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Problem 1 Suppose that an individual with income I cares about two goods, X and Y . The prices of the two goods are pX and pY . The individual has the utility function U(X, Y ) = X 2 5 Y 3 5 . (a) Derive the Marshallian demands for the two goods. (b) Find the indirect utility function. Solution (a) To derive the Marshallian demands, we use the Lagrangian method. The budget constraint is pXX + pY Y = I, which we can rewrite as I − pXX − pY Y = 0. We set up the Lagrangian funct...

Jeff consumes burrito bowls (B) and chicken tenders (C). His Marshallian demand for burrito bowls is B ∗ = I 0.4p 0.3 C 5p 0.7 B (a) Find and interpret the income elasticity of demand for burrito bowls (eB,I ) and interpret the value. Are burrito bowls an inferior or normal good? (b) Find the own price elasticity of demand for burrito bowls (eB,pB ) and interpret the value. Does the own price elasticity of demand for burrito bowls depend on the value of pB? (c) Find the cross p...

1. Which of the following would increase US GDP this year? (a) All of these would increase US GDP this year (b) A US retailer purchases shoes from a Chinese manufacturer for $30 and sells them to a US consumer for $50 (c) None of these would increase US GDP this year (d) A US retailer sells shoes out of its inventory that were produced in the previous year (e) A US retailer purchases shoes from a Chinese manufacturer and puts them in a warehouse 2. A hamburger stand purchases $100 of brea...

Complete the following questions on a separate piece of paper. 1. Write the equilibrium expression, Keq, for each of the following reactions: a) 2 NO(g) + O2(g) ⇌2 NO2(g) [ ] [ ] [ ] 2 2 2 2 NO O NO Keq  b) 4 HCl(g) + O2(g) ⇌2 H2O(g) + 2 Cl2(g) [ ] [ ] [ ] [ ] 2 4 2 2 2 2 HCl O H O Cl Keq  c) NOCl(g)⇌NO(g) + ½ Cl2(g) [ ] [ ] [ ] 2 1 2 NOCl NO Cl Keq  d) Fe3+ (aq) + SCN- (aq)⇌FeSCN2+ (aq) [ ][ ] [ ] 3 2     Fe SCN FeSCN Keq ...

The reaction between benzene and 2 moles of chlorine gas. + 2 Cl Cl Cl Cl + 2 H Cl AlCl3 Substitution Reaction benzene meta-dichlorobenzene 2. The formation of 2-hexanol from an alkene. OH + H2O H2SO4 100 C 1-hexene 2-hexanol Addition Reaction 3. The formation of 2,2-pentanediol. OH OH 2,2-pentanediol + 2 H2O 1-pentyne H2SO4 100 C Addition Reaction

ino acids (7 + 1 pts) a. You have a solution containing the following species at the stated concentrations. i. (2 pts) Is this a buffer system? Why or why not? ii. (3 pts) What pH is this solution at? (show your work!) b. (+1 serious bonus) If a solution of arginine was at a pH of 12.5, what would be the net (averaged across the population) charge per molecule

1. Amino acids and protein structure (12 pts) a. Do the following using the α-helix model provided: i. (2 pts) Notate the orientation of the N and C termini for this α-helix. ii. (2 pts) Notate the orientation of the inherent dipole moment of this α-helix iii. (1 pt) The bond labeled ‘iii’ represents a… iv. (1 pt) The bond labeled ‘iv’ represents a… b. (2 pts) Consider the polypeptide chain within a right-handed α-helix. Given the Ramachandran plot provided, what is a p...

A Predator-Prey Model Previously, we studied and simulated the Lotka-Volterra predator-prey model (which you initially saw as the "shark-tuna model"). Now, we will study a different predator-prey model, termed the Holling-Tanner model, that incorporates somewhat different (and more realistic) biological assumptions. As before, we will call our prey population and our predator population . We will assume that, in the absence of predators, the prey population would grow logistically. T...

In a recent study, scientists examined whether amount of sleep impacted response time on the MIT. The hypothesis is that people who took the MIT twice, once after getting 5 hours of sleep and once after getting 8 hours of sleep, will have different response times on the MIT. The hypothesis is that people who get less sleep before taking the MIT will have a different response time than people who got more sleep before taking the MIT. The hypothesis is that people who got 5 hours of sleep wil...

1. Which of the following is not a debt security? a. Convertible bonds b. Commercial paper c. Loans receivable d. All of these are debt securities. Ans: C 2.A correct valuation for debt securities is a. available-for-sale at amortized cost. b. held-to-maturity at amortized cost. c. held-to-maturity at fair value. d. None of these answers are correct. Ans: B 3.Unrealized holding gains or losses which are recognized in income are from debt securities classified as a. held-to-maturity...