Question

2. In the U.S. the two main sources of energy are natural gas and oil. Assume that the supply curve for natural gas (per thousand cubic feet) is given by Q = 15.9 +0.72PG + 0.05Po where Pg corresponds to the price per thousand cubic feet (Tcf) of natural gas, and Po is the oil barrel price. The demand curve for natural gas (in Tcf) is Q = 0.02 - 1.8PG + 0.69Po. (a) Are natural gas and oil complements or substitutes. How does it show up in the demand and supply curve? (b) Assume that the price of oil is determined exogenously i.e. does not depend on what happens in the U.S. market) and that is currently at $50. Find the free market equilibrium for natural gas (c) Assume that the U.S. government has a law that sets a ceiling for the price of natural gas. The (hypothetical) ceiling is set at $7 per Tcf. What is the effect of the price ceiling on the market equilibrium you found in (b) (d) The price of oil has increased to $100. The U.S. government considers that this is creating an undue burden on U.S. citizens and decides to lower the price ceiling to $3.5. What is the effect of the new price ceiling on the market equilibrium. What is the effect on consumer surplus and producer surplus (compared to the case of oil price at $100 and no price ceiling). Are consumers worse off or better off. (e) Instead of using a price ceiling to ease the situation created by the increase in oil price, the U.S. government decide to offer a subsidy of $2 per Tcf paid directly to the consumer. What will be the new market equilibrium and what will be the effect on the subsidy on consumer surplus, producer surplus, and the cost of the subsidy. Who is benefiting the most from the subsidy?

Answer 1

A)In demand ,the goods are substitue as there's positive sign subscribted along with po.,means Increase in price of oil Increases demand of natural gas.

In supply ,The goods are associated as complementary.

Qs=15.9+0.72Pg+0.05Po

Pg=(-15.9+Qs-0.05Po)/0.72

Increase in po leads to decrease in price of Natural gas ,so for seller they are complementary goods.

B)With po=50

Qs=15.9+0.72Pg+0.05*50=18.4+0.72pg

Qd=0.02-1.8pg+0.69*50=34.52-1.8pg

EQUILIBRIUM is at where Qs=Qd

18.4+0.72Pg=34.52-1.8pg

2.52Pg=16.12

Pg*=16.12/2.52=6.4

Q*=18.4+0.72*6.4~23

C) Price ceiling is the price At which seller can't charge from CONSUMER. Because equilibrium price is 6.4$ while goverment set price ceiling 7$ ,so equilibrium price is lower than price ceiling,so price ceiling is non binding and there won't be any effect on equilibrium of market from this price ceiling.

D)with po=100

New supply function;Qs=15.9+0.72Pg+0.05*100=20.9+0.72pg

New demand function; Qd=0.02-1.8pg+0.69*100=69.02-1.8p

New equilibrium,

20.9+0.72Pg=69.02-1.8pg

2.52pg=48.12

Pg=48.12/2.52=19.09

Qg=20.9+0.72*19.09=34.6448

The price ceiling is lower than equilibrium price ,so it is binding price ceiling.

Demand at pg=3.5; Qd=69.02-1.8*3.5=62.72

Supply at pg=3.5;Qs=20.9+0.72*3.5=23.42

So there is excess demand of natural gas or shortage of natural gas at price ceiling equal to 3.5$.

Sue to price ceiling equilibrium Market changed into shortage of goods in the market.

CONSUMER surplus ( no price ceiling)=1/2*34.668*(38.34-19.09)=333.45

Willingness to pay for Qd=23.42 is p=25.33

CONSUMER surplus ( with price ceiling)=(25.33-3.5)*23.42+1/2*23.42*(38.34-25.33)=518.28+152.34=670.62

So due to price ceiling , CONSUMER Increases compare to in absence of price ceiling.consumers are better off by price ceiling.

Producer surplus ( no price ceiling)=20.9*19.09+1/2*(34.6448-20.9)*19.09=398.98+131.09=530.14

Producer surplus ( with price ceiling)=20.9*3.5+1/2*(23.42-20.9)*3.5=73.15+4.41=77.56

So due to price ceiling producer surplus Decreased.so producers are worse off by price ceiling.