Question

1 - John, a consumer with preferences over oranges (O) and Sauerkraut (S) that give him a utility function U=ln(O) + S.

a. Given that John has an allowance of I and faces prices of Po and Ps, use the Lagrangian Multiplier method to find his optimal consumption of O and S.

b. Demonstrate whether Sauerkraut is a normal or inferior good for John.

c. Find John’s indirect utility function. In a world where I=20, Po = 1 and Ps=2, how much O and S does John buy, and how much utility does John get?

d. Now John’ s parents offer to transfer him to an alternate reality where the only difference is the reversal of prices (There Po = 2 and Ps=1). What would this do to John’s consumption of O and S? Would John want to move to the alternate reality? Why?  

e. Using the schema – Find John’s Hicksian demand for Oranges? What envelope theorem result did you use?

f. If John have to pay to enter the alternate reality, what is the most he would pay?

Answer 1

A) Using the Lagrangean optimization method, we can solve the problem and find the optimal bundle:

B) An inferior good is a good , consumption of which decreases with an increase in the income of the individual.

We can find the derivative of the expression for S with respect to I and see if it's greater or lesser than 0. If the derivative is greater than 0, then the commodity is normal and if it is less than 0, then it is inferior.

D) In case there is a reversal of prices , then ps = 1 Po = 2

O = Ps/Po = 1/2 = 0.5

S = (I -ps)/ps = 20-1 = 1 = 19.

Now, utility will be : U = ln(0.5) + 19 = 19-0.69 = 18.31

Since utility is greater in the alternate reality therefore john would want to move to the alternate reality.