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Intermediate Microeconomics Excel Project 1: LP. Production Function Estimation. Cost Estimation. Excel. Directions: Type your answers on this WORD file (as best you can). Use the Excel file provided...

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Intermediate Microeconomics
Excel Project 1: LP. Production Function Estimation. Cost Estimation. Excel.
Directions: Type your answers on this WORD file (as best you can). Use the Excel file provided to do your Excel work. Save your file. When you post your answers online, please use the following naming structure:
Excel Project 1 “your name”.docx.
Excel Project 1 “your name”.xlsx.    
1. Use sheets “basecase”, “tax K”, in Excel Project 1 – LP Production Cost.xlsx as posted on Canvas to answer this question.
You have two inputs to production, robotic equipment, K and labor, L. You have 10 different processes you could employ to produce your product. The K and L requirements necessary to produce one unit of your product are given in cells A:3 through K:4. The wage rate is $15 per hour and the price of using K is $7.5 per hour. You good sells for $250.
a. Use the “basecase” spreadsheet. Since you have 10 processes, you have 10 process rays. State the alge
aic formulas for each of your process rays below.
.    In cells B:10 through K:10, calculate the per unit cost of using each process (these will be your cost coefficients).
c.    If production equaled 100 units, use SOLVER to determine how much K and L use to minimize costs. What production process or processes are you employing? How much K and L are you using? What are your costs? What are your profits?
d.    In the “tax K” spreadsheet, add at 15 percent tax to the price of K (cell B:7). Re-solve your minimization problem. What production process or processes are you employing now? How much K and L are you using? What has happened to costs? What has happened to profits? Explain the economic logic behind this result.
2.    Use the Production data spreadsheet in Excel Project 1 – LP Production Cost.xlsx for this question. This data measures output, capital inputs and labor inputs for 27 primary metal manufacturing establishments in the United States.
a. In this file, in columns F, G, and H, calculate the natural log value of each of the 27 observations using the Excel function “ln”.
. Run the following regression in Excel (you may need to add in the “Data Analysis Pak” – see me and I’ll help you get started.
ln(Q) = ln(a) + α ln(L) + β ln(K)
    You can preserve the regression output in in a separate worksheet (Sheet2 for example). Note, ln(a) is the regression constant. You should also write the equation out (as above AND in its standard exponential form) with the numerical values for ln(a), α, and β.
c. What is the marginal rate of technical substitution (ΔK/ΔL)? (Round figures to out to the 100th decimal point (for example, let 10.055 = 10.06).
d. Does the production function exhibit increasing, constant, or decreasing returns to scale? Explain.
e. Suppose a firm increased capital inputs by 10 percent. What would happen to output? Explain.
f. Suppose the price of labor is $15.80 per unit L and the price of capital is $10.00 per unit K. If a firm targets an output level of 322, then what should L and K be to maximize profits? (Round figures to out to the 100th decimal point). Explain the economic logic behind this result (you can use Solver here if you want, but honestly I would solve this just using basic mathematics – you’ll understand the solution better!)
3.    Use the Cost data spreadsheet in Excel Project 1 – LP Production Cost.xlsx for this question. This data comes from a 2017 study by Acik and Baser (Journal of Transportation and Logistics) who studies economies of scale in the seaborne coal shipping business focusing on the ISDEMIR Port in Turkey. They graciously provided me with their data. We are not going to replicate their results but rather use their data as applied to procedures we discussed in this class.
    The data measure volume of coal shipped from source port to ISDEMIR as well as the distance traveled between ports over the period 2008 to XXXXXXXXXXWe are going to use volume shipped as our measure of Q (output) and distance traveled as a proxy for real shipping costs (the idea here is that we assume the cost of shipping one unit of coal one mile is constant). We are also going to estimate Average Cost (AC) directly (see class notes) and then calculate Marginal Cost (MC) values (see class notes) and the cost elasticity of output.
a.     in column F calculate distance/volume (this is our AC measure). IN column G copy volume values again (just copy column B here). In column H calculate volume squared.
