this is the question

Question 10 (11 points) [11 marks] Suppose the consumer's preferences over x and y are summarized by the utility function He has a total of $m available to spend on x and y at prices p, and p, per unit, respectively. When he maximizes his utility, his demand functions are calculated as x (P.. Py, m) = ptyP.P. and y" (px.Py, m) = +VP.P. 1. [4 marks] Assume that the income of the consumer is m = $180 and the price of good y is p, = $1 per unit. Find the quantity of x that he will choose to buy if p. = $16 and if p, = $4. Use these two points to sketch a reasonable price offer curve and demand curve for x in two carefully-drawn diagrams. Be sure to label your axes. 2. [4 marks] Calculate the total effect of the price increase of good x from $4 to $16 by using the Slutsky identity. Determine explicitly the substitution and income effects. 3. [3 marks] On a carefully drawn Slutsky diagram, show the total effect, substitution effect and income effect of the price change from p, = $4 to p. = $16. Label your initial point A, the final point C, and the Slutsky decomposition point B. Clearly show the coordinates for those points, as well as the coordinates of the intercepts of all relevant budget lines