I just want an idea on how to do this, so will only post one example:
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 overall level of utility? That is, determine which good she should spend more on and which good should she spend less on.
a. Lakshani has $200 to spend on sneakers and sweaters. Sneakers cost $50 per pair, and sweaters cost $20 each. She is thinking about buying 2 pairs of sneakers and 5 sweaters. She tells her friend that the additional utility she would get from the second pair of sneakers is the same as the additional utility she would get from the fifth sweater.
ok, say the marginal utility (MU) from the 2nd sneakers and 5th sweater is X. With the sneakers, she is $50 to get X, with the sweaters, she is spending $20 to get X. She MAY be better off if she spent more on sweaters and less on sneakers. (I say MAY because we don't know the MU of the 6th sweater and the purchase decision is lumpy (she cant buy 1 shoe or 1/2 of a sweater))
That said, in general, to maximize utility, a person should equate these two ratios MUx/MUy = Px/Py.
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 overall level of utility? That is, determine which good she should spend more on and which good should she spend less on (2-part answers)
a. Lakshani has $200 to spend on sneakers and sweaters. Sneakers cost $50 per pair, and sweaters cost $20 each. She is thinking about buying 2 pairs of sneakers and 5 sweaters. She tells her friend that the additional utility she would get from the second pair of sneakers is the same as the additional utility she would get from the fifth sweater.
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 football games and tickets to soccer games. Each football ticket 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.
. Lakshani has $200 to spend on sneakers and sweaters. Sneakers cost $50 per pair, and sweaters cost $20 each. She is thinking about buying 2 pairs of sneakers and 5 sweaters. She tells her friend that the additional utility she would get from the second pair of sneakers is the same as the additional utility she would get from the fifth sweater.
To determine whether the bundle Lakshani is considering is optimal or not, we need to calculate the marginal utility for each good and compare it to the price. Marginal utility refers to the additional satisfaction or utility gained from consuming one more unit of a good.
In this example, we have the following information:
- Price of sneakers (P_s) = $50 per pair
- Price of sweaters (P_w) = $20 each
- Quantity of sneakers (Q_s) = 2 pairs
- Quantity of sweaters (Q_w) = 5 sweaters
Now we need to calculate the marginal utility for each good. Let's assume that the utility function for sneakers is given by U_s = 10Q_s and the utility function for sweaters is given by U_w = 5Q_w.
To find the marginal utility of sneakers (MU_s):
MU_s = ΔU_s / ΔQ_s
= (U_s at Q_s + 1) - U_s at Q_s
= (10(Q_s + 1)) - (10Q_s)
= 10
To find the marginal utility of sweaters (MU_w):
MU_w = ΔU_w / ΔQ_w
= (U_w at Q_w + 1) - U_w at Q_w
= (5(Q_w + 1)) - (5Q_w)
= 5
Now let's compare the marginal utilities to their respective prices:
For sneakers:
MU_s / P_s = 10 / 50 = 0.2
For sweaters:
MU_w / P_w = 5 / 20 = 0.25
Since the ratio of MU_w / P_w is greater than the ratio of MU_s / P_s, Lakshani could improve her overall level of utility by spending more on sweaters and less on sneakers. The higher ratio indicates that she receives more utility per dollar spent on sweaters compared to sneakers.
In this case, Lakshani should consider reducing the quantity of sneakers and increasing the quantity of sweaters in her bundle. This would allow her to maximize her utility given her budget constraints.