.    Use Excel to estimate using regression the following
    Use variable labels. Put your output starting in J2.
c.    Do your estimated coefficients’ signs turn out to be as expected for a U shaped AC curve (see notes)? Explain.
d.    What do your t-statistics tell you about volume’s effect on AC? Do we have reason to believe the are dis-economies of scale for larger shipping volumes? Explain.
e.    Column V contains volume values from 500 to XXXXXXXXXXand column W contains the squared values of volume. In Column X and Y, use your estimated coefficients to calculate values for AC and MC (use your class notes for help). Produce a plot in Excel of these two AC and MC curves measured against volume.
f.    In column Z calculate the cost elasticity of output. For what level of shipping volume to we reach minimum efficient scale?
Answered Same Day Sep 14, 2021

Solution

Komalavalli answered on Sep 17 2021
147 Votes
basecase
    
        Process 1    Process 2    Process 3    Process 4    Process 5    Process 6    Process 7    Process 8    Process 9    Process 10
    L    5    6    7    8.5    10.5    13.5    17    23    32    45
    K    30    22    17    12.5    9    6.5    4.5    2.5    1.5    1
    w    15    
    r    7.5    
    cost coeff    300    255    232.5    221.25    225    251.25    288.75    363.75    491.25    682.5
        q1    q2    q3    q4    q5    q6    q7    q8    q9    q10
    Production    436865560.40787    63161294.3963188    94741936.5944782    110532257.693558    105268817.327198    68424734.7626787    15790331.0990798    -89478476.2281181    -268435448.684355    -536870907.368709
    min cost    -291,745,887,094         
    production target    100.0000001192    =    100
                                                Total inputs
    L    2,184,327,802.04    378,967,766.38    663,193,556.16    939,524,190.40    1,105,322,581.94    923,733,919.30    268,435,628.68    0    0    0    6,463,505,444.89
    K    13,105,966,812.24    1,389,548,476.72    1,610,612,922.11    1,381,653,221.17    947,419,355.94    444,760,775.96    71,056,489.95    0    0    0    18,951,018,054.08
    price of the good    250
    profit    -239,085,192,079
tax K
    
        Process 1    Process 2    Process 3    Process 4    Process 5    Process 6    Process 7    Process 8    Process 9    Process 10
    L    5    6    7    8.5    10.5    13.5    17    23    32    45
    K    30    22    17    12.5    9    6.5    4.5    2.5    1.5    1
    w    15    
    r    8.625    
    cost coeff    333.75    279.75    251.625    235.3125    235.125    258.5625    293.8125    366.5625    492.9375    683.625
        q1    q2    q3    q4    q5    q6    q7    q8    q9    q10
    Production    143568385.009102    82861116.2176787    126017942.37272    151048901.542643    151336613.71701    115372591.921143    61282703.1401582    -50349620.5142143    -244267626.037532    -536870907.368709
    min cost    -284,114,353,262         
    production target    100    =    100
                                                Total inputs
    L    717,841,925.05    497,166,697.31    882,125,596.61    1,283,915,663.11    1,589,034,444.03    1,557,529,990.94    1,041,805,953.38    0    0    0    7,569,420,270.42
    K    4,307,051,550.27    1,822,944,556.79    2,142,305,020.34    1,888,111,269.28    1,362,029,523.45    749,921,847.49    275,772,164.13    0    0    0    12,548,135,931.75
    price of the good    250
    profit    -221,768,951,468
Q2
    SUMMARY OUTPUT
    Regression Statistics
    Multiple R    0.97
    R Square    0.94
    Adjusted R Square    0.94
    Standard E
or    0.19
    Observations    27
    ANOVA
        df    SS    MS    F    Significance F
    Regression    2    14.21    7.11    200.25    0.00
    Residual    24    0.85    0.04
    Total    26    15.06
        Coefficients    Standard E
or    t Stat    P-value    Lower 95%    Upper 95%
    Intercept    1.17    0.33    3.58    0.00    0.50    1.85
    LN(L)    0.60    0.13    4.79    0.00    0.34    0.86
    LN(K)    0.38    0.09    4.40    0.00    0.20    0.55
Q2 f
    
        Process 1    Process 2    Process 3    Process 4    Process 5    Process 6    Process 7    Process 8    Process 9    Process 10
    L    5    6    7    8.5    10.5    13.5    17    23    32    45
    K    30    22    17    12.5    9    6.5    4.5    2.5    1.5    1
    w    15.8    
    r    10    
    cost coeff    379    314.8    280.6    259.3    255.9    278.3    313.6    388.4    520.6    721
