A monopoly is facing a downward sloping linear demand given by p=a-Q. Monopoly's unit production cost is given by c>0. Assume that the government imposes a specific tax of t dollars per unit on each unit of output sold to consumers.

Show that this tax will raise the price paid by consumers by less than t. (I did this part)

a) How is it possible? Is not the case that a monopoly should pass all per unit taxes to consumers?

b) Would your answer change if the market demand curve has a constant elasticity and is given by p=Q-1/2 ?

Please I want answers and explanations for parts a and b (in bold)