OPTIONAL PROBLEM SET 1 ECONOMICS 200A R. R. RUSSELL FALL 2008
1. Show that, if continuity (C5) is not assumed, each of the following statements is false: (a) (C7)' (C7). (b) (C7)" (x) is convex for all x X. 2. Show that strict convexity of (x) re
HOMEWORK ECONOMICS 200A V. PRODUCER THEORY R. R. RUSSELL 1. The single-output production function is f (x) = x1 x2 , 1 2 where , 1 and 2 are positive parameters satisfying 1 + 2 < 1. (a) Derive the cost function. (b) Derive the profit function and th
HOMEWORK ECONOMICS 200A IV. TOPICS IN DEMAND THEORY R. R. RUSSELL FALL 2008
1. Do the two assignments on page 41 of the overhead handouts, mathematically if you have the time and inclination, graphically if you don't. 2. In leisure/income space, (a)
HOMEWORK ECONOMICS 200A III. DEMAND THEORY AND DUALITY R. R. RUSSELL FALL 2008
1. Consider the following three utility functions: U (x1 , x2 ) = (x1 )1/2 + x2 , U (x1 , x2 ) = x1 + ln x2 U (x1 , x2 ) = (x1 - ) x2 , > 0.
(a) Restricting prices to t
HOMEWORK ECONOMICS 200A II. PREFERENCE AND UTILITY THEORY R. R. RUSSELL FALL 2008
1. Prove the following: (a) Reflexivity, transitivity, and connectedness of weak preference imply irreflexivity, transitivity, and asymmetry of strict preference and r