Answer the following question. Please show all steps and use graphs if it makes it easier. The question is worth 8 marks.

People in Edmonton interested in buying local food have created a co-operative retail outlet. The co-operative purchases food from local producers and sells it to co-operative members. The demand by co-operative members for local produce (fruit and vegetables, per month, in kilograms) is of the following form:

Q_Produce = 1300 - 24 P_P, where P_Pis the price per KG of produce.

The Total Cost ($) function for produce provided by the co-operative is :

TC (Produce) = 775 + .005 (Q_Produce)²

1. The co-operative sells Q_produce (produce, Kg) at the optimal price for a co-operative. What is that price? How many kilograms of produce would be sold by the co-operative, if it maximized member welfare?
2. New research by the University of Alberta shows that the environmental benefits from purchasing local food significantly reduces the GHG emissions for Edmonton. This increases the number of people wanting to become members of the co-op. What is the quantity of produce that would be sold if the co-operative demand equation changes to:

Q_produce = 2000 - 30 P_P, where P_P is the price per KG of produce. What is the new price? (assume still maximizing member welfare)?

3. What is the aggregate consumer surplus for members at the original price and quantity and at the new price and quantity after the new members join? On a per kilogram basis, are the original members obtaining more or less consumer surplus per unit of produce?

4. The total costs of selling produce increase to:

TC (Produce) =800 + .005 (Q_Produce)

Does this increase in fixed costs change the price or quantity sold by the co-operative if it wishes to continue selling at the price that maximizes member welfare? If so what are the new quantity and price?

Bonus question

What is the cooperative profit associated with the co-operative selling at the optimal co-operative price before andafter the new members join? (calculate at the original TC function).