Question

This question examines the utility that a consumer derives from consuming various quantities of two different goods. You will identify the consumer’s utility-maximizing bundle and calculate the total utility associated with consuming a particular bundle of the two goods.

Suppose Steven has an allowance of $14 and he consumes only pineapples and pretzels. Below you are provided with the marginal utility that each unit of the two goods offers Steven.

Pineapples Quantity of Pineapples Marginal Utility 1 36 2 32 3 24 4 12

Pretzels Quantity of Pretzels Marginal Utility 1 36 2 28 3 16 4 2

Task 1: Suppose the price of a pineapple is $2 and the price of a pretzel is $6. How many of each will Steven purchase with his $14?

Task 2: Suppose the price of a pineapple is $2 and the price of a pretzel is $6. When Steven purchases his utility-maximizing bundle, how much utility does he receive?

Task 3: Suppose the price of a pineapple is $4 and the price of a pretzel is $2. How many of each will Steven purchase with his $14?

Task 4: What is the maximum amount of utility that Steven can enjoy from purchasing pineapples and pretzels?

Answer 1

1)

Pineapple	Pretzels
Quantity of pineaaples	MUa	MUa/Pa	Quantity of pretzels	MUp	MU p/Pp
1	36	18	1	36	6.00
2	32	16	2	28	4.67
3	24	12	3	16	2.67
4	12	6	4	2	0.33

Steven will prefer the good where marginal utility per dollar spent is higher amongst the avaiable options to maximize utility.

(MU/P) for first four units of pineapple is greater than or equal to (MU/P) for first unit of Pretzels. So, Steven will choose 4 units of pineaaple and 1 unit of Pretzels.

Amount needed for this consumption=4*2+1*6=$14

Which is equal to given budget. So, utility maximizing consumption requires 4 units of pineapples and 1 unit of pretzel.

2)

Utility gained from pineapples=36+32+24+12=104

Utility gained from pretzel=36

Total utility=104+36=140 utils

3)

Pineapple	Pretzels
Quantity of pineaaples	MUa	MUa/Pa	Quantity of pretzels	MUp	MU p/Pp
1	36	9	1	36	18.00
2	32	8	2	28	14.00
3	24	6	3	16	8.00
4	12	3	4	2	1.00

Steven will prefer the good where marginal utility per dollar spent is higher amongst the avaiable options to maximize utility.

(MU/P) for first 2 units of pritzel is greater than or equal to (MU/P) for first unit of Pineapple. So, Steven will choose 1 units of pineaaple and 2 unit of Pretzels.

Amount needed for this consumption=1*4+2*2=$8

Now (MU/P) for second unit of pineapple is equal to 3 rd unit of pritzel. Stevel will go for 3rd unit of Pritzel and 2nd unit of pineapple.

Amount needed for this consumption=2*4+3*2=$14

Which is equal to given budget. So, utility maximizing consumption requires 2 units of pineapples and 3 units of pretzel.

Utility gained from pineapples=36+32=68

Utility gained from pretzel=36+28+16=80

Total utility=68+80=148 utils

4)

Maximum utility from pineaaple=36+32+24+12=104

Maximum utility from pritzels=36+28+16+2=82

Total maximum utility=104+82=186 utils