Question

) For each o the following utility functions derive direclly from the definition not using the formula(s) from class or the text- the MRS (marginal rate of substitution) of y for at the points (1, 1) and (2,4) a) a(x, y)+y (c) u(r,y)3ry

Answer 1

a) using basic intuition and not using any mathematical form (which are usually mentioned in the textbook) we can say that all the 3 functions are perfect substitutes.(here we consider u= x +y) (by definition) Now if we take (a) then we can see that x and y can be used in 1:1 proportion so definitely the marginal rate of substitution is 1. As MRS is the slope of the indifference curve and for straight line i.e. perfect substitutes case it is constant. Here it is 1.(at point (1,1) and (2,4)). as the slope is constant. Or in other words we shall get 1 unit of good x if we give up 1 unit of good y. Here the slope will be 1 irrespective of the (1,1) or (2,4) point.

b) Using the similar logic MRS of u = x+2y will be 1/2 if we take x axis as horizontal and y axis as vertical. goods will be consumed with 1:2 proportion.(irrespective of the points (1,1) or (2,4))

c) Using the similar logic MRS of u = 3x+y will be 3 if we take x axis as horizontal and y axis as vertical. goods will be consumed with 3:1 proportion.(irrespective of the points (1,1) or (2,4))