Demand and Consumer Surplus
There is a seller of a commodity, measured by variable x, and this seller has 40 units to offer. The consumer will spend some money on buying the commodity and then retain the leftover money, measured by variable m. This consumer’s preferences can be represented, at least on the range of consumption we are studying, by the function
u(x, m) = 100x − x2 + m.
The consumer’s income is 1250. Remember: stay within the model. The utility function completely describes the agent’s behavior. There are no side-deals between consumer and seller; this model contains no social relations of any kind.
1) Find the formula for the consumer’s demand of x when that demand is interior, that is, when the Lagrange formula is valid.
Hvordan er det helt man skal finde svar til opgave 1?