Florida Worldwide University

ECOSYSTEM 4933 Issues in Theory – Fall 2014

Homework #1 – Deadline 09/25/14 – Answer Important

Notice: Produce your home work in a letter size sheet. Make sure to include your personal information. Should your homework is far more than two sheets very long number and staple them together. Handwritten submissions aren't accepted.

1 . Consider a client with cuasi-linear preferences showed by the energy function:

U c, g c three or more g in which c is a private very good and g is a genuine public very good. The price of the private great is $12 per unit and the value of the public good $1. Assume the customer has $1, 000 to spend. Calculate the utility maximizing quantities of c* and g*. Response:

Max U c, g c several g

s i9000. t. 12c g 1000

c0

g0

L c 3 g 0 1000 12. c g 1c 2 g

The first order conditions are:

L

one particular 0. 12 1 0

c

(1. 1)

L one particular a couple of 3

g 0 2 0

g 3

(1. 2)

0, 1, 2 zero

(1. 3)

0 1000 doze. c g 0

(1. 4)

1. c zero

(1. 5)

2. g zero

(1. 6)

1

Our company is interested in an inside solution with c, g 0, so we all assume 0 zero, 1 0, 2 0. We rewrite (1. 1) as

and (1. 2) as

0

1

12

you

33 g 2

0.

Merging (1. 1) and (1. 2) we get

1

2

1

4-g 3 1 g

2

doze

4

thirty-three g

1

2

several

g* 8

To obtain the optimum value of c, we replace g in the finances constraint.

doze. c g 1000

doze. c 8 1000

1000 almost eight

c

c* 82. 67

12

2 . Now imagine the consumer features $1, 800 to spend. How will the enhancements made on income impact the optimal quantities of c and g. Why?

Answer:

g* 8

c* 149. 33

The brand new optimal principles show us that with a cuasi-linear utility function all the salary affect will be absorbed by the private very good.

3. At this point the power function is usually U c, g 5c g as well as the consumer features $1, 500 to spend. Find the principles of c and g that improve his electricity.

Answer:

g* 1 ) 44

c* 124. 88

two

4. FIU offers bus service involving the Modesto Maidique Campus as well as the Biscayne Campus. Suppose that a bus gets to the Golden Parking Storage area every thirty minutes between 6AM and 11PM during weekdays. Students get to the shuttle bus stop at unique times. The time students wait is consistently distributed coming from 0 to 30 minutes.

a. Draw a graph of the distribution.

Answer:

0. 035

0. 03

0. 025

0. 02

0. 015

0. 01

0. 005

0

zero

5

15

15

20

25

40

35

n. Show the fact that area of this kind of distribution is usually 1 . 00.

Answer:

Location = (height)(base) =

you

31 0 you

35 0

c. What is the imply waiting period? What is the conventional deviation of the waiting time? Answer:

a m 0 30

15

2

2

a b

12

two

0 30

12

a couple of

8. 66

3

d. Precisely what is the likelihood a student can wait much more than 25 mins? Answer:

S x 25

1

5

30 25 zero. 1667

40 0

30

elizabeth. What is the probability a student will wait between twelve and 20 minutes? Solution:

P 10 x 20

1

12

20 15 0. 3333

35 0

30

5. The following data is about the earnings per share of a sample of 12-15 software businesses for the year 2013.

$0. 09

$1. 20

$7. 83

$0. 13

$1. 49

$8. 92

$0. 41

$3. 18

$12. 13

$0. 51

$3. 50

$12. 99

$1. 12

$6. 36

$16. 40

Compute the mean, median and standard deviation. Find the coefficient of skewness applying Pearson's estimation and also the computer software method. What is their conclusion regarding the shape of the distribution?

Answer:

x

zero. 09

zero. 13

zero. 41

zero. 51

1 . 12

1 . 20

1 ) 49

3. 18

3. 50

six. 36

six. 83

eight. 92

15. 13

12. 99

xx

t

3

-0. 8066

-0. 7868

-0. 6575

-0. 6150

-0. 3948

-0. 3706

-0. 2911

-0. 0390

-0. 0214

0. 0197

0. 1677

0. 4392

0. 9758

3. 6493

4

sixteen. 40

12. 5412

Mean

Median

St . Dev.

some. 950667

three or more. 18

five. 221764

eleven. 8100

sk

1 . 017281

sk comp

0. 973355

6. Consider three voters indexed by simply i ∈ 1, 2, 3, each characterized by an intrinsic unbekannte

ai, in which a1 a a couple of a3....