For each of the following situations, decide whether the bundle Lakshani is thinking about consuming is optimal or not. If it is not optimal, how could Lakshani improve her over-all level of utility? That is, determine which good she should spend more on and which good should she spend less on.
b. Lakshani has $5 to spend on pens and pencils. Each pen costs $0.50 and each pencil costs $0.10. She is thinking about buying 6 pens and 20 pencils. The last pen would add five times as much to her total utility as the last pencil
c. Lakshani has $50 per season to spend on tickets to foot-ball games and tickets to soccer games. Each football tick-et costs $10 and each soccer ticket costs $5. She is thinking about buying 3 football tickets and 2 soccer tickets. Her marginal utility from the third football ticket is twice as much as her marginal utility from the second soccer ticket
sorry first timer
Ok first timer Lisa.
We, the homework help providers, generally like to see some effort on the part of the student. We are not here to do your homework, but to guide your thinking.
But since you asked.
Optimal consumption will occur when MUx/MUy = Px/Py (where x and y are alternative goods.)
In b) let x be pens, let y be pencils. You have MUx=5, MUy=1, so MUx/MUy=5. You have Px=0.50, Py=0.10, so Px/Py = .5/.1 = 5. Finally, Lak is spending her entire budget. So, Lak's consumption is optimal.
c) let x=football, y=soccer. MUx/MUy = 2. Px/Py = 2. So far, Lak is consuming optimally. However, she is only spending $40; she still has $10 remaining. Further, there is not enough information to determine where (if anyplace) she should spend her last $10.
I hope this helps.
b. To determine if the bundle Lakshani is thinking about consuming is optimal or not, we need to compare the marginal utility per dollar spent for pens and pencils.
First, let's calculate the total utility for 6 pens and 20 pencils separately:
Total utility from 6 pens = (Utility from the first pen) + (Utility from the second pen) + ... + (Utility from the sixth pen)
Total utility from 20 pencils = (Utility from the first pencil) + (Utility from the second pencil) + ... + (Utility from the twentieth pencil)
We know that the last pen adds five times as much utility as the last pencil. So, to calculate utility, we can assign a value of 1 to the utility of the last pencil and 5 to the utility of the last pen.
Now, we can compare the marginal utility per dollar spent for pens and pencils. The marginal utility per dollar spent is the additional utility gained from spending one more dollar on a particular good. In this case, we can compare the marginal utility per dollar spent on the last pen and the last pencil.
If the marginal utility per dollar spent on the last pen is greater than the marginal utility per dollar spent on the last pencil, then the bundle Lakshani is thinking about consuming is optimal. Otherwise, she can improve her overall level of utility by reallocating her spending.
c. Similarly, to determine if the bundle Lakshani is thinking about consuming is optimal or not, we need to compare the marginal utility per dollar spent for football tickets and soccer tickets.
First, let's calculate the total utility for 3 football tickets and 2 soccer tickets separately:
Total utility from 3 football tickets = (Utility from the first football ticket) + (Utility from the second football ticket) + (Utility from the third football ticket)
Total utility from 2 soccer tickets = (Utility from the first soccer ticket) + (Utility from the second soccer ticket)
We know that the marginal utility from the third football ticket is twice as much as the marginal utility from the second soccer ticket. So, to calculate utility, we can assign a value of 1 to the marginal utility from the second soccer ticket and 2 to the marginal utility from the third football ticket.
Now, we can compare the marginal utility per dollar spent for football tickets and soccer tickets. If the marginal utility per dollar spent on the third football ticket is greater than the marginal utility per dollar spent on the second soccer ticket, then the bundle Lakshani is thinking about consuming is optimal. Otherwise, she can improve her overall level of utility by reallocating her spending.
Remember, to determine the optimal bundle, you need to compare the marginal utility per dollar spent on different goods in order to maximize overall utility.