        q1    q2    q3    q4    q5    q6    q7    q8    q9    q10
    Production    -15558518997.56    1728724368.84    1728724368.84    1728724368.84    1728724368.84    1728724368.84    1728724368.84    1728724368.84    1728724368.84    1728724368.84
    min cost    -135,704,740,916         
    production target    321.9999995232    =    322
                                                Total inputs
    L    - 0    10,372,346,213.04    12,101,070,581.88    14,694,157,135.14    18,151,605,872.82    23,337,778,979.34    29,388,314,270.28    39760660483.32    55319179802.88    77792596597.8    280,917,709,936.50
    K    - 0    38,031,936,114.48    29,388,314,270.28    21,609,054,610.50    15,558,519,319.56    11,236,708,397.46    7,779,259,659.78    4321810922.1    2593086553.26    1728724368.84    132,247,414,216.26
    price of the good    250
    profit    -5,760,973,878,659
Production data
    Observation Number Obs    Value Added (Output) Q    Labor Input L    Capital Input K        LN(Q)    LN(L)    LN(K)
    1    657.29    162.31    279.99        6.4881253214    5.0895080869    5.6347538882
    2    935.93    214.43    542.5        6.8415406874    5.3679833448    6.2961880854
    3    1110.65    186.44    721.51        7.0127007085    5.2281094715    6.5813462381
    4    1200.89    245.83    1167.68        7.0908182275    5.5046402401    7.0627741532
    5    1052.68    211.4    811.77        6.9590945723    5.3537520734    6.6992170488
    6    3406.02    690.61    4558.02        8.1332997332    6.537575265    8.4246435977
    7    2427.89    452.79    3069.91        7.7947778464    6.1154284418    8.0294035242
    8    4257.46    714.2    5585.01        8.3564280173    6.5711630352    8.627841502
    9    1625.19    320.54    1618.75        7.393380011    5.7700070736    7.3894095254
    10    1272.05    253.17    1562.08        7.1483850513    5.5340611998    7.3537735455
    11    1004.45    236.44    662.04        6.912195407    5.465694476    6.4953259771
    12    598.87    140.73    875.37        6.3950445462    4.946843161    6.7746466541
    13    853.1    145.04    1696.98        6.7488767739    4.9770095664    7.4366054797
    14    1165.63    240.27    1078.79        7.0610169924    5.481763291    6.9835953217
    15    1917.55    536.73    2109.34        7.5588036085    6.2854951748    7.6541303813
    16    9849.17    1564.83    13989.55        9.1951424667    7.3555324709    9.5460659013
    17    1088.27    214.62    884.24        6.9923445584    5.3688690225    6.784728519
    18    8095.63    1083.1    9119.7        8.9990796889    6.9875825788    9.1181921878
    19    3175.39    521.74    5686.99        8.0631857384    6.2571693795    8.6459363889
    20    1653.38    304.85    1701.06        7.4105769565    5.7198198524    7.4390068651
    21    5159.31    835.69    5206.36        8.5485581286    6.7282577309    8.5576362341
    22    3378.4    284    3288.72        8.1251575036    5.6489742382    8.0982537103
    23    592.85    150.77    357.32        6.3849414159    5.0157554968    5.8786317388
    24    1601.98    259.91    2031.93        7.3789956432    5.5603354172    7.6167413593
    25    2065.85    497.6    2492.98        7.633297043    6.2097965414    7.821234061
    26    2293.87    275.2    1711.74        7.7379956265    5.6174981061    7.445265676
    27    745.67    137    768.59        6.6142831431    4.9199809258    6.6445576674
Cost data
    YEAR    VOLUME    DISTANCE    PORT        AC    VOLUME    Volume squared                                                        V    V^2    AC    MC    Eco
    2008    2095    1016    ROMANIA-CONSTANTA        0.4849642005    2095    4389025        SUMMARY OUTPUT                                                500    250000    0.2449417979    0.2466307406    -0.0068808921
    2011    2439    1542    ITALY-SAVONA        0.6322263223    2439    5948721                                                        1000    1000000    -0.003374207    0.0000107274    0.999000999
    2008    2902    1016    ROMANIA-CONSTANTA        0.350103377    2902    8421604        Regression Statistics                                                1500    2250000    -0.0050562542    0.0000317211    1.0000000028
    2010    2969    1468    RUSIA-ROSTOV ON DON        0.4944425733    2969    8814961        Multiple R    0.55                                            2000    4000000    -0.0067416723    0.000056393    1
