1. Consider the following utility function: U = min[4;r, 33;). Answer the following questions. (a) Assume that Py = 3. Solve for the optimal consumption of a: in terms of PI and I. (b) Draw the demand curve that is described by this equation1 assuming at income is equal to $30. Mark a couple of points on the graph. (0) Draw the Engel curve associated with this equation, assuming the price of :1: is equal to $1. Mark a couple of points on the graph. 2. Assume Sarah has a utility function of the following form U = 3x + 2y. Answer the following questions. (a) What is Sarah's optimal consumption bundle assuming her income is $15 and the prices of :1: cookies and y cookies are $0.50 and $1 respectively. (b) Graph Sarah's demand curve for a: if he price of y is $1 and income is equal to $10. Hint: this graph will be a bit different than you've seen before. (c) Graph Sarah's Engel curve for :1: assuming the price of a: is $1 and the price of y is $1. 3. Consider the example we did in with the utility function U = ding. (a) Solve for the optimal bundle when P3 = 2, Pg 2 1 and I = 20 (you can refer back to the demand curves we derived in class to do this quickly). Draw the optimal consumption bundle on a graph with the budget constraint and indifference curve. Solve for the value of utility this consumer gains with this bundle. (b) Solve for the optimal bundle when P5,: = 1, Pg = 1 and I = 20. Draw the optimal consumption bundle on a graph with the budget constraint but omit the difference curve