Microeconomics - Assignment Example

1b) Marginal rate of substitution of food for water is the quantity of water a consumer is willing to give up to have one additional quantity of food, keeping the level of utility unchanged. MRSw,f = MUw/MUf where MUw is marginal utility of water and MUf is marginal utility of food. The value of MUw when W=1 is 4 and value of MUf is 1 as derived from the utility function. Therefore MRSw,f = 4 which is a constant. Therefore the consumer is willing to give up 4 quantity of water to have one additional quantity of food. 1d) At the given budget constraint, the consumer optimum is that the consumer ends up buying 4 units of water and 1 unit of food.

The slope of indifference curve > the slope of budget constraint. We get the corner solution. The graph is given below: The consumer optimum is given by MRS= Pw/Pf. The MRS is 4 and the ratio of prices is 1. Therefore the marginal rate of substitution is not same as that ratio of prices. This is because the goods water and food in question are perfect substitutes. Here the consumer buys in extremes. He either buys 4units of water or 1 unit of food. With the given income of 4, he buys 4unit of water and 0 unit of food.

To get the Marshallian demands for x2 and y2 where x2 is the quantity of X good purchased by consumer 1 and y2 is the quantity of Y good purchased by consumer2, we set up a Lagrangian function: Z= u(x,y) – l(Px.X+Py.Y-M2) where l is the lambda i.e lagrangian multiplier. 2c) Suppose there are two consumers in the market. For consumer 1 the demand curve is P= a-b Q1 and for consumer 2 the demand curve is P= c-dQ2 where a,b,c,d are constant. To get the market demand curve we have to solve the individual demand curve first.

For Consumer 1 the demand is Q1= (a-P)/b and for consumer 2 the demand is Q2= (c-P)/d. The market demand is Q= Q1+Q2. Therefore Q= (a-P)/b +