Question

Q1. Suppose the government is considering an increase in the toll on a certain stretch of highway from $3 to $4. At present, 1 million cars per week use that highway stretch; after the toll is imposed, the number of cars per week will change according to its price elasticity of demand of -0.8 (this elasticity value is estimated based on the initial-value method).

If the marginal cost of highway use is constant (i.e., the supply curve is horizontal) and equal to $3 per car, what is the net annual cost to society attributable to the increase in the toll? (your answer must be rounded off to the nearest million dollars per year, i.e., no decimal places; there are 52 weeks in a year)

Q2. The price of coal in 2020 is $54 per ton. The annual inflation between 2020 and 2030 is expected to be 4.7%. The price of coal is assumed to escalate at an annual average rate of 6.7% as a result of resource depletion (i.e., this escalation is independent of inflationary effects).

What is the price of coal in the year 2030, expressed in 2000 dollars? (your answer must be rounded-off to the nearest dollars per billion joules, i.e., no decimal places)

Answer 1

1)

elasticity of demand = -0.8

ed={ (Q1-Q)*P}/{(P1-P)*Q}

-0.8={(1,000,000-Q)*3}/{(4-3)*Q}

-0.8*Q=3,000,000-3Q

2.2Q= 3,000,000

Q= 1363636

the net annual cost to society attributable to the increase in the toll = deadweight loss done to society

= 4(4-3)(1363636-1000000) = 1454544per week

annual cost = 1454544*52= 75,636,288

2)

the price of coal in 2020 is $54 per ton

inflation rate is 4.7% and increasing 6.7% annually

so the inflation rate in 2030= 8.425

and the price will be 54*8.425= $455 per ton in 2039