Economics 2010a Fa2003 Edward L. Glaeser ecture 2
Economics 2010a Fall 2003 Edward L. Glaeser Lecture 2
2. Choice and Utility Functions Choice in Consumer Demand Theory and Walrasian Demand b. Properties of demand from continuity and properties from WARP C. Representing Preferences with a Utility Function d. Demand as Derived from Utility Maximization e. Application: Fertility
2. Choice and Utility Functions a. Choice in Consumer Demand Theory and Walrasian Demand b. Properties of demand from continuity and properties from WARP c. Representing Preferences with a Utility Function d. Demand as Derived from Utility Maximization e. Application: Fertility
x i denotes commodities continuous numbers x=(x1, x2,..xL) vector of discrete commodities p=(p1, p2,.pr) vector of prices w= wealth available to be spent The budget constraint pox ∑ Pix≤w
xi denotes commodities, continuous numbers x x1, x2,.... xL vector of discrete commodities p p1, p2,....pL vector of prices w wealth available to be spent The budget constraint p x i1 L pixi w
MWG Definition 2.D. 1 The Walrasian Budget set Bpm={x∈界:p·x≤w} is the set of all feasible consumption bundles for the consumer faces market prices p and has wealth w Note: We will be treating all prices and consumption levels as being weakly posItive. Prices are treated as exogenous-as they will be in the production case. While neither consumer nor producer chooses prices (generally) prices are the extra parameter in each sides problem that ensures that demand and supply are equal Non-linear prices are certainly possible
MWG Definition 2.D.1 The Walrasian Budget Set Bp,w x L : p x w is the set of all feasible consumption bundles for the consumer faces market prices p and has wealth w. Note: We will be treating all prices and consumption levels as being weakly positive. Prices are treated as exogenous– as they will be in the production case. While neither consumer nor producer chooses prices (generally) prices are the extra parameter in each side’s problem that ensures that demand and supply are equal. Non-linear prices are certainly possible
(example 2. D 4 The Walrasian Demand function is the set C(Bp, w)which is defined for all (p, w), or at least for a full dimensional subset L+1 (P,)∈9 We generally assume that C(Bp, w) has a single element(for convenience) but it doesnt need to We write (Bp.w)=x(p, w)=(xi(p, w),.xL(p, w) We will also generally assume that demand is continuous and differentiable MWG Definition 2.E1: The Walrasian Demand function is
(example 2.D.4). The Walrasian Demand Function is the set CBp,w which is defined for all p,w, or at least for a full dimensional subset p,w L1 We generally assume that CBp,w has a single element (for convenience) but it doesn’t need to. We write CBp,w xp,w x1p,w,... xLp,w We will also generally assume that demand is continuous and differentiable. MWG Definition 2.E.1: The Walrasian Demand Function is