Question

In: Economics

In Example 9.1 LOADING... ​, we calculated the gains and losses from price controls on natural...

In Example 9.1 LOADING... ​, we calculated the gains and losses from price controls on natural gas and found that there was a deadweight loss of​ $5.68 billion. This calculation was based on a price of oil of​ $50 per barrel and utilized the following​ equations: Supply​: QS ​= 15.90​ + 0.72PG ​+ 0.05PO Demand​: QD ​= 0.02minus−1.8PG ​+ 0.69PO where QS and QD are the quantities supplied and​ demanded, each measured in trillion cubic feet​ (Tcf), PG is the price of natural gas in dollars per thousand cubic feet​ ($/mcf), and PO is the price of oil in dollars per barrel​ ($/b). If the price of oil were ​$65.0065.00 per​ barrel, what would be the​ free-market price of​ gas? With a ​$65.0065.00 price of oil per​ barrel, the​ free-market price of gas would be ​$10.2110.21 per thousand cubic foot. ​(Enter your response rounded to two decimal places.​) How large a deadweight loss would result if the maximum allowable price of natural gas were ​$4.004.00 per thousand cubic​ feet? Deadweight loss if the price of natural gas were regulated to be ​$4.004.00 would be ​$ ??? billion. ​(Enter your response rounded to two decimal places.​)

Solutions

Expert Solution

QD = 0.02 - 1.8PG + 0.69PO

QS = 15.9 + 0.72PG + 0.05PO

(1) Plugging in PO = 65,

QD = 0.02 - 1.8PG + (0.69 x 65) = 0.02 - 1.8PG + 44.85 = 44.87 - 1.8PG

QS = 15.9 + 0.72PG + (0.05 x 65) = 15.9 + 0.72PG + 3.25 = 19.15 + 0.72PG

In equilibrium, QD = QS.

44.87 - 1.8PG = 19.15 + 0.72PG

2.52PG = 25.72

PG = $10.21

Q = 44.87 - (1.8 x 10.21) = 44.87 - 18.378 = 26.492

(2) When PG = 4 (assuming PO = 65),

QD = 44.87 - (1.8 x 4) = 44.87 - 7.2 = 37.67

QS = 19.15 + (0.72 x 4) = 19.15 + 2.88 = 22.03

Since consumers can buy only what producers will sell,

Market quantity = 22.03

When Q = 22.03, From demand function: 22.03 = 44.87 - 1.8PG, or 1.8PG = 22.84, or PG = 12.67 (Demand price)

When Q = 22.03, From supply function: 22.03 = 19.15 + 0.72PG, or 0.72PG = 2.88, or PG = 4 (Supply price)

Deadweight loss = (1/2) x (Demand price - Supply price) x Change in quantity

= (1/2) x $(12.67 - 4) x (26.492 - 22.03) = (1/2) x $8.67 x 4.462 = $19.34


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