A consumer's utility function is given by: U(x,y) = 10xy ...

[ereecah]

A consumer's utility function is given by: U(x,y) = 10xy
 
  Currently, the prices of goods x and y are 3 and 5, respectively, and the consumer's income is 150.
  a. Find the MRS for this consumer for any given bundle (x,y).
  b. Find the optimal consumption bundle for this consumer.
  c. Suppose the price of good x doubles. How much income is required so that the consumer is able to purchase the original consumption bundle (if you were unable to solve d., then take a guess at what the optimal bundle is before solving this)
  d. Now that the price of good x has doubled, how much income is needed for the consumer to reach the original level of utility? Is this more or less that what you found in e.?

Question 2

An advantage of a negative income tax is that there are no disincentives to earning additional income.
 
  a. True b. False

[carojassy25]

Answer to Question 1

a. MRS = y/x
b. The MRS=MRT condition says y/x = 3/5. Plug into the budget constraint yields 3x + 3x = 150, or simply x = 25, y = 15.
c. Now the price of x is 6. To be able to purchase y=15 and x=25, this consumer will need an income of 225 which means we will need to increase her income by 75
d. The original bundle gave this person a utility of: U(25,15 )=3750. Now we wish to find how much income is needed to get this level of utility when the prices are now 6 and 5. So the first equation to consider is the indifference curve representing this utility level given by: 10xy = 3750

We also know that in order to be on this IC, the consumer will be at a point where the
MRS = MRT condition holds or: y/x = 6/5

And then plug this into the IC equation to get y = 21.2 and x = 17.7. To be able to purchase the bundle (17.7,21.2 ) the consumer will need an income of 212.2. Thus we need to give her 62.20.

Answer to Question 2

b