3. Now, suppose you don't know the prices and income for Lavarre's scenario. Let px be the price of good x,py be the price of good y, and m be income. a. Use the three steps from lecture to find the demand function for good x,x(px,py,m), and the demand function for good y,y(py,px,m). You must show your work (e.g., how you derive the tangency condition from the given utility function). (hint: when you come up with your demand function you should be able to plug in the prices and income from (a) and get the same answerl) b. Given the demand functions you determined, calculate and interpret pxxPyx and mx b. always eats 2 cookies wiwn me to cookies (is neuliral) c. likes ice cream bars but doesn't care about cookies (is neurral) 2. Lavarre's utility function is U(x,y)=x6y4, where x is the number of units of the x-good and y is the number of units of the y-good. The price of x is $4 and the price of y is $3. Lavarre has $30 to spend on these two goods. What is Lavarre's optimal bundle (use math and a graph to support your answer)? 3. Now, suppose you don't know the prices and income for Lavarre's scenario. Let px be the price of good x,py be the price of good y, and m be income. a. Use the three steps from lecture to find the demand function for good x,x(px,py,m), and the demand function for good y1y(py,px,m). You must show your work (e.g. how you derive the tangency condition from the given utility function). (hint when you come up with your demand function you should be able to plug in the prices and income from (a) and get the same answerl). 3. Now, suppose you don't know the prices and income for Lavarre's scenario. Let px be the price of good x,py be the price of good y, and m be income. a. Use the three steps from lecture to find the demand function for good x,x(px,py,m), and the demand function for good y,y(py,px,m). You must show your work (e.g., how you derive the tangency condition from the given utility function). (hint: when you come up with your demand function you should be able to plug in the prices and income from (a) and get the same answerl) b. Given the demand functions you determined, calculate and interpret pxxPyx and mx b. always eats 2 cookies wiwn me to cookies (is neuliral) c. likes ice cream bars but doesn't care about cookies (is neurral) 2. Lavarre's utility function is U(x,y)=x6y4, where x is the number of units of the x-good and y is the number of units of the y-good. The price of x is $4 and the price of y is $3. Lavarre has $30 to spend on these two goods. What is Lavarre's optimal bundle (use math and a graph to support your answer)? 3. Now, suppose you don't know the prices and income for Lavarre's scenario. Let px be the price of good x,py be the price of good y, and m be income. a. Use the three steps from lecture to find the demand function for good x,x(px,py,m), and the demand function for good y1y(py,px,m). You must show your work (e.g. how you derive the tangency condition from the given utility function). (hint when you come up with your demand function you should be able to plug in the prices and income from (a) and get the same answerl)