Αποτελέσματα Αναζήτησης
7. Hicksian Demand (25 points) An agent consumes quantity (x1;x2) of goods 1 and 2. She has utility u(x1;x2) = x1x22 The prices of the goods are (p1;p2). (a) Set up the expenditure minimisation problem. (b) Derive the agent’s Hicksian demands. (c) Derive the agent’s expenditure function. Solution (a) The agent minimises L = p1x1 +p2x2 ...
The solution to this problem is called the Hicksian demand or compensated demand. It is denoted by hi(p1;:::;pN;u) The money the agent must spend in order to attain her target utility is called her expenditure. The expenditure function is therefore given by e(p1;:::;pN;u) = min x1;:::;xN XN i=1 pixi subject to u(x1;:::;xN) ‚ u xi ‚ 0 for all i
(b) Show that the Hicksian demand functions for goods 2,...,n are independent of the target utility. (c) Argue that the indirect utility function can be written in the form v(p,w) = w+φ(p)
Connections between Walrasian and Hicksian demand functions. The direct e¤ect of the parameter q is on both the value of evaluated at the maximizer x (q) but also on the constraints. In the consumer s problem, the entire di¤erential e¤ect of price and wage changes on indirect utility occurs via the budget constraint.
Walrasian and Hicksian demand coincide if computed according to the same prices, income, and utility. The proposition implies that e(p;v(p;w)) = w and v(p;e(p;v)) = v so for a –xed price vector p, the functions e(p;) and v(p;) are inverses of each other.
1.4 Marshallian and Hicksian demand Alfred Marshall was the first economist to draw supply and demand curves. The ‘Marshallian cross’ is the staple tool of blackboard economics. Marshallian demand curves are simply conventional market or individual demand curves. They answer the question:
Hicksian (or Compensated or Utility constant demand functions) yield the amount of good x1 purchased at prices p1 and p2 when income is just high enough to get utility level u0. For Hicksian demand, utility is held constant.
