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PS1 SP100

# PS1 SP100 - Econ 100A Dr Famulari Practice Problems Spring...

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Econ 100A, Dr. Famulari, Practice Problems, Spring 2010 Week 1 See Calculus Appendix, CA.3 or Machina Handout A. Find the first and second derivatives for the following functions of x. (1) f(x) = a+bx+cx 2 +dx 3 (2) f(x) = ln(4x 3 ) B. Let z = 4x 4 y 3 -5x 2 y+xy 2 (1) Derive the first and second partial derivatives for z. What is true about the cross partials? (2) Derive the total differential of z C. Calculate the slope and the elasticity of the following functions. See Perloff 2.5 (Chpt 2, section 5) for a review of elasticity. (1) f(x)=3+4x (2) f(x)=12+5x (3) f(x)=10x 2 (4) f(x)=2x 3 (5) What types of functions have constant slope? constant elasticity? D. Solve the following : 2 2 max x yx x - (1) What is (are) the choice variable(s)? (2) What is the solution function? (3) What is the optimal value function (the maximal value of the function). E. A consumer is asked to rank order the commodity bundles below (see class notes): X Y Bundle A 9 3 Bundle B 25 1 Bundle C 4 2 (1) For the consumer’s preferences to be rational, what conditions MUST hold? (2)

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PS1 SP100 - Econ 100A Dr Famulari Practice Problems Spring...

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