lectures in microeconomics-charles w. upton extending the problem

Lectures in Microeconomics-Charles W. Upton

Extending the Problem

V=180,000-20,000pc

V=120,000-10,000pa

20,000pc


A Golden Oldie

• Demand for the park:VC =180,000 - 20,000pc

VA = 120,000 - 10,000pa


A Golden Oldie


VA = 120,000 - 10,000pa

• Capacity = 200,000


A Golden Oldie


VA = 120,000 - 10,000pa

• Capacity = 200,000• Adding Capacity $3 a visit.


A Golden Oldie

• If demand is to be restricted to 200,000 what single fee would you recommend?


A Golden Oldie


• If children and adults can be charged a separate fee, what fees would you recommend?


A Golden Oldie


• If children and adults can be charged a separate fee, what fees would you recommend?

• Should the park expand capacity in that case?


Charging a Single Fee


VA = 120,000 - 10,000pa




VA = 120,000 - 10,000pa

• When p = 0, demand is 300,000



Children Adults

V=180,000-20,000pc

V=120,000-10,000pa



Children Adults

V=180,000-20,000pc

V=120,000-10,000pa

20,000pc



Children Adults

V=180,000-20,000pc

V=120,000-10,000pa

20,000pc 10,000pa



Children Adults

V=180,000-20,000pc

V=120,000-10,000pa

20,000pc 10,000paac ppTrip 1000020000



Children Adults

V=180,000-20,000pc

V=120,000-10,000pa

20,000pc 10,000papTrip

ppTrip ac

30000

1000020000



Children Adults

V=180,000-20,000pc

V=120,000-10,000pa


ppTrip ac

30000

1000020000

To eliminate 100,000 trips set p = $3.33



Children Adults

V=180,000-20,000pc

V=120,000-10,000pa


ppTrip ac

30000

1000020000

To eliminate 100,000 trips set p = $3.33

But is there a better way of doing

it, so as to minimize DWL?



Children Adults

V=180,000-20,000pc

V=120,000-10,000pa



Children Adults

V=180,000-20,000pc

V=120,000-10,000pa

20,000pc 10,000pa



Children Adults

V=180,000-20,000pc

V=120,000-10,000pa

20,000pc 10,000pa

Dead Weight Loss from Children is (1/2) (20,000pc )(pc )=

10,000pc2



Children Adults

V=180,000-20,000pc

V=120,000-10,000pa

20,000pc 10,000pa

Dead Weight Loss from Adults is (1/2) (10,000pa )(pa )=

5,000pa2



Children Adults

V=180,000-20,000pc

V=120,000-10,000pa

20,000pc 10,000pa

DWL= 10,000pc2 +5,000pa

2



Children Adults

V=180,000-20,000pc

V=120,000-10,000pa

20,000pc 10,000pa

DWL= 10,000pc2 +5,000pa

2

ac ppTrip 1000020000


Charging Separate Fees

• Many different adult and child’s fees will cut demand




• But

20,000pc + 10,000pa=100,000




• But

20,000pc + 10,000pa=100,000

pa = 10– 2pc



• Deadweight loss is

10,000pc2 + 5,000pa

2

• The two prices are

pa = 10– 2pc

• Deadweight loss is

10,000pc2 + 5,000(10-2pc)2



10,000pc2 + 5,000(10-2pc)2



10,000pc2 + 5,000(10-2pc)2

10,000pc2 + 5,000(100-40pc+4pc

2)



10,000pc2 + 5,000(10-2pc)2

10,000pc2 + 5,000(100-40pc+4pc

2)

10,000pc2 + 500,000-

200,000pc+20,000pc2



10,000pc2 + 5,000(10-2pc)2

10,000pc2 + 5,000(100-40pc+4pc

2)

10,000pc2 + 500,000-

200,000pc+20,000pc2

DWL =500,000-200,000pc+30,000pc2



500,000-200,000pc+30,000pc2



500,000-200,000pc+30,000pc2

• In sum, we can achieve our objective with many different values of pc (and pa).



500,000-200,000pc+30,000pc2


• Lets find the one that minimizes DWL.



500,000-200,000pc+30,000pc2



• To do that….



500,000-200,000pc+30,000pc2



• To do that….– Take the derivative– Set it equal to zero



500,000-200,000pc+30,000pc2

• Differentiating

-200,000+60,000pc



500,000-200,000pc+30,000pc2

• Differentiating

-200,000+60,000pc

33.3$cp



500,000-200,000pc+30,000pc2

• Differentiating

-200,000+60,000pc

33.3$cp

pa = 10– 2pc



500,000-200,000pc+30,000pc2

• Differentiating

-200,000+60,000pc

33.3$cp

pa = 10– 2pc

pa=$3.33


The Dead Weight Loss

DWL = 500,000-200,000pc+30,000pc2



DWL = 500,000-200,000pc+30,000pc2

DWL = 500,000-200,000($3.33)+30,000($3.33)2



DWL = 500,000-200,000pc+30,000pc2

DWL = 500,000-200,000($3.33)+30,000($3.33)2

DWL = $55,556



DWL = 500,000-200,000pc+30,000pc2

DWL = 500,000-200,000($3.33)+30,000($3.33)2

DWL = $55,556 ?DWL

Cost

lectures in microeconomics-charles w. upton extending the problem

Documents