Homework #3
1. Suppose Sammy only consumes 2 goods, wooden pencils and mechanical pencils. Also, Sammy considers two wooden pencils to be a perfect substitute for one mechanical pencil.
(a) Draw a few of Sammy's indifference curves (at least four).
(b) Suppose that Sammy makes $12 dollars per week and that mechanical pencils each cost $3 and that wooden pencils each cost $2. Draw Sammy's budget line. What is the equation of this line?
(c) What is Sammy's optimal consumption bundle? How many wooden pencils and how many mechanical pencils will Sammy consume each week?
2. Using table (1), suppose that apples cost $1 each and tacos cost $2 each. If Sally has income equal to $9, how much of each will she consume and why?
|
Apples
|
Tacos
|
|
Quantity
|
Total Utility From Apples
|
Quantity
|
Total Utility From Tacos
|
|
0
|
0
|
0
|
0
|
|
1
|
5
|
1
|
10
|
|
2
|
9
|
2
|
18
|
|
3
|
12
|
3
|
24
|
|
4
|
15
|
4
|
28
|
|
5
|
16
|
5
|
30
|
Table 1: Sally's utility from taco and apple consumption.
3. Suppose Jane consumes two goods, x and y. The utility that Jane receives from consuming these two goods is given by U (x, y) = xy. Thus, if she consumes 4 units of x and 5 units of y she will receive total utility equal to 5.4 = 20.
(a) Draw indifference curves for U (x, y) = 2, U (x, y) = 4, U (x, y) = 6 and U (x, y) = 8.
(b) Suppose that the price of good x is px = $4 and the price of good y is py = $2 and that Jane has income of I = $16. Draw in and give the equation for Jane's budget line. Label this budget line BL1 in your graph.
(c) Given the indifference curves you've drawn from part (a) and the bud- get line you've drawn from part (b), what is Jane's optimal consumption bundle? (Hint: look at the different possible consumption bundles on the budget line and see which one yields the highest utility. You need only check integer values for x and y).
(d) How much utility does Jane receive from this consumption bundle?
(e) Suppose now that the price of good y quadruples to py = $8. Draw the new budget line and find the new optimal consumption bundle. Label this new budget line BL2 in your graph.
(f) What is the smallest amount of income Jane would need at these new prices to get her back to her original indifference curve? (Hint: Find values of x and y that give her the same utility as in part (d). You need only check integer values of x and y. Which one of these - at the new prices - requires the smallest amount of income?)
(g) Label the original consumption bundle point A, the new consumption bundle point B and the hypothetical consumption bundle she would consume with additional income found in part (f) - label this point C.
(h) Clearly label the substitution effect on good y created by the price in-crease. How much is this amount? (Hint: The substitution and income effects will be measured as changes in good y since it is the price of good y that changes in this example.)
(i) Clearly label the income effect on good y created by the price increase. How much is this amount? (Hint: The substitution and income effects will be measured as changes in good y since it is the price of good y that changes in this example.)
(j) Is good y a normal or inferior good?