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Nitella [24]
4 years ago
12

Jane receives utility from days spent traveling on va- cation domestically (D) and days spent traveling on vacation in a foreign

country (F), as given by the util- ity function U(D,F) = 10DF. In addition, the price of a day spent traveling domestically is $100, the price of a day spent traveling in a foreign country is $400, and Jane’s annual travel budget is $4000.
a. Illustrate the indifference curve associated with a utility of 800 and the indifference curve associated with a utility of 1200.
Business
1 answer:
sammy [17]4 years ago
7 0

Answer:

Explanation:

A point on U=800 is (5, 16)

From BL:

400*F+100D =4000

400*5+100*16 =3600<4000

Therefore u = 800 affordable.

U= 1200

F = 1200/10D

If D = 20

F = 1200/200

=6

Now from BL:

400*6+100*20= 2400+2000=4400>4000

Not affordable.

Maximization:

L = 10DF+ʎ[100*D+400*F – 4000]

Differentiating wrt D and F:

dL/dD = 10F + ʎ*100

dL/dF = 10D +ʎ*400

equating to zero;                      

ʎ= -F/10

ʎ=-D/40

equating the two:

F/10=D/40

D = 4F

From BL:

400*F+100*D = 4000

400F+100*4F = 4000

800F = 4000

F = 5

D = 4*5=20

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4 0
3 years ago
In response to a change in the price of good X from $10 to $6, the quantity demanded of good X increases from 100 to 150 units.
andreev551 [17]

Answer:

- 0.80

Explanation:

Price elasticity of demand describes the extent to which the quantity demanded of good X changes as result of a change in its own price.

The midpoint formula for price elasticity of demand is presented and used as follows:

Percentage change in quantity = %ΔQ = [Q2 - Q1] / [(Q2 + Q1) ÷ 2] × 100

Percentage change in quantity = %ΔP = [P2 - P1] / [(P2 + P1) ÷ 2] × 100

Midpoint price elasticity of demand = %ΔQ / %ΔP

Where:

Q2 = New quantity of good X = 150

Q1 = Initial quantity of good X = 100

P2 = New price of good X = $6

P1 = Initial price of good X = $10

Therefore,

Percentage change in quantity = %ΔQ = [150 - 100] / [(150 + 100) ÷ 2] × 100

                                                                = [50/(250 ÷ 2)] × 100

                                                                 = (50/125) × 100

                                                                 = 40.00%

Percentage change in quantity = %ΔP = [$6 - $10] / [($6 + $10) ÷ 2] × 100

                                                                = [-$4/($16 ÷ $2)] × 100

                                                                 = (-$4/$8) × 100

                                                                 = - 50.00%

Price elasticity of demand = 40% / 50% = - 0.80

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