ECON 356

Homework Assignment Two

Due Thursday, Sept. 23 at the beginning of class.

Directions:  Copy and paste this into a word document and then type your answers.  Graphs do not have to be typed - PLEASE - when you copy this into a word document, leave enough space between questions so that you can put your graphs (answers) below the question you are answering - not on a separate sheet of paper.

(40 pts.) and (9 pts. extra credit - optional)

1.  Assume the following about Sue:  Her income per week is $120.  The price of a cup of coffee is $4.00 (she drinks fancy coffee that is a normal good). 

    a.  Right now she is drinking 14 cups of coffee per week.  Draw Sue's budget constraint and indifference curve with this information (use the composite good on the other axis with a price = $1).  Be sure to label everything (you should have four different numbers on your graph). (3 pts.)

    b.  Then Sue loses a part-time job she had and her weekly income goes to $100.  Sandy cuts back to 10 cups of coffee per week.  Show this on your graph (the same graph) -- label your new points (so you should now have a total of 8 numbers on your graph).  (3 pts.)

    c.  Now the price of coffee decreases to $3.50 per cup (she buys 12 cups), then $3.00 per cup (she buys 15 cups), then $2.50 per cup (she buys 16 cups).  On a new graph, show how the budget constraint and indifference curves change (starting with a price of $4 and quantity of 10 cups) - plotting the preferred bundles.  You don't have to plot the composite good amount - just the coffee.  Then draw in your price consumption curve.  (5 pts.).

    d.  Now derive Sue's demand curve for coffee -- make sure you put both prices (all 4 of them) and consumption numbers on your graph.  (3 pts.)

3.  Using the same information in the problem above regarding Sue -- with one exception:  we are now looking at the preferences of Sam -- who views coffee as an inferior good.  Answer a - b as above.  Assume that in "b" Sam increases his consumption of coffee to 18 cups per week. (For a - b, 6 pts.)

4.  Bob has a weekly income of $20, all of which he spends on French fries and hamburgers, whose respective prices are $1 and $4.  His total utility from these purchases is given by U(F) + U(H). 

If the values of U(F) and U(H) are as shown in the table.

a.  Fill out the following table. (5 pts.)

b.  Is Bob a utility maximizer if he buys 3 French fries and 4 hamburgers?  Explain your answer.  (3 pts.)

c.  If Bob is not maximizing his utility, how should he reallocate his income?  Explain your answer.  (4 pts.)

5.  According to standard theory, a change in quantity demanded by a person due to a change in price is made up of two different effects - the substitution effect and the income effect. 

a.  Assume that Bob is buying 20 steaks per month at a price of $20 each.  Draw a budget constraint and indifference curve - put the quantity of steaks on your graph (use a composite good for your other axis - and he is buying 50 units of it - put this on your graph too).  Label pt. A where Bob is maximizing his utility subject to his budget constraint.  (3 pts.)

b.  Then the price of steak drops to $15 each.  Show what will happen to Bob's budget constraint and indifference curve -- clearly separate out the substitution effect and how you derived it (label A to B) and the income effect (label B to C).  Assume steaks are a normal good and that Bob ends up buying 28 steaks after the price drop. (5 pts.)

c.  How would your graphical analysis differ if steaks were an inferior good?  Show this graphically.  Start with the same information (price goes from $20 to $15) - demand starts at 20 -- then choose your own final demand after the price drops (make sure it makes sense from the quantity demanded when steaks were a normal good). Show both the substitution and income effects.  (5 pts.)  Since we didn't quite get this far - this is extra credit - optional.

d.  Now - on the same graph - derive Bob's demand curves from the information above -- one when steaks are a normal good and one when steaks are an inferior good.  Put all numbers on your graph.  Hint:  both of your curves will go through the data point at a price of $20 and quantity demanded of 20 steaks. (4 pts.)  Since we didn't quite get this far - this is extra credit - optional.