Questions: At all Sports Bar, a bottle of beer costs 4; a slice of pizza costs 2; Jimmy has 10 to spend for beer and pizza; Jimmy will consume slices of pizza and bottles of beer A) 5: 0 B) 3: 1 C) 4: 3 D) 1: 2

The answer is B: 3 slices of pizza and 1 bottle of beer.

To determine the optimal combination of pizza and beer that Jimmy should consume, we need to consider the marginal utility per dollar spent on each item. This is calculated by dividing the marginal utility of each item by its price.

1. Marginal Utility per Dollar for Pizza:

   • 1st slice: \( \frac{100}{2} = 50 \)
   • 2nd slice: \( \frac{80}{2} = 40 \)
   • 3rd slice: \( \frac{60}{2} = 30 \)
   • 4th slice: \( \frac{40}{2} = 20 \)
   • 5th slice: \( \frac{20}{2} = 10 \)

2. Marginal Utility per Dollar for Beer:

   • 1st bottle: \( \frac{400}{4} = 100 \)
   • 2nd bottle: \( \frac{200}{4} = 50 \)
   • 3rd bottle: \( \frac{80}{4} = 20 \)
   • 4th bottle: \( \frac{30}{4} = 7.5 \)
   • 5th bottle: \( \frac{20}{4} = 5 \)

Jimmy has $10 to spend. We need to maximize his total utility by choosing the combination of pizza and beer that gives the highest marginal utility per dollar.

Let's start by selecting the highest marginal utility per dollar:

• The 1st bottle of beer gives the highest marginal utility per dollar (100), so Jimmy buys 1 bottle of beer for $4.
• Jimmy has $6 left. The next highest marginal utility per dollar is the 1st slice of pizza (50), so he buys 1 slice of pizza for $2.
• Jimmy has $4 left. The next highest marginal utility per dollar is the 2nd slice of pizza (40), so he buys 1 more slice of pizza for $2.
• Jimmy has $2 left. The next highest marginal utility per dollar is the 3rd slice of pizza (30), so he buys 1 more slice of pizza for $2.

Now Jimmy has spent all his $10:

• 1 bottle of beer: $4
• 3 slices of pizza: $6

Therefore, Jimmy will consume 3 slices of pizza and 1 bottle of beer.