代写Economics类程序、代写R、SPSS经济类程序

日期：2018-05-06 06:54

This assignment is worth 20% of your final grade.

Limit your answer to 8 pages (single-sided).

The assignment should be submitted to the reception of the Economics Department, which is

located on level 4 of FBE building. No late submissions will be accepted. Please ensure that

the coversheet is attached. The assignment must be stapled with the coversheet. Write

your name and student number at the top of each page of the answer sheet.

In our experience, neater assignments receive higher marks, conditional on content. As such,

you are strongly encouraged (but not required) to type your assignments. Mathematical

symbols and formulas can remain hand-written.

Please complete the declaration and list the student number and name of the student

contributing to this assignment.

Declaration

We hereby certify that this assignment is our own work, based on our personal study and/or

research and that we have acknowledged all material and sources used in the preparation of

this assignment. We also certify that the assignment has not previously been submitted for

assessment and that we have not copied in part or whole or otherwise plagiarised the work of

other students or authors.

Student Number Family Name First Name Signature

1

ECON30025/ECOM90020 Computational Economics and Business

Assignment B

You must attach the coversheet to your answers. Read the instructions on the

coversheet. Try to keep your answers short and clear. This assignment has a total

of 20 marks. There are 5 parts. Each Part carries 4 marks.

Part I (4pts)

Consider a Leslie population model for the female population with the following

parameters:

Prob(age 1-20 -> age 1-20) = 0.12

Prob(age 21-40->age 1-20) =0.70

Prob(age 41-60->age 1-20) =0.12

Prob(age 1-20 -> age 21-40) = 0.98

Prob(age 21-40 -> age 41-60) = 0.99

Prob(age 41-60 -> age 61+) = 0.8

Prob(age 61+ -> age 61+) = 0.2

The other transition probabilities are zero. The transition probability is interpreted as

the conditional probability of being in the state 20 years later, conditional on being in

the state now.

1.(1pt) Write down the model as a Markov model with four states.

2.(1pt) The initial state vector is [1 1 1 0]’. Simulate the total female population for

400 years and report the result on a graph. Show your codes.

3.(1pt) Suppose medical technology increases the survival rate of people aged 61+ by

3 percentage points every 20 years. Simulate the total female population for

400 years and report the result on a graph. Show the new part of the code that

generates this result.

4.(1pt) Suppose the government will trigger an immigration program whenever the

total female population drops strictly below 3. The program restricts the

immigrants’ age range to 21-40 and the total number of female immigrants is 3%

of the total female population (both measured within a 20-year interval).

Simulate the total female population for 400 years and report the result on a

graph. Show the new part of the code that generates this result.

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Part II (4pts)

A factory employs x1 units of high-skilled labour and x2 units of low-skilled labour.

One unit of high-skilled labour costs $8 and one unit of low-skilled labour costs $4.

The factory needs to accomplish two tasks. First, it needs to produce at least 20 units

of rubber. Second, it needs to produce at least 30 units of glass.

Each unit of rubber requires 1 unit of high-skilled labour, or 4 units of low-skilled

labour, or a linear combination of both. Each unit of glass requires 1 unit of

high-skilled labour, or 1 unit of low-skilled labour, or a linear combination of both.

The factory also has to satisfy the regulation that at least 10 units of low-skilled

labour are employed. Assume that products and labour are all continuous variables.

(a)(1pt) Write down the factory’s cost minimization problem.

(b)(1pt) Draw all the constraints on a graph (x1 on the horizontal axis), label the

constraints, and highlight the feasible area.

(c)(1pt) Without using software, compute the solution and the level of minimized cost.

Show your working.

(d)(1pt) At what relative cost of labour will regulation become a binding constraint?

3

Part III (4pts)

We will use data envelopment analysis on the following data:

DMU Input Output

X1 X2 Y1 Y2 Y3

1 5 14 9 4 16

2 8 15 5 7 10

3 7 12 4 9 13

1.(1pt) Write down the linear programming problem for DMU2 under the assumption

of variable returns to scale.

2.(1pt) Under variable returns to scale, the optimal DMU weights of the linear

programming problem for DMU2 are w1=0.2, w2=0, w3=0.8. Without using

the EMS software, compute the efficiency score of DMU2. Show your

working.

3.(1pt) Now assume constant returns to scale. Use the EMS software to compute both

the efficiency score and optimal DMU weights for DMU2.

4.(1pt) Does the virtual DMU in #3 produce more outputs than the virtual DMU in #2?

Briefly explain why.

Part IV (4pts)

1.(1pt) Consider an IEEE standard 8-bit floating point data type SEEEFFFF where S

stores the sign (0 indicates positive), EEE stores the exponent with bias equal

to 3, and FFFF stores the fractional part of the mantissa. What is the floating

point number that represents “01001100”? Show your working.

2.(1pt) What is the maximum floating point number that can be encoded by this data

type?

3.(1pt) Use the linear congruential generator to simulate a standard normal

distribution consisting of 1000 values. Show your code, and plot a histogram

with a bin width of 0.25 and an overlay of a normal density curve. (Hint: use

I0=8, a=5, c=3, m=2501).

4.(1pt) Use the SAS built-in uniform distribution generator to simulate a standard

normal distribution consisting of 1000 values. Show the new part of the code,

and plot a histogram with a bin width of 0.25 and an overlay of a normal

density curve. (Hint: use seed number 32).

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Part V (4pts)

We will modify the inventory model in the tutorial (tut_w10.pdf) as follows:

- Keep the order point fixed at 30.

- Evaluate the effect of setting the order size at 5, 10, 15, 20, 25, 30.

- Evaluate three outcomes: service level, inventory proportion, and number of

orders.

Keep all other aspects of the model unchanged.

For your reference, the original code is posted below.

data inven;

do r_p = 25 to 35 ;

do it = 1 to 100 ;

nday = 30 ;

inv = 50 ;

inv_p = 50 ;

n_o = 50 ;

do ii = 1 to nday ;

b_inv = inv ;

if ii = or_time then inv = inv + 50 ;

demand = rantbl(9897653,.01,.02,.04,.06,.09,.14,.18,.22,.16,.06,.02) - 1 ;

if demand <= inv then sales = demand; else sales = inv ;

unmet_d = abs(sales - demand) ;

inv = inv - sales ;

inv_p = inv_p - sales ;

if inv_p <= r_p then do;

or_time = ii + rantbl(9897653,.2,.6,.2) + 3 ;

inv_p = inv_p + 50 ;

end;

output ;

end;

end;

end;

run;

1.(2pt) Modify the original code to simulate the new model. Write down your new

code and highlight where you have made changes.

2.(1pt) Show three sets of side-by-side box plots by the order size: one for service

level, one for inventory proportion, and one for the number of orders.

3.(1pt) Briefly describe the results shown in the box plots.