Question

Alice consumes bread and cheese. Bread is sold in an unusual way, x1 units of Bread will cost Alice x2 dollars. Cheese is sold in a usual way at a price of $1 per unit. Her income is $25 and his utility function is u(x1 , x2 ) = 2x1 + x2 , where x1 is his consumption of bread and x2 is his consumption of cheese.

1. Write the equation for Alices burget set and then sketch it

2. Compute the marginal utilities for each good and then the MRS. Explain the meaning of these numbers.

3. Sketch some of the indifference curves

4. Calculate the amount of cheese and the amount of Bread that Alice demands at these prices

   and this income (Hint: you can use substitution or Lagrangian method)

Now consider that the price of good one is given by (x^2)1. Answer the four previous questions for this case.

Answer 1

The budget line is given by:

Marginal utilities have been derived below:

Marginal utility means utility derived from consuming one additional unit of a commodity.

At equilibrium, marginal rate of substitution is equal to the ratio of prices of the two goods,

Substituting the value in the consume's budget line: