# 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 =…