^{2 n+1}}{(2 n)!} $ b. $ \sum_{n=0}^{\infty} \frac{(-1)^{n} 4^{n} x^{2 n+1}}{(2 n)!} $ C. $ \sum_{n=0}^{\infty} \frac{(-1)^{n+1} 4^{2 n} x^{2 n-1}}{(2 n)!} $ d. $ \sum_{n=0}^{\infty} \frac{(-1)^{n} 4^{2 n} x^{2 n}}{(2 n)!} $ e. $ \sum_{n=0}^{\infty} \frac{(-1)^{n} 4^{2 n} x^{2 n+1}}{n!} $ Clear my choice Trang tr??c Trang ti?p

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4. Given a project with the following tasks, their durations and dependencies, draw a CPM chart. Find the Early and Late times for each event and determine the critical path. (20) Task ID Duration (Days) Immediate Predecessor A 2 - B 2 - C 4 A D 3 B E 2 C F 6 D G 4 E H 6 F I 4 G,H

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Peter laments to his friend, "I've got to make an A in Organic Chemistry. If I don't get a top grade, I'll be a failure to myself and a disgrace to my parents!" According to Carl Rogers, what is Peter applying to himself? ? self-discrepancy ? unconditional positive regard ? conditions of worth ? a malevolent attitude

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6. Let A and B be two nonempty set of reals such that $A \subseteq B$. Prove that (a) $\inf A \leq \sup B$ (b) $\sup A \leq \sup B$ (c) $\inf A \geq \inf B$ 7. Suppose $\alpha$ is a real number and E is a non-empty set of real numbers. Define $\alpha E = \{\alpha x : x \in E\}$. How is $\sup \alpha E$ related to $\sup E$ and $\inf E$? Conjecture and then prove your claim.

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8. (10 points) How many ways are there to choose a dozen donuts from 10 varieties 1. If there are no two donuts of the same variety? 2. If all donuts are of the same variety? 3. If there are no restrictions? 4. If there are at least two varieties among the dozen donuts chosen?

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For the utility function $u(x, y) = x^{1/5}y^{1/4}$, (i) Calculate the optimal demand functions $x^*$ and $y^*$. (ii) From the maximized utility function $u(x^*, y^*)$, determine whether the associated preferences are risk-averse, risk-seeking, or risk-neutral. (You may find it convenient to write the maximized function in the form $u(x^*, y^*) =$ $\phi\omega$ to avoid clutter - but it's up to you.) For a bonus point, what do you think is the condition for utility function $u(x, y) = x^a y^b$ to represent risk-averse preferences?

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For the circuit shown find the current $i_1$ using Super position theorem.

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3.10 (a) How much energy is released if 1g $^2$H were fused: $^2$H+$^2$H=$^4$He+Q? (b) How much energy is required to drive the two atoms together?

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2.The open-loop transfer function of a unit feedback system is $G(s) = \frac{K(s+1)}{s^3 + as^2 + 2s + 1}$. When the system is in critical stable state, the oscillation frequency is 2 rad/s. Determine the value of K and a by Nyquist criterion.

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madison b.