Question

Assuming each carnival game costs $1 and each Ferris wheel ride costs $2, a consumer with $16 to spend will optimally choose to consume at point...

Answer 1

The consumer with $16 to spend will optimally choose to consume at point E, where they spend $8 on carnival games and $8 on Ferris wheel rides.

Step-by-step explanation:

The consumer with $16 to spend will optimally choose to consume at point E, where they spend $8 on carnival games and $8 on Ferris wheel rides.

To find the optimal point, we need to maximize the total utility obtained from consuming carnival games and Ferris wheel rides. Since each carnival game costs $1 and each Ferris wheel ride costs $2, the consumer can buy 8 carnival games and 4 Ferris wheel rides with $16. At this point, the consumer is spending an equal amount on both activities, resulting in the optimal consumption.

In terms of the figure mentioned in the question, point E represents this optimal choice, where the consumer is consuming both carnival games and Ferris wheel rides.

Answer 2

The consumer will optimally choose to spend $1 on carnival games (buying 1 game) and $2 on Ferris wheel rides (taking 1 ride). This way, they spend a total of $3 and maximize their overall utility with the remaining $16 - $3 = $13 unspent.

To find the optimal consumption point for a consumer with $16 to spend on carnival games ($1 each) and Ferris wheel rides ($2 each), we can use the concept of marginal utility and equate the marginal utility per dollar spent for both activities. The consumer will choose the point where the marginal utility per dollar is the same for both options.

Let's calculate the marginal utility for each activity first:

1. Carnival games:

- Each game costs $1, so the marginal utility for the first game is 1 utility.

- The consumer's total utility for carnival games will increase by 1 utility for each additional $1 spent.

2. Ferris wheel rides:

- Each ride costs $2, so the marginal utility for the first ride is 1 utility.

- The consumer's total utility for Ferris wheel rides will increase by 1 utility for each additional $2 spent.

Now, we want to equate the marginal utility per dollar for both activities to find the optimal point:

Marginal Utility per Dollar for Carnival Games = Marginal Utility per Dollar for Ferris Wheel Rides

Let's denote the number of carnival games as "C" and the number of Ferris wheel rides as "F."

Marginal Utility per Dollar for Carnival Games = (Marginal Utility for Carnival Games) / (Cost of Carnival Games)

Marginal Utility per Dollar for Ferris Wheel Rides = (Marginal Utility for Ferris Wheel Rides) / (Cost of Ferris Wheel Rides)

So, we have the equations:

(1 utility) / ($1) = (1 utility) / ($2)

Now, solve for C and F:

C = 1 * $1 = $1

F = 1 * $2 = $2