    2009    3065    1429    RUSSIA-AZOV        0.4662316476    3065    9394225        R Square    0.30                                            2500    6250000    -0.0084270904    0.0000881141    1
    2009    3112    1429    RUSSIA-AZOV        0.4591902314    3112    9684544        Adjusted R Square    0.29                                            3000    9000000    -0.0101125084    0.0001268842    1
    2010    3117    1429    RUSSIA-AZOV        0.4584536413    3117    9715689        Standard E
or    0.11                                            3500    12250000    -0.0117979265    0.0001727036    1
    2010    3200    1468    RUSIA-ROSTOV ON DON        0.45875    3200    10240000        Observations    313                                            4000    16000000    -0.0134833446    0.000225572    1
    2009    3206    1429    RUSSIA-AZOV        0.4457267623    3206    10278436                                                        4500    20250000    -0.0151687627    0.0002854896    1
    2009    3250    1429    RUSSIA-AZOV        0.4396923077    3250    10562500        ANOVA                                                5000    25000000    -0.0168541807    0.0003524562    1
    2010    3450    1378    UKRAINE-MARIUPOL        0.3994202899    3450    11902500            df    SS    MS    F    Significance F                            5500    30250000    -0.0185395988    0.0004264721    1
    2008    3690    1016    ROMANIA-CONSTANTA        0.2753387534    3690    13616100        Regression    2    1.49    0.74    65.62    0.00                            6000    36000000    -0.0202250169    0.000507537    1
    2010    3874    1429    RUSSIA-AZOV        0.3688693856    3874    15007876        Residual    310    3.52    0.01                                    6500    42250000    -0.021910435    0.000595651    1
    2009    3914    1429    RUSSIA-AZOV        0.3650996423    3914    15319396        Total    312    5.00                                        7000    49000000    -0.023595853    0.0006908142    1
    2009    3954    1208    CROTIA-PLOCE        0.3055134041    3954    15634116                                                        7500    56250000    -0.0252812711    0.0007930265    1
    2010    4044    1355    UKRAINE-BERDYANSK        0.3350642928    4044    16353936            Coefficients    Standard E
or    t Stat    P-value    Lower 95%    Upper 95%    Lower 95.0%    Upper 95.0%                8000    64000000    -0.0269666892    0.000902288    1
    2009    4166    1355    UKRAINE-BERDYANSK        0.3252520403    4166    17355556        Intercept    0.25    0.01    23.85    0.00    0.23    0.27    0.23    0.27                8500    72250000    -0.0286521073    0.0010185985    1
    2009    4382    1378    UKRAINE-MARIUPOL        0.3144682793    4382    19201924        VOLUME    -0.0000033708361    0.00    -8.56    0.00    -0.00    -0.00    -0.00    -0.00                9000    81000000    -0.0303375253    0.0011419582    1
    2009    4420    1378    UKRAINE-MARIUPOL        0.3117647059    4420    19536400        Volume squared    0.0000000000141    0.00    5.66    0.00    0.00    0.00    0.00    0.00                9500    90250000    -0.0320229434    0.001272367    1
    2008    4468    1378    UKRAINE-MARIUPOL        0.3084153984    4468    19963024                                                        10000    100000000    -0.0337083615    0.001409825    1
    2008    4500    1378    UKRAINE-MARIUPOL        0.3062222222    4500    20250000                                                        10500    110250000    -0.0353937795    0.001554332    1
    2010    4598    1355    UKRAINE-BERDYANSK        0.2946933449    4598    21141604                                                        11000    121000000    -0.0370791976    0.0017058882    1
    2011    4606    1355    UKRAINE-BERDYANSK        0.2941815024    4606    21215236                                                        11500    132250000    -0.0387646157    0.0018644935    1
    2010    4633    1429    RUSSIA-AZOV        0.3084394561    4633    21464689                                                        12000    144000000    -0.0404500338    0.002030148    1
    2008    4688    1396    RUSIA-YEİSK        0.29778157    4688    21977344                                                        12500    156250000    -0.0421354518    0.0022028515    1
