Answer - If the people of lower income group are demanding lower prices for gasoline , the government can set up the price ceiling on gasoline. This will be set below the equilibrium price and will be effective because now , the price will be less than equilibrium and people will be able to buy it at lower prices.
But , it is not fair. This is because , firstly , it will cause the shortage of gasoline in the market as supply would be less below the equilibrium price. Secondly , as the price will be set below the equilibrium price , the producer surplus will fall and hence it will lead to the creation of deadweight loss in the market making the market inefficient. Hence it will not be fair.
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