Emilie Chang

9/19/2001

Econ 360

 

Homework 2

 

1)

According to the budget constraint line, Bobby is better off with the $300 dollar gift certificate.  He is able to purchase more books if he needs to.  However, Bobby cannot purchase more pizza (which is represented by the dotted line graph) than before because the gift certificate is only for books.  He has the same pizza purchasing power as before.  So if Bobby prefers pizza over books, he is not better off.

 

2)

 

This is the poor person’s budget constraint line before receiving the food stamps where Pf is the price of food and Po is the price of the other good.

 

This is the poor person’s budget constraint line after receiving the food stamps and before selling them on the black market.  Although this person is able to purchase more food, the person cannot purchase more of the other good (which is represented by the dotted line graph) since food stamps may not be used for anything else other than food.

 

After selling the food stamps on the black market for a value less than the face value, the budget constraint line decreases from the top most curve to the middle curve, X.  Since the person cannot sell the food stamps for its face value, the person’s budget constraint line will be to the left of the budget constraint line that includes the face value of the food stamps.  But since the person now has a higher income then his/her initial income of $1000, the budget constraint line will be to the right of the initial budget constraint line, thus placing it in the middle of each.

 

3) x = 10; U(x,y) = 255; U(x,y) = 5xy

 

    U(x,y) = U(10,y) = 255 = (5)(10)y

                                     255 = 50y

                                     y = 255/50

                                     y = 5.1

 

The individual must consume 5.1 units of y.

 

   x = 15; y = 3

 

   U(x,y) = U(15,3) = (5)(15)(3)

                               = 225

                            U = 225

 

The first combination of x and y (U(10,5.1)) would be preferred over the second combination (U(15,3)) because U(10,5,1) = 255 and U(15,3) = 225.  255 is greater than 225 and thus is a combination with greater utility.

 

Chapter 3; Exercises 3 and 11

 

3)

Philip is already bought 3 tapes.  His budget restraint line at this point is shown above.

 

With the rest of the $70, Philip has decided to purchase another tape and 4 CD’s.  His consumption choice is represented by the budget constraint line above.

 

11)

a)

b) If U(m,p) = 2m + p, any combination of meat and potatoes will maximize her utility.  When two goods are perfect substitutes of each other, the slope of the curve, which is the utility, is constant.  U(m,p) = 2m + p is a linear equation, thus making the indifference curve linear with a constant slope.  A constant slope results in a constant utility with any pair of points (combination of meat and potatoes).

 

c)

After the first 20 pounds of potatoes, Connie gains more potato purchasing power because she is given 10 free pounds of potatoes.  Thus, her budget constraint line shifts upward only after she purchases 20 pounds of potatoes.  Connie still does not have more meat purchasing power (represented by the dotted line curve) than she has previously.

 

d)

Connie’s budget constraint pivots on the x – axis from 100 pounds of potatoes to 50 pounds of potatoes.  Due to the increase in the price of potatoes, she can no longer purchases as many potatoes as she used to.  Since the price of potatoes per pound decreased while the price of meat per pound and Connie’s income remained the same, her utitity per potato has also increased.  However, each good is still a perfect substitute of each other and thus has a constant slope.  Therefore, any combination of meat and potatoes will maximize her utility as long as is remains on the indifference curve and the budget constraint line.