Question

7. Use the following table to answer the questions below.

Quantity Consumed                   Total Utility                    Total Utility

     (per week)                            of Pizza                       of Pepsi

            0                                         0                                     0

            1                                     242                                 668

            2                                     552                               1200

            3                                     792                               1632

            4                                     996                               2016

            5                                 1176                               2316

            6                                 1344                               2556

            7                                 1506                               2712

            8                                 1626                               2736

            9                                 1728                               2664

            10                                 1818                               2448

Answer the following questions. Assume that the price of pizza is $1 per slice and the price of a large Pepsi is $2.

1.         Calculate the marginal utility of each unit of pizza and Pepsi.

           

2.         Using the prices mentioned above, calculate the marginal utility per dollar of pizza and Pepsi.

           

3.         With $20 to spend per week, what amount of pizza and Pepsi will maximize satisfaction?
   (Find the utility-maximizing combination of pizza and Pepsi).

4.         What is the total amount of utility from the combination computed in part C, i.e. the total utility from the pizza
               slices plus the total utility from Pepsis?

           

5.         Given your answer in C, explain why buying two more slices of pizza and 1 less Pepsi makes the person
               worse off.

Answer 1

Quantity consumed per week	Total utility of pizza	Total utility of pepsi	MU of pizza	MU of pepsi	MU of pizza per dollar	MU of pepsi		Units of pizza	Units of pepsi	MC $	TC $
0	0	0	-	-				0	1	2	2
1	242	668	242	668	242	334		0	1	2	4
2	552	1200	310	532	310	266		1	0	1	5
3	792	1632	240	432	240	216		1	0	1	6
4	996	2016	204	384	204	192		1	0	1	7
5	1176	2316	180	300	180	150		0	1	2	9
6	1344	2556	168	240	168	120		1	0	1	10
7	1506	2712	162	156	162	78		0	1	2	12
8	1626	2736	120	24	120	12		1	0	1	13
9	1728	2664	102	-72	102	-36		1	0	1	14
10	1818	2448	90	-216	90	-108		1	0	1	15
								0	1	2	17
								1	1	3	20
								8	6
								pizzas	pepsi
Price of pizza is $1 per slice
Price of pepesi is $2
Budget is $20
MU of pizza per dollar	MU/price of pizza
MU of pepsi per dollar	MU/price of pepsi
First compare MU/$ for pizza, Mu/$ for pepsi, which is 242 for pizza and 334 for pepsi. The MU per dollar for pepsi is higher. So the consumer will buy one unit of Pepsi, enter 0 for pizza and 1 forpepsi in the table.
Next compare MU/$ for pizza, Mu/$ for pepsi, which is 242 for pizza and 266 for pepsi. The MU per dollar for pepsi is higher. So the consumer will buy one unit of Pepsi, enter 0 for pizza and 1 forpepsi in the table.
Next compare MU/$ for pizza, Mu/$ for pepsi, which is 242 for pizza and 216 for pepsi. The MU per dollar for pizza is higher. So the consumer will buy one unit of Pizza, enter 1 for pizza and 0 for pepsi in the table.
Next compare MU/$ for pizza, Mu/$ for pepsi, which is 310 for pizza and 216 for pepsi. The MU per dollar for pizza is higher. So the consumer will buy one unit of Pizzai, enter 1 for pizza and 0 for pepsi in the table.
Next compare MU/$ for pizza, Mu/$ for pepsi, which is 240for pizza and 216 for pepsi. The MU per dollar for pizza is higher. So the consumer will buy one unit of Pizza, enter 1 for pizza and 0 for pepsi in the table.
Next compare MU/$ for pizza, Mu/$ for pepsi, which is 204for pizza and 216 for pepsi. The MU per dollar for pepsi is higher. So the consumer will buy one unit of Pepsi, enter 0 for pizza and 1 for pepsi in the table.											6
Next compare MU/$ for pizza, Mu/$ for pepsi, which is 204 for pizza and 192 for pepsi. The MU per dollar for pizza is higher. So the consumer will buy one unit of Pizza , enter 1 for pizza and 0 for pepsi in the table.
Next compare MU/$ for pizza, Mu/$ for pepsi, which is 180 for pizza and 192 for pepsi. The MU per dollar for pepsi is higher. So the consumer will buy one unit of Pepsi , enter 0 for pizza and 1 for pepsi in the table.											8
Next compare MU/$ for pizza, Mu/$ for pepsi, which is 180 for pizza and 150 for pepsi. The MU per dollar for pizza is higher. So the consumer will buy one unit of Pizza , enter 1 for pizza and 0 for pepsi in the table.											9
Next compare MU/$ for pizza, Mu/$ for pepsi, which is 168 for pizza and 150 for pepsi. The MU per dollar for pizza is higher. So the consumer will buy one unit of Pizza , enter 1 for pizza and 0 for pepsi in the table.
Next compare MU/$ for pizza, Mu/$ for pepsi, which is 162 for pizza and 150 for pepsi. The MU per dollar for pizza is higher. So the consumer will buy one unit of Pizza , enter 1 for pizza and 0 for pepsi in the table.
Next compare MU/$ for pizza, Mu/$ for pepsi, which is 120 for pizza and 150 for pepsi. The MU per dollar for pepsi is higher. So the consumer will buy one unit of Pepsi , enter 0 for pizza and 1 for pepsi in the table.
Next compare MU/$ for pizza, Mu/$ for pepsi, which is 120 for pizza and 120 for pepsi. The MU per dollar for pizza and pepsi is same and there is enough money to buy both. So the consumer will buy one unit of Pepsi , enter 0 for pizza and 1 for pepsi in the table.
He will buy 8 slices of pizza and 6 large pepsis
d)
Total utility is
Pizza is 1626 from 8 pizzas
Pepsi is 2556 from 6 pepsis
Total utility 4182
e) Total will be 4134 which is less than 4182
So the consumer is worse off.