Assume that there are 2 firms locating in Hotelling’s linear city of length 1. Each firm has a constant marginal cost of c. Consumers are uniformly distributed and have identical preferences represented by U=V-Pi-t(x*-xi)2 . where V-is consumer’s reservation value (consumer surplus from consuming her ideal product at zero price), Pi is the price of firm i’s product, x* is consumer’s location, 0≤x 1 and xi is firm i’s location. a) If both firms are required to locate in the middle, what price would they charge? b) If both firms are required to locate at two different ends of the city what price will they charge?

Question 6. There are two bidders in a sealed-bid, second-price auction. The object for sale has a common value. Each bidder, i = 1,2, receives a signal i that is independently and uniformly distributed on the interval [0, 1]. The true value of the object, v, is the average of the two signals,

v = (σ1 + σ2) / 2

(a) If bidder 1 gets the signal σ = 0.7, how much does he think the object is worth?

(b) Suppose that each bidder submits a bid equal to the expected value of the object (conditional on his signal). If bidder 1 submits the winning bid, what is the expected value of the object?

(c) What is the expected surplus for bidder 1 under the assumptions in (b)?

On a weekly basis KleineFirma producing a product has overheads (i.e., fixed costs) of $12,000. The product additionally costs $15 per unit to produce and, because the firm is small, all output can be sold at a unit price of $22. (i) Calculate the break-even quantity. (ii) Calculate the new break-even quantity if the selling price falls to $20. (iii) Calculate the new break-even quantity if fixed costs change to $20,000. (iv) Calculate the new break-even quantity if variable costs change to $16. (v) Show (and hence confirm) your answers graphically. NOTE: in specific looking for the answer to v but would like to get confirmation on the other answers too

A powerful bipolar permanent magnet stepper motor used for positioning a valve has a rated current of 13 A, a winding resistance of 60 mΩ, a winding inductance of 0.77 mH, a 0.16Nm detent torque, holding torque: 9.5 N.m, torque at 50 steps per second [sps]: 8 N.m. Its step rate is 200 steps per revolution, and the rotor inertia is 0.7x 10- 3 kg.m2.

The motor is chopper-driven at 65 V and it develops a torque of 2.2 N.m at 10000 sps. Calculate:

1. The speed [rpm] and power [hp] of the motor when it is running at 10000 sps.

2. The time constant of the windings

3. The time to reach 13 A when 65 V is applied to the winding

This multimedia deals with the issue of growing economic inequality in the US. There are three parts to it. (Due Sept 9th) The first link shows that what we believe our economic reality to be is far from accurate. http://www.youtube.com/watch?v=QPKKQnijnsM This second link provides some important information about just how many of us are actually donating to political campaigns. http://www.opensecrets.org/overview/donordemographics.php. The third link deals with who makes the laws governing this country, and why. https://www.youtube.com/watch?v=5tu32CCA_Ig In one, single-spaced page, summarize what you've learned and draw some conclusions about what your insights might mean for democracy.

We are given a set of vectors S = {V1, V2, V3} in R 3 where eV1 = [ 2 −1 3 ] , eV2 = [ 5 7 −1 ] , eV3 = [ −4 2 9 ]

Problem 1

• Prove that S is a basis for R^3 .

• Using the above coordinate vectors, find the base transition matrix eTS from the basis S to the standard basis e.

Problem 2 Using your answers in Problem 1

• Compute the base transition matrix STe from the standard basis e to the basis S.

• If eV = [ 5 1 7 ], compute SV (the coordinate vector of V with respect to the basis S). Use this to express V as a linear combination of the vectors in S.

These are all part of the same question

Consider the following capital budgeting and cash flow estimation problem. You have developed a new energy drink that uses various vegetables. The drink is called V-DRINK. You have an existing building that you are using to produce V-DRINK. The building is fully depreciated. You determine a need to buy $400,000 in equipment. Shipping and installation is an additional $50,000. Additionally you determine you will need to have $14,257 in inventory. What is the total initial outlay associated with the project?

The equipment cost (equipment plus shipping and installation) can be depreciated at the rate of 21% the first year. The remaining 5 years (years 2-6) the depreciation will be equal to $30,000 per year. What is the amount of depreciation in year 1?

Based on some market research you expect to sell around 200,000 bottles of V-Drink a year at wholesale price of $2.7. Operating costs (excluding depreciation) are expected to be 50% of revenue. The firms tax rate is 40%. What is the annual operating cash flow associated with this project in year 2. (Note you will need to factor in $30,000 in depreciation in year 2 from the prior question).

a. Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)

f(x) = x² − 5x + 4

b. Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)

f(x) = x(18x + 4)

c. Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)

f(x) = 7x^2/5 + 8x^−4/5

^d. Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)

f(x) = sqaureroot 2

e. Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative. Remember to use absolute values where appropriate.)

f(x) = 4/5-6/x,  x > 0

f. Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)

g(v) = 5 cos(v) − 9/squareroot(1-v^2)

g. Find f.

f ''(x) = −2 + 12x − 12x²,    f(0) = 9,    f '(0) = 18

2. (a) For each of the following statements, indicate whether it is a positive statement or a normative statement and why. 4 marks

i. A fundamental assumption of the economic theory of consumer behavior is that consumers always prefer having more of any good to having less of it.

ii. Provincial governments should not subsidize private corporations by training welfare recipients.

iii. To make the good available to more people, a lower price should be set.

iv. When the price of a good goes up, consumers tend to buy less of it.

(b) Nancy’s marginal rate of substitution of good X for good Y is MRS XY = 3 2 Y X . She is currently consuming 4 units of Y and 2 units of X. Based on this information, should she accept an offer to trade 2 units of Y for 1 unit of X? Why? 4 marks

(c) Suppose Amr manages to survive by eating Cereal (C) and Vegetables (V) only. His utility function is U =(C+V) = 8C + 4V. His weekly budget is $60, one kg of Cereal costs $6 and one kg of Vegetables costs $3. What is Amr preferred bundle of Cereal and Vegetables, (C*, V*). Explain your answers.

Let G = (V, E) be a directed acyclic graph modeling a communication network. Each link e in E is associated with two parameters, w(e) and d(e), where w(e) is a non-negative number representing the cost of sending a unit-sized packet through e, and d(e) is an integer between 1 and D representing the time (or delay) needed for transmitting a packet through e. Design an algorithm to find a route for sending a packet between a given pair of nodes in G such that the total delay is no more than k and the total cost is minimized. Your algorithm should run in O(k(|E| + |V |)) time and O(k|V |) space (additional to space for storing the graph). Hint: It is possible to use a linear time (i.e., O(n + m) time) algorithm called topological sort to compute the shortest path between any pair of vertices in a unit-weighted (i.e., all edges have weight 1) graph with n vertices and m edges.

Actually the question is this much only. I have been given HW and this question has been asked. I am unable to understand this that is why I posted here.