Question

Need help in solving this question

• 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 P_t = 15 - q_t
• Marginal cost of extracting the resource is the same in both periods and is given by MC_t=$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

Answer 1

$$Solution$$

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

given : $P=15-Qt\\$

$MC=\$3$

$Q1+Q2=10$

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

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

$Q2=10-Q1$

$13-3.5Q1=\frac{13}{1.07}-\frac{3.5(10-Q1)}{1.07}$

$13-\frac{13}{1.07}+\frac{35}{1.07}=\frac{3.5Q1+3.5Q2}{1.07}$

$33.5607=\frac{7Q1}{1.07}$

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

$Q1=5.130$

for period 1 is $5.130$