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1. For an acyclic network G with a specified source node s, outline an algorithm that enumerates all distinct directed paths from the source node to every other node in the network. The running time of your algorithm should be proportional to the total length of all the paths enumerated (i.e., linear in terms of the output length.)
2. In an undirected connected graph G = (N, A), an Euler tour is a walk that starts at some node, visits each arc exactly once, and returns to the starting node. A graph is Eulerian if it contains an Euler tour. Show that in an Eulerian graph, the degree of every node is even. Next, show that if every node in a connected graph has an even degree, the graph is Eulerian. Establish the second result by describing an O(m) algorithm for determining whether a graph is Eulerian and, if so, will construct an Euler tour. (Hint: Describe an algorithm that decomposes any graph with only even-degree nodes into a collection of arc-disjoint cycles, and then converts the cycles into an Euler tour.)
1. go back to the numerical example with no factor substitution that leads to the production possibility frontier.a.
Refer to part b. Find the correlation between u and u2, u and u3, and u2 and u3. What do you observe? Is the level of correlation reduced for all three pairs?
Restricting your attention to the range of prices that exceed the dominant firm's marginal cost, what is the equation of the residual demand curve?
If you work for 30 years and wish to retire for 15 years on 50 percent of your working income, how much of your income must be saved when working? (Assume that the interest rate and income when working are constant, and that there are no taxes.)
Are the workers in country 1 better o¤ as a result of the tax? What about the impact of the tax on the welfare of the workers in non taxing countries?
suppose that the interest rate on a one year bond is 7 percent today and the interest rates expected on one year bonds in the future are 6 percents in one year, 5 percent in 2-year , and 4 percent in three years bond. what are interest rate today ..
c) Compute the elasticity of supply with respect to technology. d) Compute the elasticity of supply with respect to wage rate. e) Based on the elasticity of supply with respect to wages, what would happen to supply if the average wage increased fro..
List the three types of binary relationships and give an example of each. Do not use the examples given in this text.
Southwestren Moving and storage wants to have enough money to purchase a new tractor-trailor in 5 years at a cost of $290,000. If the company set aside $100,000 in 2 years and $75,000 in 3 years how much will the company have to set aside in 4 yea..
Under what circumstances does the potential for migration raise the speed of convergence in the Solow-Swan model? What about in the Ramsey model? What are the sources of the effects on convergence?
Suppose that the economy is thought to be 2% above potential (that is, the output gap is 2%) when potential output grows 4% per year. Suppose also that the Fed is following the Taylor rule, with an inflation rate of 2% over the past year.
As an alternative, the company offers a 24-month lease with a single up-font payment of $ 12,780 plus a $500 refundable security deposit. The security deposit will be refunded at the end of 24-month lease.
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