    2010    4693    1429    RUSSIA-AZOV        0.304496058    4693    22024249                                                        13000    169000000    -0.0438208699    0.0023826042    1
    2010    4733    1429    RUSSIA-AZOV        0.3019226706    4733    22401289                                                        13500    182250000    -0.045506288    0.002569406    1
    2010    4932    1468    RUSIA-ROSTOV ON DON        0.297648013    4932    24324624                                                        14000    196000000    -0.0471917061    0.0027632569    1
    2009    4966    3458    BELGIUM-ANTWERPEN        0.6963350785    4966    24661156                                                        14500    210250000    -0.0488771241    0.002964157    1
    2010    4972    1429    RUSSIA-AZOV        0.2874094932    4972    24720784                                                        15000    225000000    -0.0505625422    0.0031721062    1
    2008    5002    1396    RUSIA-YEİSK        0.2790883647    5002    25020004                                                        15500    240250000    -0.0522479603    0.0033871045    1
    2011    5002    1239    UKRAINE-KHERSON        0.2477009196    5002    25020004                                                        16000    256000000    -0.0539333784    0.0036091519    1
    2008    5004    1396    RUSIA-YEİSK        0.2789768185    5004    25040016                                                        16500    272250000    -0.0556187964    0.0038382485    1
    2008    5021    1239    UKRAINE-KHERSON        0.2467635929    5021    25210441                                                        17000    289000000    -0.0573042145    0.0040743942    1
    2010    5085    1429    RUSSIA-AZOV        0.2810226155    5085    25857225                                                        17500    306250000    -0.0589896326    0.004317589    1
    2010    5157    1429    RUSSIA-AZOV        0.2770990886    5157    26594649                                                        18000    324000000    -0.0606750507    0.0045678329    1
    2010    5178    1264    UKRAINE-KERCH        0.2441096949    5178    26811684                                                        18500    342250000    -0.0623604687    0.004825126    1
    2009    5205    1355    UKRAINE-BERDYANSK        0.260326609    5205    27092025                                                        19000    361000000    -0.0640458868    0.0050894681    1
    2011    5228    1378    UKRAINE-MARIUPOL        0.2635807192    5228    27331984                                                        19500    380250000    -0.0657313049    0.0053608594    1
    2010    5240    1468    RUSIA-ROSTOV ON DON        0.2801526718    5240    27457600                                                        20000    400000000    -0.0674167229    0.0056392999    1
    2010    5259    1239    UKRAINE-KHERSON        0.2355961209    5259    27657081                                                        20500    420250000    -0.069102141    0.0059247894    1
    2011    5291    1239    UKRAINE-KHERSON        0.2341712342    5291    27994681                                                        21000    441000000    -0.0707875591    0.0062173281    1
    2010    5348    1429    RUSSIA-AZOV        0.2672026926    5348    28601104                                                        21500    462250000    -0.0724729772    0.0065169159    1
    2010    5408    1239    UKRAINE-KHERSON        0.2291050296    5408    29246464                                                        22000    484000000    -0.0741583952    0.0068235528    1
    2009    5439    1429    RUSSIA-AZOV        0.2627321199    5439    29582721                                                        22500    506250000    -0.0758438133    0.0071372389    1
    2010    5500    1542    ITALY-SAVONA        0.2803636364    5500    30250000                                                        23000    529000000    -0.0775292314    0.0074579741    1
    2011    5628    1417    ITALY-PIOMBINO        0.2517768301    5628    31674384                                                        23500    552250000    -0.0792146495    0.0077857584    1
    2010    5701    1016    ROMANIA-CONSTANTA        0.1782143484    5701    32501401                                                        24000    576000000    -0.0809000675    0.0081205918    1
