If Carla maximizes her utility function ( , ) = 1^ + 2 subject to

+ = , where x1 is cheese and x2 is bread.

1. Obtain the Engel curve of good x1. Is the slope of the Engel curve positive? And

   what is the type of good x1?

2. Given that p1 is LE10, p2 is LE6 and Carlas income is LE1200, if the producer of bread decided to raise the price of his product to LE8 to increase his revenue. Is his expectation rational? Show your answer mathematically and interpret it.

3. What is the consumer surplus change after the increase of the price of bread to LE8? (Hint: it is better to use a simple integral we saw in class, since using the area of a triangle will give you an approximate answer.)

III. If Carla maximizes her utility function U(X1, X2) = 2x} + 4lnx, subject to P1X1 + P2X2 = m, where xi is cheese and x2 is bread. a) Obtain the Engel curve of good xi. Is the slope of the Engel curve positive? And what is the type of good x? b) Given that pi is LE10, p2 is LE6 and Carla's income is LE1200, if the producer of bread decided to raise the price of his product to LE8 to increase his revenue. Is his expectation rational? Show your answer mathematically and interpret it. c) What is the consumer surplus change after the increase of the price of bread to LES? (Hint: it is better to use a simple integral we saw in class, since using the area of a triangle will give you an approximate answer.) d) Find another utility function representing the same preference and prove it mathematically. e) Suppose that cheese prices increase by 10%, and the total quantity of groceries in the market increases by 8%. What is the elasticity of supply of groceries? Interpret your answer in the context of a 1% change in groceries prices. IV. where 9 Suppose the individual's utility function is U(x1, x2) = (a + + 982) 82 1/81 91,92 20 and 8 = 0. If 81 = 8z = 8. Show that a) when 8 = 1 the goods are perfect substitutes b) as 8 0 preferences tend to Cobb-Douglas with equal budget shares III. If Carla maximizes her utility function U(X1, X2) = 2x} + 4lnx, subject to P1X1 + P2X2 = m, where xi is cheese and x2 is bread. a) Obtain the Engel curve of good xi. Is the slope of the Engel curve positive? And what is the type of good x? b) Given that pi is LE10, p2 is LE6 and Carla's income is LE1200, if the producer of bread decided to raise the price of his product to LE8 to increase his revenue. Is his expectation rational? Show your answer mathematically and interpret it. c) What is the consumer surplus change after the increase of the price of bread to LES? (Hint: it is better to use a simple integral we saw in class, since using the area of a triangle will give you an approximate answer.) d) Find another utility function representing the same preference and prove it mathematically. e) Suppose that cheese prices increase by 10%, and the total quantity of groceries in the market increases by 8%. What is the elasticity of supply of groceries? Interpret your answer in the context of a 1% change in groceries prices. IV. where 9 Suppose the individual's utility function is U(x1, x2) = (a + + 982) 82 1/81 91,92 20 and 8 = 0. If 81 = 8z = 8. Show that a) when 8 = 1 the goods are perfect substitutes b) as 8 0 preferences tend to Cobb-Douglas with equal budget shares