Question

Jack and Jill are in the checkout line at Walmart. In Jack’s basket he has 4 DIGIORNO Original Thin Crust Supreme Frozen Pizza and 2 half-gallons of Blue Bell Chocolate Chip Cookie Dough. Jill has in her basket 6 of the DIGIORNO pizzas and 1 half-gallon of the Blue Bell ice cream. You know that the pizza are selling for $5.00 each while ice cream costs $4.00 per half-gallon. If both Jack and Jill are utility maximizers, which of the following statements is incorrect.

1. Jack and Jill have different budgets to spend on pizzas and ice cream.
2. Given what is in his basket, Jack’s marginal utility for pizzas is 1.25 his marginal utility for ice cream.
3. Jill’s marginal rate of substitution between pizzas and ice cream is larger than Jack’s since she has more pizzas than ice cream in her basket compared to the ratio in Jack’s basket.
4. Given what is in her basket, Jill’s marginal utility for ice cream is 0.8 her marginal utility for pizzas.
5. All the above are correct.

Answer 1

Price of pizza = $5

Price of icecream = $4

• Jack's basket has 4 pizza and 2 half-gallon ice cream.

Jack's budget to spend on pizzas and icecream = ($5 * 4) + ($4 * 2) = $28

• Jill's basket has 6 pizzas and 1 half-gallon of icecream

Jill's budget to spend on pizzas and icecream = ($5 * 6) + ($4 * 1) = $34.

They both have a different budget to spend on pizzas and ice cream.

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Jack maximizing utility at the following point:

(MUp / MUic) = (Price of pizza / Price of icecream)

Where MUp is the marginal utility of pizza and MUic is the marginal utility of icecream.

(MUp / MUic) = ($5 / $4)

(MUp / MUic) = 1.25

MUp = 1.25 * MUic

Jack’s marginal utility for pizzas is 1.25 his marginal utility for ice cream.

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MRS between pizza and icecream = (MUp / MUic)

Jack's MRS = 1.25

Jill's MRS = (MUp / MUic) = (Price of Pizza / Price of icecream)

Jill's MRS = (MUp / MUic) = ($5 / $4)

Jill's MRS = (MUp / MUic) = 1.25

Hence, Jill's MRS is 1.25

So, both Jack and Jill has same MRS.

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Jill's MRS = (MUp / MUic) = (Price of Pizza / Price of icecream)

Jill's MRS = (MUp / MUic) = ($5 / $4)

Jill's MRS = (MUp / MUic) = 1.25

=> MUic = (MUp / 1.25)

=> MUic = 0.8 MUp

Jill’s marginal utility for ice cream is 0.8 her marginal utility for pizzas.

Answer: Option (C) i.e., the statement given in option C is incorrect.