    2011    5729    1468    RUSIA-ROSTOV ON DON        0.2562401815    5729    32821441                                                        24500    600250000    -0.0825854856    0.0084624744    1
    2008    5968    1231    UKRAINE-NIKOLAYEV        0.206266756    5968    35617024                                                        25000    625000000    -0.0842709037    0.0088114061    1
    2008    6000    1355    UKRAINE-BERDYANSK        0.2258333333    6000    36000000                                                        25500    650250000    -0.0859563218    0.0091673869    1
    2008    6114    1378    UKRAINE-MARIUPOL        0.2253843638    6114    37380996                                                        26000    676000000    -0.0876417398    0.0095304168    1
    2008    6178    1378    UKRAINE-MARIUPOL        0.2230495306    6178    38167684                                                        26500    702250000    -0.0893271579    0.0099004958    1
    2011    6196    6111    COLOMBIA-BARRANQUILL        0.9862814719    6196    38390416                                                        27000    729000000    -0.091012576    0.010277624    1
    2009    6200    1208    CROTIA-PLOCE        0.1948387097    6200    38440000                                                        27500    756250000    -0.0926979941    0.0106618013    1
    2011    6237    6111    COLOMBIA-BARRANQUILL        0.9797979798    6237    38900169                                                        28000    784000000    -0.0943834121    0.0110530278    1
    2011    6312    1355    UKRAINE-BERDYANSK        0.2146704689    6312    39841344                                                        28500    812250000    -0.0960688302    0.0114513033    1
    2008    6386    1016    ROMANIA-CONSTANTA        0.1590980269    6386    40780996                                                        29000    841000000    -0.0977542483    0.011856628    1
    2010    6770    1378    UKRAINE-MARIUPOL        0.2035450517    6770    45832900                                                        29500    870250000    -0.0994396663    0.0122690018    1
    2010    6823    1378    UKRAINE-MARIUPOL        0.2019639455    6823    46553329                                                        30000    900000000    -0.1011250844    0.0126884247    1
    2009    7100    1264    UKRAINE-KERCH        0.178028169    7100    50410000                                                        30500    930250000    -0.1028105025    0.0131148968    1
    2010    7101    1355    UKRAINE-BERDYANSK        0.1908181946    7101    50424201                                                        31000    961000000    -0.1044959206    0.0135484179    1
    2009    7457    1208    CROTIA-PLOCE        0.1619954405    7457    55606849                                                        31500    992250000    -0.1061813386    0.0139889883    1
    2008    7693    1355    UKRAINE-BERDYANSK        0.1761341479    7693    59182249                                                        32000    1024000000    -0.1078667567    0.0144366077    1
    2011    7718    1355    UKRAINE-BERDYANSK        0.1755636175    7718    59567524                                                        32500    1056250000    -0.1095521748    0.0148912762    1
    2010    7724    1378    UKRAINE-MARIUPOL        0.1784049715    7724    59660176                                                        33000    1089000000    -0.1112375929    0.0153529939    1
    2008    7756    455    EGYPT-ALEXANDRIA        0.0586642599    7756    60155536                                                        33500    1122250000    -0.1129230109    0.0158217607    1
    2010    7814    1355    UKRAINE-BERDYANSK        0.1734067059    7814    61058596                                                        34000    1156000000    -0.114608429    0.0162975766    1
    2009    7883    1378    UKRAINE-MARIUPOL        0.1748065457    7883    62141689                                                        34500    1190250000    -0.1162938471    0.0167804417    1
    2011    7937    1378    UKRAINE-MARIUPOL        0.1736172357    7937    62995969                                                        35000    1225000000    -0.1179792652    0.0172703559    1
    2010    8000    5943    VENEZUELA-PUNTA...
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