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