Suppose that the demand and supply for pack of cigarettes is represented by the given equations.

Demand: p=502d

supply: p= 15+3Qs

where P stands for price, Qd stands for quantity demanded, and Qs stands for quantity supplied.

a) Calculate the equilibrium price and quantity and draw a diagram to illustrate your answer. Your answers must include both a diagram and words to clearly explain your diagram. In addition, your diagram must be fully labelled and therefore you must label both axes, correctly determine the vertical axis and horizontal axis intercepts, and show the equilibrium price and quantity associated with it.

b) Assume that each pack of cigarettes incurs an additional external cost of $5 due to the health risks associated with second-hand smoke. Analyse if the equilibrium quantity in part (a) reflect the socially optimal level of quantity? Support your answer by examining the presence of deadweight loss (DWL) on your graph

c) Suppose you've been appointed by the government to evaluate the effects of imposing a tobacco excise tax on cigarette suppliers to address public health issues. What specific corrective tax per pack of cigarettes would you propose, and what rationale would you provide to support your recommendation?

D) What are the new prices paid by consumers and received by producers, and what is the new quantity bought?

e) For the scenario after the introduction of the tax, illustrate on your diagram and compute the following:

(i) Consumer surplus

(ii) Producer surplus

(iii) Deadweight loss

(iv) Total Surplus

F) Based on your analysis, determine which party bears a greater proportion of the tax burden

in this example and briefly explain why.

G) Is society worse off or better of as a result of the imposition of the per unit tax? Briefly explain

your answer.

H) Suppose the average price of a pack of cigarettes fell by 14%, resulting in a 36% decrease in the number of vapes sold in 2021 and a 7% increase in the number of packs of cigarettes sold during the same period. Based on this information:

(i) Determine whether cigarettes and vapes are substitutes, complements, or unrelated goods. Support your answers by referencing the appropriate elasticity. (2 marks)

(ii) If the government wanted to increase its tax revenue, would you suggest an increase in the tax per unit on cigarettes? Support your answer by referencing the appropriate elasticity. (2 marks)

can you please draw diagrams and labels it for an better understand and elaborate how you draw the diagram and what it represents