Clearly identify the solution. Show your work. You are encouraged to type your solutions. It is your responsibility to make sure that the solution is legible, correctly uploaded and viewable through the system. You may discuss the problems with classmates but you are required to write down your own solutions. Problem 1. Write down and graph the equation for the budget line when: 1. z denotes the quantity of product 1, and y denotes the quantity of product 2.The prices of goods 1 and 2 are p, = 6 and p, = 12 respectively. The individual has an income of m = 60 2. a lump-sum tax of $12 is imposed; 3. In addition to the lump-sum tax, the government decides to provide a subsidy of $6 for the first unit consumed of good 2. Problem 2. For each of the following utility functions for goods z and y 2.1. calculate the marginal of utility for z; 2.2. calculate the marginal utility for y; 2.3. calculate the marginal rate of substitution; 2.4. graph two indifference curves; identify which one yields higher utility; 2.5. using the definition of convex preferences, verify whether the preferences are convex. Choose two bundles that belong to the same indifference curve. Label them a and b. Define a third bundle that mixes one half of each of the previous ones. Label it c. Evaluate whether it is at least as good as both a and b. cufr,y) = (z2)" = (y - 3) u(z,y) = & + 2zy + y? cu(zy) =z +y ) - b e cu(z,y) =22 4+ 92