("Macron and the yellow vests) Consider the following economic inference: If the government introduces a fuel tax, then the supply curve of fuel shifts up if the fuel tax is paid by producers. If the supply curve of fuel shifts up, then the equilibrium price of fuel increases and the equilibrium quantity of fuel decreases. The fuel tax is paid by producers or the fuel tax must be paid by consumers. Therefore, if the government introduces a fuel tax and the equilibrium quantity of fuel does not decrease, the fuel tax must be paid by consumers. 9 (a) Formalise this inference using the following formalisation key. The fuel tax is paid by producers. The fuel tax must be paid by consumers. ri The equilibrium price of fuel increases. r2 The equilibrium quantity of fuel decreases. The supply curve of fuel shifts up The government introduces a fuel tax. (b) Show that the conclusion is indeed derivable from the premises by reconstructing the informal deduction below as a correct derivation in our system of natural deduction. Feel free to add missing steps. S t Suppose the government introduces a fuel tax and the equilibrium quantity of fuel does not decrease. Then we can infer from the first premise that the supply curve of fuel shifts up if the fuel tax is paid by producers. Now assume for reductio that it is not the case that the fuel tax must be paid by consumers. Then it follows that the fuel tax is paid by producers. Hence, the supply curve of fuel indeed shifts up. Thus, the equilibrium price of fuel increases and the equilibrium quantity of fuel decreases. But the latter contradicts our initial hypothesis. So we can conclude that the fuel tax must be paid by consumers. Hence, if the government introduces a fuel tax and the equilibrium quantity of fuel does not decrease, the fuel tax must be paid by consumers. ("Macron and the yellow vests) Consider the following economic inference: If the government introduces a fuel tax, then the supply curve of fuel shifts up if the fuel tax is paid by producers. If the supply curve of fuel shifts up, then the equilibrium price of fuel increases and the equilibrium quantity of fuel decreases. The fuel tax is paid by producers or the fuel tax must be paid by consumers. Therefore, if the government introduces a fuel tax and the equilibrium quantity of fuel does not decrease, the fuel tax must be paid by consumers. 9 (a) Formalise this inference using the following formalisation key. The fuel tax is paid by producers. The fuel tax must be paid by consumers. ri The equilibrium price of fuel increases. r2 The equilibrium quantity of fuel decreases. The supply curve of fuel shifts up The government introduces a fuel tax. (b) Show that the conclusion is indeed derivable from the premises by reconstructing the informal deduction below as a correct derivation in our system of natural deduction. Feel free to add missing steps. S t Suppose the government introduces a fuel tax and the equilibrium quantity of fuel does not decrease. Then we can infer from the first premise that the supply curve of fuel shifts up if the fuel tax is paid by producers. Now assume for reductio that it is not the case that the fuel tax must be paid by consumers. Then it follows that the fuel tax is paid by producers. Hence, the supply curve of fuel indeed shifts up. Thus, the equilibrium price of fuel increases and the equilibrium quantity of fuel decreases. But the latter contradicts our initial hypothesis. So we can conclude that the fuel tax must be paid by consumers. Hence, if the government introduces a fuel tax and the equilibrium quantity of fuel does not decrease, the fuel tax must be paid by consumers