Question

Joaquin consumes pizza and beer. His utility function is where P is the number of pizzas and B is the number of glasses of beer. Joaquin has $30, and he plans to spend all of it on pizza and beer today. The price of one pizza is $10, and the price of beer is $3 per glass. Joaquin is allowed to purchase fractions of a pizza by buying individual slices at the same average price (thus, one quarter of a pizza would cost $2.50). Suppose the price of beer decreases to $2. The total effect is to increase pizza consumption by ____ pizzas and increase beer consumption by ____ beers.

Answer 1

Answer:

the maximum level of utility can be achieved by consuming:

1.75 pizzas x 6 beers = 10.5 utils, or

1.5 pizzas x 7 beers = 10.5 utils

Explanation:

Assuming that the utility function is U (P,B) = PB

If Joaquin wants to maximize his utility, he should he spend half his money in pizza and half his money in beer:

U = 1.5 x 5 = 7.5 utils

if the price of beer decreases from $2.50 to $2, it will result in an increase in the consumption of pizza and an increase in the consumption of beer:

If Joaquin consumes 1.75 pizzas and 6 beers, his total utility will be 1.75 x 6 = 10.5 utils

He can also obtain that level of utility by consuming 1.5 pizzas x 7 beers = 10.5 utils

All other consumption levels will result in a lower total utility:

• 2.25 pizzas x 3 beers = 6.75 utils
• 2 pizzas x 5 beers = 10 utils
• 1.25 pizzas x 8 beers = 10 utils
• 1 pizza x 10 beers = 10 utils
• 0.75 pizzas x 11 beers = 8.25 utils

Answer 2

Answer:

the maximum level of utility can be achieved by consuming:

1.75 pizzas x 6 beers = 10.5 utils, or

1.5 pizzas x 7 beers = 10.5 utils