Duncan has made so much money from his ramen business that he now has enough money to achieve his dream of opening up a coffee shop. Suppose the coffee shop market in Dallas has a perfectly competitive market structure, in which each coffee shop produces identical lattes. Let Duncan's cost function be given by: C(Q) = 2/3 Q³ 3/2Q² + 2Q + 2

1. Find Duncan's marginal cost, average cost, and average variable cost function. Sketch these out graphically.

2. Suppose Duncan did not do his research before paying the fixed cost for rent for the shop, and finds that the market price for a latte is given P = 2. Sketch it out graphically and show profit on the graph. What is Duncan's profit? What is your shutdown and entry/exit recommendation for Duncan? Sketch out on your graph what would happen to market supply and price if Duncan and other coffee shop owners followed this recommendation.

3. Duncan decides he is not going to listen to any advice and give up on his dream. Duncan adds pumpkin spice to his lattes (despite it being June), something no other coffee shop owner is doing. It's a big hit, and Duncan now enjoys a monopolistic demand curve of P = 5 Q. Sketch this out on a new graph, find Duncan's profit.

4. September comes around and all of the other coffee shops begin adding pumpkin spice to their lattes as well. On your graph from (4), sketch out what you predict will happen.