Write two separate programs (completed code) for the following questionsProgramming ChallengeWrite two separate programs (completed code) for the following questions1. Implement a Binary Tree via a Linked Listo After constructing a binary tree, use Preorder traversal to display the nodes in the tree2. Iteratively insert a node in Binary Tree (NOT recursively)o Use Inorder traversal to display the nodes in the treeThe followings are the requirements for this homework:

ECON 533 & ECON 602Quiz 2, November 15, 2020Profesor: Manuel S. SantosFall 2020PLEASE SUBMIT BEFORE NOVEMBER 22. PLEASE, DO NOT COMMUNICATEWITH YOUR CLASSMATES. You can answer 5 out of 8 short questions, and 2 problems.Grad students must answer 5 short questions (including VI-VIII), and two problems (including problem 3). If you answer six short questions, then one short question counts as bonus.Same for problem 3.

QUESTION I: Can you write down a CES production function? Which parameter determines the (constant) elasticity of substitution? And the labor income share? Whichassumptions would you need to make in the evolution of wages and rental rates inorder to replicate the declining US labor income share?
QUESTION II: Suppose that we have increasing returns to scale. Would the costfunction be concave or convex in output? Would the marginal cost be increasing ordecreasing? Would the optimization problem be well defined?
QUESTION III: In some textbooks we are told that @[email protected] = @[email protected] This looks counterintuitive. How would you explain this?
QUESTION IV: What does it mean third-degree price discrimination? Would youprovide some examples?
QUESTION V: Please, discuss. Does it make sense for Zara to have these short sellingcycles? How Zara grew into the World’s Largest Retailer. ”When you went to Gucci orChanel in October, you knew the chances were good that clothes would still be there inFebruary,”BUT ”With Zara, you know that if you don’t buy it, right then and there,within 11 days the entire stock will change. You buy it now or never. And because theprices are so low, you buy it now.”
QUESTION VI: Could you write down the first-order condition of the prototypicalmoral hazard model (hidden e↵ort) as a function of the likelihood ratio? How wouldyou interpret this condition to provide optimal incentives for rewarding e↵ort?
QUESTION VII In the adverse selection model discussed in class, we encounteredthe following condition: ✓L C(0, ✓L) ✓H C(t,ˆ ✓L). Please, explain this condition.Moreover, how does this condition get translated in an insurance market with twotypes of consumers (the bad type and the good type). Hint: Mas-Colell, 13.D.2.1
QUESTION VIII In our corruption paper, is Equation (5) an IR constraint or anIC constraint? Explain the meaning of this constraint (is it a moral hazard model?).Would you suggest any changes to this constraint?
PROBLEM 1: A monopolist (AT&T) is facing the following demand schedule P =243Q. That is, Q = 0 implies P = 24, then Q = 1 implies P = 21, and Q = 2 impliesP = 18, and so one. Fixed costs will be neglected in this analysis. The marginal costis constant and equal to 6 for every unit produced. Determine:(i) The quantity produced corresponding to the amount of maximum profit.(ii) Equilibrium price if a new competitor, Vodafone, enters the market with a MC =6under both Cournot and Bertrand Competition.(iii) Equilibrium price if a new competitor, Vodafone, enters the market with a MC=7under Bertrand Competition.(iv) Equilibrium price if a new competitor, Vodafone, enters the market with a MC=5under Bertrand Competition.
PROBLEM 2: Spotify o↵ers a hassle-free (no-commercials) program. Here, at UM, aprofessor would be willing to subscribe for a monthly free of $30, and a student wouldbe willing to subscribe for $10. There is a second program in which commercials taketen percent of the time. The company will get one-dollar revenue for running thesecommercials in all cases. However, the disutility of the commercials to each studentwould be $2, and to a professor would be $8.00. Assume that half of the populationare professors and half are students, and Spotify is committed to serve both markets.A. (Market segmentation) Compute the optimal price(s) for each type in the case thatSpotify has access to the UM records and is able to tell who is a professor and a student.B. (Hidden Types). Compute optimal price(s) in the case that Spotify has no accessto UM records, and cannot identify types.C. (Hidden Types). Assume linear preferences and linear revenues. An undergrad student from ECO 533 has suggested to Spotify to change the second program so thatcommercials should take 20 percent of the time. Again redo part B, assuming that inthe second program commercials take 20 percent of the time.D. (Hidden Types) Actually, our student goes further and claims to have computed theoptimal percentage amount of advertising for the second program under the linearityassumption on preferences and commercial revenues. Following part B, are you able tocompute the optimal amount of advertising for Spotify serving UM?
PROBLEM 3: This is Mas-Collel, 13.C.6. Let us assume the following condition: pG⇧(1 + r) > pB⇧ (1 + r) > 0. Now, following this problem in the book:(i) Find the level of Ri (i = 1, 2) in a separating equilibrium.(ii) Find the level of R in a pooling equilibrium.2(iii) How a separating equilibrium will look like in case that the bank can also o↵er anew contract in which the entrepreneur is required to contribute a fraction x of the onedollar initial outlay. Assume that the entrepreneur can get this money at an interestrate ⇢ slightly higher than r. (Else, assume that the entrepreneur has the cash.)3

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