Tutorial 5 (MicroEconomics) px/PY

5. Marginal utility problem

Consumer has a choice of goods, x and y. X is $2 and Y is $3. How much of x and y will the UT maximizing consumer purchase with an income of $17? Show your answer graphically.

UNITS MUx MUy

1 10 5
2 8 4
3 2 3
4 2 2
5 1 2

6. Calculating utility, with graph

You are choosing between two goods, X and Y, and your total utility from each is shown below.

Units TUx TUy

1 10 8
2 18 15
3 24 21
4 28 26
5 31 30
6 33 33

a. If your income is $9 and the prices of X and Y are $2 and $1, respectively, what quantities of each will you purchase in maximizing utility.

b. Specify the amount of total utility you will realize.
c. Assume that, other things remaining unchanged, the price of X falls to $1. What quantities of X and Y will you now purchase?

7. Equilibrium price

1. A consumer is at equilibrium at one of the 4 points (A, B, C, or D) shown in Figure 1 (attached to this assignment).
a. If we know that the consumer is maximizing his/her utility, and that the price of Skittles is not the same as the price of M&M's, at what point is the consumer operating? Explain your logic.
b. If the price of M&M's is $.50 each, what is the income of the consumer described above? Explain.
c. How much does the consumer spend on M&M's? On Skittles? Explain your logic.
d. What is the price of Skittles for this consumer? Explain how you reached your answer.

8. Draw the budget line in each case. For each case, calculate the slope and then compare cases (b) through (f) to case (a).

	income	price of X good	price of Y good
(a)	100	10	5
(b)	100	10	20
(c)	100	5	5
(d)	200	10	5
(e)	50	10	5
(f)	200	20	10

9. Jack spends all of his income on books and CDs. The price of one book is $30 and the price of one CD is $20. Then, at his optimal choice of consumption, what’s the value of the slope of the indifference curve? (put the books on the X-axis and CDs on the Y-axis.)

(a) –2/3
(b) –3/2
(c) –20
(d) –30
(e) It depends on the size of his income.

Q10. The following table gives four indifference schedules of an individual

1. 
   Using graph paper, plot the four indifference curves on the same set of axes.
   
2. 
   Calculate the marginal rate of substitution of X for Y between the various points on U1
   
3. 
   On the same set of axes, draw the budget line:
   

1. 
   One with income I = $10 (call it 1), and another with I = $15 (label it 3), and with prices unchanged at PX = PY = $1
   
2. 
   One with PX = $0.50, PY = $1, and I = $10 (label it 2A)
   

Q10. The table below shows the information about Utility of Ice cream cones and Candy.

1. 
   Complete the table by filling in the blank spaces.
   
2. 
   Suppose Lilly purchases 2 ice cream cones and 1 candy bar. Is she consuming the optimal consumption bundle? If so, explain why. If not, what combination should she buy and why?
   

1. Nicole’s utility function is U(x, y) = x^1/2y^1/2. The prices are px = 1, py = 1, and income is I = 100.

(a) Find the optimal bundle (x0, y0) and show it on the graph. What is the corresponding utility level?
(b) Suppose that the price of good y increases to p1y = 4, find the new optimal bundle (x1, y1) and show it on the graph.
(c) Find the decomposition basket (xd, yd), and show it on the graph. Hint: After the price change, if Nicole’s income adjusts so she can achieve exactly the same utility level as before the price change, which bundle would she choose?
(d) Find the substitution, income, and total effects of the price change on the consumption of x and y and show them on the graph.