A monopoly with constant marginal costs mc = $20 has two potential groups of customers, whose demands are Q1=100-0.8p and Q2=100  p respectively and who cannot trade with each other. 

i.(5%) If the monopolist were allow to perfectly price discriminate and use non-linear pricing schemes, what strategy would it use? ii.(5%) Assume instead that the monopolist can identify the group type of each individual consumer but can charge only uniform prices. Find the optimum price-quantity combination that the monopolist will set for each group . iii. (5%) Now suppose that the monopolist only knows that there are two groups of

consumers in the market with demand functions as above but is unable to identify the type of each individual consumer. What would be the profit-maximizing non-linear pricing strategy for the monopolist? iv.(5%) Show on three different diagrams the amount of profit the monopolist would earn in each case. Which strategy gives the highest profit and which gives the lowest (use diagrams only, no calculations required).