Numerade

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1. DeÖnitions:(a) What is a hypothetical budget line? Which consumption bundle doesit go through?(b) What are income and substitution e§ects? Explain.2. Suppose that Mikeís demand curve for commodity 1 is vertical (price in-elastic).(a) Draw his price o§er curve for commodity 1 in a (x1; x2) space byÖxing p2 and m. (Draw two budget lines corresponding di§erentp1s (p1 and p01) and indi§erence curves to describe Mikeís optimalconsumption bundle for each p1.)(b) Is commodity 1 a normal good or an inferior good? Explain why.3. Suppose u(x1; x2) = ln x1 + x2.(a) Let p2 = 1 and m = 2 > 1. Find x1 = x1(p1; p2; m) = x1(p1; 1; 2). Inother words, Önd the optimal x1 for each p1.(b) Draw the price o§er curve for p1.(c) Suppose that initially p1 = 2 holds, then it goes down to p01 = 1.Draw two budget lines with the optimal choices A and B.(d) Draw the hypothetical budget line, and Önd the hypothetical con-sumption point C.(e) What are income and substitution e§ects for commodity 1 by thisprice change?

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Question 5 (2 points) According to Newton's Universal Law of gravitation, which of the following is not a possible orbit of one body around another? a) An ellipse b) A straight line c) A parabola d) A hyperbola

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de Web A protocol that associates domain names with unique IP addresses service provider A technology that provides wireless internet connectivity through wireless routers A company that provides access to the internet An interconnected global public computer network An information system that connects documents to each other by hypertext links

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Find the solution $u = u(x, t)$ of \begin{cases} \qquad u_t = k u_{xx} + \gamma u, \quad x \in \mathbb{R}, t \in \mathbb{R}^+_+ \\ \qquad u(x, 0) = f(x) \qquad x \in \mathbb{R}. \end{cases} where $\gamma$ is a positive constant.

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Using the carbon-containing starting material(s), propose a synthesis by drawing structures for all intermediates. The carbon atoms in the product must originate from the starting material(s) (or a carbene/carbenoid or CO$_2$), but you may use as many equivalents of each starting material as you would like, and any reagent/reaction you know. (note: no mechanisms are required).

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9 What is the value of $V_x$ ? A) 0 V B) 1.25 V C) 1.875 V D) 1.67 V E) None of these 2.5 ? + 2.5 ? 5 ? 5 v + 2.5 ? $V_x$

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What is the term for the ability to understand and produce spoken language? a. Phonetics b. Syntax c. Morphology d. Linguistics

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You work for a marketing firm that has just landed a contract with Run-of-the-Mills to help them promote three of their products: penguin pops, frizzles, and candies. All of these products have been on the market for some time, but, to entice better sales, Run-of-the-Mills wants to try a new advertisement that will market two of the products that consumers will likely consume together. As a former economics student, you know that complements are typically consumed together while substitutes can take the place of other goods. Run-of-the-Mills provides your marketing firm with the following data: When the price of penguin pops increases by 10%, the quantity of frizzles sold decreases by 26% and the quantity of candies sold increases by 14%. Your job is to use the cross-price elasticity between penguin pops and the other goods to determine which goods your marketing firm should advertise together.

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Use Newton's method to approximate a root of the equation $e^{0.9x^2} = 6 - x$ as follows. Let $x_1 = 2$ be the initial approximation. The second approximation $x_2$ is and the third approximation $x_3$ is

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3. (10 pts) When an action potential reaches an axonal terminal, synaptic vesicles release their contents of neurotransmitters into the synaptic cleft to diffuse and bind to post-synaptic receptor proteins that in turn modulate membrane conductances. A simplified transfer function governing this system is given by function $h(t)$, which we will represent as a single decaying exponential with $\tau = 3ms$ and time delay of 1ms. Consider a burst release of neurotransmitters represented by the periodic delta function input $x(t)$ occurring at a rate of 250Hz over 20ms. a. (6 pts) Calculate the system response $y(t)$ by hand. b. (4 pts) In MATLAB, plot the system response, $y(t)$.

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adam b.