problem-set-4

# G u x y min 2 x x y 5 m 10 p x 1 p y 0 5 p x 5 p y 5

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(g) u ( x, y ) = min { 2 x, x + y + 5 } , m = 10 , ( p x = 1 , p y = 0 . 5) ( p x = 5 , p y = 0 . 5) . (h) u ( x, y ) = min { 2 x, x + y + 5 } , m = 10 , ( p x = 5 , p y = 1) ( p x = 0 . 5 , p y = 1) . (i) u ( x, y ) = min { 2 x, x + y + 5 } , ¯ x = 5 , ¯ y = 10 , ( p x = 1 , p y = 0 . 5) ( p x = 5 , p y = 0 . 5) . 3. Consider an individual who lives two periods. His first period income is y 1 = 1000 and second year income is y 2 = 100. His utility is defined on cunsumption in two periods and given as u ( c 1 , c 2 ) = c 1 / 2 1 c 1 / 2 2 where c 1 , c 2 are the first and second period consumptions respectively. (a) Find the individual‘s consumption and saving decisions for the two periods as a function of the interest rate. (b) Suppose the interest rate was r = 0 . 5 and increased to r = 0 . 9. Calculate the income (both ordinary and endowment) and substitution effects for both Slutsky and Hicks. (c) Comment on income effect depending on individual‘s position as a net bor- rower or lender. 1

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4. (Labor Supply) Consider an individual who allocates 20 hours of her time between leisure ( l ) and work through which she earns money for her consumption ( c ) everyday. Her utility function is u ( c, l ) = c.l nad the hourly wage rate is denoted as w . (a) Derive her daily consumption and supply of labor as functions of the current wage rate.
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