Question #171768

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  • Allocate resource between two time periods t=1,2
  • The fixed supply of the resource is 10 barrels 
  • Demand is same in both periods and given by Pt = 15 - qt
  • Marginal cost of extracting the resource is the same in both periods and is given by MCt=$3
  • The discount rate is 7%

1. What is the dynamically efficient allocation of this resource in period 1? Please enter this number rounded to the hundredths place in the 1st box below

1
Expert's answer
2021-03-18T16:29:18-0400
SolutionSolution

PMC(Q1)=[PMC(Q2)]1+rP-MC(Q1)=\frac{[P-MC(Q2)]}{1+r}\\


given : P=15QtP=15-Qt\\

MC=$3MC=\$3

Q1+Q2=10Q1+Q2=10

153+3.5Q1=[15(3+3.5Q2)1+0.0715-3+3.5Q1=\frac{[15-(3+3.5Q2)}{1+0.07}


13+3.5Q1=[133.5Q2]1.0713+3.5Q1=\frac{[13-3.5Q2]}{1.07}


Q2=10Q1Q2=10-Q1


133.5Q1=131.073.5(10Q1)1.0713-3.5Q1=\frac{13}{1.07}-\frac{3.5(10-Q1)}{1.07}


13131.07+351.07=3.5Q1+3.5Q21.0713-\frac{13}{1.07}+\frac{35}{1.07}=\frac{3.5Q1+3.5Q2}{1.07}


33.5607=7Q11.0733.5607=\frac{7Q1}{1.07}


Q1=33.56076.5420Q1=\frac{33.5607}{6.5420}


Q1=5.130Q1=5.130


for period 1 is 5.1305.130



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