Please answer these questions

1. (7 points) Rachel has the utility function u(x, y) = Zlnx2 + lny. (a) (3 points) Find the utility maximizing bundle if both prices are $2 and the income is 100. (b) (4 points) Suppose that the price of the rst good falls to $1 and the price of the second rises to $3. Find the CV from the price change. 2. (6 points) Abigail has the utility function u(l, c) = l + C which is dened over leisure l and consumption 6. She has T = 80 hours to use in leisure or working W, so that W + l = 80. For each hour she works, she gets $5. The price of consumption is $10 per unit. She also has a xed non-wage income of $ 100. (a) (3 points) Find the amount of time she will work W and the amount of consumption 6 she will choose to maximize her utility. (b) (3 points) If the hourly wage increases to $20, then what is her optimal amount of consumption and work? 3. (7 points) Monty has the following production function z = f (x, y) = 3V} + . (a) (4 points) Find the cost function as a function of the level Z of the output and px = 3 and py = 1. (b) (3 points) Find the Average Cost and marginal Cost functions as function of the output level 2 for the given input prices px = 3 and py = 1