1) Suppose the budget constraint is given by wL = pq, where L is labor hours, w is the wage, q is a consumption good and p is its price.

1) Suppose the budget constraint is given by wL = pq, where L is labor hours, w is the wage, q is a consumption good and p is its price. Each household has a unit of time, normalized to 1, that they can spend on labor, L or leisure l. The MRS is given by q 1−L . a) Using the budget constraint and time constraint solve for q,L and l. b) plot the income offer curve, Engel curve, price offer curve and demand curve for both q and L, appropriately labeling each graph. c) Provide a few sentences on the tension arising between the different goods.
2) What are the conditions on preferences that we require in order to say that a consumers choices are rational? a) List and define each one and provide a brief explanation of the problems our analysis would face if these conditions were violated. b )Can you use these definitions to say why two indifference curves with different values never cross?
3) Define the following terms and give an example: a) Pareto efficiency b) Pareto inefficiency (Discuss why it is inefficient) c) Ordinal Utility d) Cardinal Utility (Discuss why this is rarely used) e) Monotonic Transformation (example below) f) Necessary good g)Luxury good h) Giffen goods i) Suppose I have a function f(x1,x2) = √x1 +√x2. Provide two examples of monotonic transformations and two examples of transformations that are not monotonic. j) Discuss why monotonicity is required in order to have a well defined inverse demand function. Give an example when this holds and when this fails.
Running head: BUDGET CONSTRAINT 1 Budget ConstraintStudent’s nameInstitution BUDGET CONSTRAINT 2 1. a) Calculation of the q, l and IWL = PQ where w= wages, l = labor, P = price and Q =…