Question

The following table shows​ William's total utility from consuming Pita Wraps and Bubble Tea.

Pita Wraps

Bubble Tea

Quantity	Total Utility
1	72
2	156
3	222
4	276
5	318
6	354
7	378
8	396
9	405
10	411
11	414
12	414

Quantity	Total Utility
1	60
2	126
3	180
4	230
5	276
6	318
7	354
8	372
9	381
10	387
11	390
12	390

Suppose William has​ $30 to spend on Pita Wraps and Bubble Tea. The price of a Pita Wrap is​ $6; the price of a Bubble Tea is​ $3.

What is​ William's optimal consumption​ bundle?

4 4

Pita​ Wrap(s) and

2 2

Bubble​ Tea(s)

​Now, suppose the price of a Bubble Tea increases to​ $6, and the price of a Pita Wrap does not change. Find​ William's new optimal consumption bundle.

3 3

Pita​ Wrap(s) and

2 2

Bubble​ Tea(s)

What are two points on​ William's demand curve for Bubble​ Tea?

P1​ =

​$3 3     

Q1​ =

2 2   

​[This is point A on the​ graph] (2​ pts)

P2​ =

​$6 6     

Q2​ =

2 2   

​[This is point B on the​ graph] (2​ pts)

Answer 1

Q Utility Marginal Utility

(Wraps)

1 72

2 156 84

3 222 66

4 276 54

5 318 42

6 354 36

7 378 24

8 396 18

9 405 9

10 411 6

11 414 3

12 414 0

Q Utility Marginal Utility

(Tea)

1 60

2 126 66

3 180 54

4 230 50

5 276 46

6 318 42

7 354 36

8 372 18

9 381 9

10 387 6

11 390 3

12 390 0

The optimal pointoccurs where ,

Ratio of price = Ratio of marginal utilities.

(i) In the first part, this occurs at Wraps = 2 and Tea = 6 ( where the ratio of their marginal utilities is equal to their price ratio)

(ii) In the second part ( when the price of tea changes) the optimal point occurs at Wraps = 3 and Tea = 2 ( where the ratio of their marginal utilities is equal to their price ratio)