DOC PREVIEW
CORNELL ECON 2040 - solutions-midterm

This preview shows page 1 out of 2 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 2 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 2 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Networks: Fall 2013 Midterm Answer KeyDavid Easley and´Eva Tardos(1) [7 points]Yes, the buyers should bid truthfully.We know that truthful bidding is a dominant strategy in a second-price auction, so includingthe seller as another bidder does not matter. Alternative explanations are: (i) that overbiddingmakes winning and overpaying possible and underbidding makes losing possible when the biddercould have won at less than the value, or (ii) that your bid affects only whether or not you winand not how much you pay if you do win, and you wan to win if you can do so at a price nomore than your value.(2)[10 points](a) [5 points] The most powerful is node a. The least powerful is node d. Nodes b and c havepowers between the powers of nodes a and d. The explanation is that a can exclude d who isvery weak, b and c can exchange with each other and they have equal outside options of dealingwith the stronger a, and d has no one to exchange with other than the more powerful node awhich makes d weak.Computing the power of the nodes in a balanced outcome is an alternative explanation: Nodea has power 3/4 and node d has power 1/4.(b) [5 points] The power of a decreases and the powers of b, c and d increase. This occursbecause adding weak potential partners for b and c makes them more powerful, this in turn makesa less powerful (as a’s potential partners b and c have become more powerful) and because a isless powerful node d, who can only exchange with node a, becomes more powerful.Computing the power of the nodes in a balanced outcome is an alternative explanation: Nodesa, b and c have power 2/3, node d has power 1/3.(3)[10 points](a) [5 points] This network does not satisfy the double strong triadic closure. The edges thatneed to be added are (A, C), (B, D).(b) [5 points] This network does satisfy the property.(4)[13 points](a) [1 point] See Figure 1.(b) [4 points] The solution with two routes equal must satisfy 1 + (2 + x/100) = y/100 + 2,and x + y = 500. Solving this we get 1 + x/100 = y/100, and so x = 200 and y = 300.Saying that these values make the two travel times (5 hours) equal is a good explanation.(c) [4 points] The travel time in the previous solutions on both Routes I and II is 5 hours.As a result, the new Route doesn’t change the equilibrium. It remains x = 200 and y = 300.A good explanationis that Route III is longer than Routes I and II.(d) [4 points] Now we need to solve 1 + (2 + x/100) = y/100 + 2 = 4, and x + y + z = 500,which solves to x = 100, y = 200 and hence z = 200.As in (b) saying that all routes have equal travel times is a good explanation.A D C B 2+ x/100 1 y/100 2 Figure 1: Question 4 network(5)[10 points](a) [5 points] The simplest set of prices is (3, 1, 0) for A, B, C respectively. Other prices thatwork are (4, 2, 1), (3, 3, 0), (4, 3, 1) or (4, 4, 1). For any market clearing prices x should have B ashis preferred item, and y and z should both be indifferent between A and C and prefer it to B.The figure below illustrates what happens if you run the market clearing algorithm (this wasnot necessary).z x y C B A z x y C B A 1 0 0 0 0 0 z x y C B A 2 0 0 z x y C B A 3 1 0 1 2 3 4 Figure 2: Question 4 network(b) [5 points] There are two assignments that maximize total value: (x, B), (y, A) and (z, C);or, (x, B), (y, C) and (z, A). Both have a total value of


View Full Document

CORNELL ECON 2040 - solutions-midterm

Download solutions-midterm
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view solutions-midterm and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view solutions-midterm 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?