Author Question: A consumer's utility function is given by: U(x,y) = 10xy Currently, the prices of goods x and y ... (Read 58 times)

ereecah

  • Hero Member
  • *****
  • Posts: 530
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

  • Sr. Member
  • ****
  • Posts: 299
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



Related Topics

Need homework help now?

Ask unlimited questions for free

Ask a Question
 

Did you know?

The newest statin drug, rosuvastatin, has been called a superstatin because it appears to reduce LDL cholesterol to a greater degree than the other approved statin drugs.

Did you know?

Your heart beats over 36 million times a year.

Did you know?

Autoimmune diseases occur when the immune system destroys its own healthy tissues. When this occurs, white blood cells cannot distinguish between pathogens and normal cells.

Did you know?

People who have myopia, or nearsightedness, are not able to see objects at a distance but only up close. It occurs when the cornea is either curved too steeply, the eye is too long, or both. This condition is progressive and worsens with time. More than 100 million people in the United States are nearsighted, but only 20% of those are born with the condition. Diet, eye exercise, drug therapy, and corrective lenses can all help manage nearsightedness.

Did you know?

Before a vaccine is licensed in the USA, the Food and Drug Administration (FDA) reviews it for safety and effectiveness. The CDC then reviews all studies again, as well as the American Academy of Pediatrics and the American Academy of Family Physicians. Every lot of vaccine is tested before administration to the public, and the FDA regularly inspects vaccine manufacturers' facilities.

For a complete list of videos, visit our video library