Step by step calculation is important!

Partial Equilibrium Consider a market for a single commodity. There is a single consumer with {inverse} demand curve IUDElle. There is a single supplier with [inverse] supply curve 1U +43. 1. Find the competitive equilibrium in this market [that is, assuming the con sumer and supplier act like price takers, even though the market is really too small for that]. '2. Calculate the producer and consumer surplus at competitive equilibrium (from 1} 3. Now suppose there is a tax of '2 per unit. Calculate the new equilibrium, consumer surplus, producer surplus, government revenue, and deadweight loss (again assuming that agents act as price takers}. 4. Now suppose the supplier realizes she has a monopoly, but the consumer still acts as a pricetaker. What price will the supplier charge if she uses a uniform pricing strategy?I 5. Finally, suppose the supplier realises she can use a more sophisticated plicing strategy. In particular, she will use a twopart pIicing strategy {as in the amuse-ent park model where there is an \"entry fee\" and then a fee per ride}. Calculate the two-part tari