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Unformatted text preview: Talia Bar Econ313-1 Prelim 2 Question 1 (Consumer theory) (30) A consumer has a utility function u & x , y Â¡ = x + ln & y 2 Â¡ The consumer maximizes utility subject to a budget constraint. Prices are p x = 1, p y > 0, and income is m > . a. max x + ln & y 2 Â¡ s.t x + p y y = m x â€¡ 0, y â€¡ 0. b. In an interior solution: MRS = p x p y & 1 2 y y 2 = y 2 = 1 p y & y = 2 p y . Using the budget, x = m ? p y y = m ? 2. There is an interior solution only if both x and y are positive, or m > 2. For lower levels of income, m Â² 2, there is a corner solution with x = and y = m p y . i.e. demand is: x = m ? 2, y = 2 p y if m > 2 x = 0, y = m p y if m Â² 2 . (It is also ok to write the weak inequality at the top and the strict at the bottom). c. The Engel curve is the graph of the demand for one of the goods as a function of income. Engel curves are graphed with m on the vertical axis and the quantity demanded on the horizontal axis. Use part b. to draw the graphs. (The bold curves)....
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This test prep was uploaded on 02/23/2008 for the course ECON 3130 taught by Professor Masson during the Spring '06 term at Cornell University (Engineering School).
- Spring '06