Coursework 1 - University College London
ME: October 2006. Coursework 1
Problem 1 Graph a typical indifference curve for the following utility functions and determine whether they have convex indifference curves, that is, whether the MRS declines as x increases.
a. U(x, y) =3x+y
b. U(x, y) =x2+y
c. U(x,y) =(x2-y2)0.5
d. U(x,y) =xαyβ with α>0, β>0. This is called the Cobb-Douglas utility function
Problem 2 Provide examples of utility functions that imply the same ranking over bundles of goods as U(x,y) = xy. Check that the MRS is the same in all the examples that you provide.
Problem 3 Many advertising slogans seem to be asserting something about people’s preferences. How would you capture the following slogans with a mathematical utility function?
- Promise margarine is just as good as butter
- Things go better with coke
- Krispy Kreme glazed doughnuts are just better than Dunkin
- Miller Brewing advises us to that drinking too much beer is not good for us
Problem 4 An individual is consuming 5 apples and 20 pears. We define the marginal rate of substitution as the rate that he is willing to trade pears for an additional apple. At the consumption bundle 5 apples and 20 pears, his Marginal Rate of Substitution is 4.
a. Will he be better off consuming 6 apples and 20 pears than consuming 5 apples and 20 pears?
b. Will he be better off consuming 6 apples and 15 pears than consuming 5 apples and 20 pears?
c. Will he be better off consuming 7 apples and 16 pears than consuming 5 apples and 20 pears?
d. Will he be better off consuming 6 apples and 16 pears than consuming 5 apples and 20 pears?
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