If Leila maximizes her utility function (, y ) = ^ + y subject to + y = , where x is honey and y is bread. where the price of honey is p1 and the price of bread is p2

a) Obtain the Engel curve of good x. Is the slope of the Engel curve positive? And what is the type of good x?

b) Given that p1 is $10, p2 is $6 and Leila's income is $1200, if the producer of bread decided to raise the price of his product to $8 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 $8? (Hint: it is better to use a simple integral)

d) Find another utility function representing the same preference and prove it mathematically.

e) Suppose that honey 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.