Đề thi giữa kỳ hệ E - Toán Kinh Tế UEL

COURSEREVIEW 3: Mathematics for economics andbusiness Question 1 (1.5p): A company sells fast food including mineral water (abbreviated NS), milk tea (abbreviated TS), dumplings (abbreviated BB) and cold meat sandwiches (abbreviated BM) at a Fair. There are 4 places where the Fair takes placeincluding4areas:North(N),South(S),East(E),West(W).Thenumberoffoodunitsmentionedabovesold in one dayoftheFairandthesellingpriceofeachunit(inthousandsofVND)ofNS(unit:bottle),ST(unit:box),BB( unit: pieces),BM(unit:pieces)aregivenbythetablebelow. Area Products Priceper unit NS TS BB BM N NS p1 100 50 80 90 S TS p2 150 80 120 100 E BB p3 80 70 100 120 W BM p4 70 100 50 90 a) CreateamatrixmodeltocalculaterevenueofeachregionNorth,South,East,West. b) EstablishconditionsfortheNorth'srevenuetobegreaterthanorequalto4000(unit:thousandsofVND) c) CalculatethepriceperunitofproductknowingthattherevenueofeachregionNorth,South,East,Westare5,10, 20, 15respectively. Question 2 (1.5p): A country has three production sectors: Agriculture (NN), Industry (CN), and Services (DV). Knowing that to produce 1 USD of output value, we have the following information. - Theagriculturalsectorneedstouse0.3USDofitsvalue;0.2USDbuysindustrialgoodsand0.2USDbuysservice industry goods. - Theindustrialsectorneedstouse0.3USDofitsvalue;0.2USDbuysagriculturalgoodsand0.3USDbuysservice industry goods. - Theservicesectorneedstouse0.3USDofitsvalue;0.1USDbuysagriculturalgoodsand0.4USDbuysindustrial goods. a. Findaninputmatrix(A)forthiseconomy. b. EstabletheInput-Outputmodelinthiscase. c. Findthetotaloutputx1,x2,x3ofeachsectorstosatisfyfinaldemandas85,40,5respectively.(Note:resultsare used to 2decimalplaces). Question 3 (1p): A country's economy includes 3 sectors: Industry, Agriculture, and Services. To convert to a digital economy in each key area (CDKTS) or in a province or any company or corporation, people need to invest money (unit: million USD)tobuynewsoftwareandequipment(TB),hiretrainingexperts(CG)andannualequipmentmaintenance costs (BT).Thus,eachsectorofindustry,agriculture,serviceoraprovinceoracompanyorcorporationwhen implementing the KTS will have data represented by a certain vector (x, y, z) in 𝑅3 with x , y, z are the amount of money spentonTB,CG,BTrespectively.KnowingthattheCDKTSineachsectorofindustry,agricuture,andservice are given bythefollowingvectors: CN = (100, 200, 300), NN = (300, 100, 200), DV = (200, 300, 100). a) Considerthelinearindependenceofthesystem(B)includes3vectorsCN,NN,DVin𝑅3. b) If itema)issatisfied,findthecoordinatesinthebase(B)ofaprovinceknowingthatprovince'sCDKTSvector is (200,300,500). Question 4 (2p):Acompanyproducesandhasexclusiveconsumptionofaproductwithdemandgivenby Q = 3000 – 10P(measuredintermsofquantityQandpricePinUSD). Assuming the averagecostisAC=0,1Q+50. a) DeterminethemarginalprofitwithrespecttoQatQ=500,andexplainthemeaningsoftheobtainedvalues b) Find Q>0tooptimizeprofits. Question 5 (1.5p):ApurecompetitiveenterprisehasaproductionfunctiongivenbyQ=K(L+10).It’sknownthatwK= Q=10000units. 10USD and the wagerateforlaboriswL=40USD.Supposetheenterprisereceivesanordertoproduce Determine the Hicks’demandforcapitalandlaborthattheenterpriseneedstousetominimizecosts. Question 6 (1.5p): A company producesandexclusivelysellsaproductintwodifferentmarketswithrespectiveunitpricesforeachmarket: p1 = 700, p2 = 550(unit:thousandVNĐ).Supposethetotalproductioncostofthecompanyisasfollows: C = Q2 1 Q 1Q 2 Q 22 50Q2 100Q ; 0,Q2 0 . 1 Here,Q1,Q2arethequantities of theproductsoldineachmarket.Determinehowmanyproductsthecompanyneedstosell ineachmarkettooptimize its profit. Question7(1p):Ifthe net investmentfunctionisgivenby 𝐼(𝑡)=800𝑡1/3 (a) Determine the capital formulation K (b) Calculate the capital formation from the end of the first year to the end of the eighth year; (c) Calculate the number of years required before the capital stock exceeds $48 600. Hint: see p507 Ian Jacques