please do these questions from the bottom to the up

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1 Firms in the Global Economy [30 points] Consider an automobile industry where firms are symmetric. Fixed costs in the industry (start-up costs of factories, capital equipment, and so on) are F = 5 and variable costs are equal to c = 1 per finished automobile. Because more firms increase competition in the market, the market price falls as more firms enter an automobile market, or specifically,| P =1+ AN (1) where N represents the number of firms in a market. Assume that the initial size of the U.S. and the European automobile markets are SUS = 180 and SED = 320, respectively. Instructions: Please show all your derivations. 1. What is the average cost function of production of automobile? Can you argue that there are increasing returns in production of cars? [5 points] 2. Using the properties of a symmetric equilibrium and the information on total output (i.e., market size) in the US and Europe, find the average cost function in the U.S. and Europe as a function of the number of firms active in the market, i.e. find the two "CC" curves. [Please do not just write the curve, derive it. Hint: leave formulas in fraction terms] [5 points]3. What is the equilibrium condition consistent with free entry and hence zero profits of all firms? [3 points] 4. Calculate the equilibrium number of firms and equilibrium prices in the U.S. and European automobile markets without trade. [Hint: the number of firm is an integer number, while the price is a fraction. You should keep the price in its fraction form] [5 points] Country: Country: 5. Now suppose the United States decides on free trade in automobiles with Europe. The trade agreement with the Europeans adds S" consumers to the automobile market, in addition to the SUS in the U.S. (i) How many automobile firms will there be in the United States and Europe combined? (ii) What will be the new equilibrium price of automobiles? [5 points]6. How are car prices in the United States affected by trade? How does trade affect consumers' welfare in this model? [Hint: You can answer this question even if you did not solve the questions above] [7 points]