'Please illustrate your logic. reasoning. equations. steps and calculations clearly! The demand curve for pizza in the Smalltown is: Q, = 120 - P. where 0.; represents the quantity demanded of pizza in the Smalltown. and P represents the market price of pizza. There are TWO pizza restaurants in Smalltown now: Restaurant A and Restaurant B. Both of them have the same cost of production. that is Restaurant A's total cost of production is TCA= 600 + 24:}... . and Restaurant B's total cost of production is: TCE.I 600 + 24qg. where q... and of; are the output level chosen by Restaurant A and B. respectively. Restaurant A and B strategically interact with each other. a) If RestaurantA and B enter into a collusion agreement and split the market. what will be the market (total) equilibrium quantity and market equilibrium price? (4 points) b) It Restaurant A and B choose their output (quantity produced) to maximise profit. do you think that they will both honor their collusion agreement? What are the levels of output for each restaurant and the market equilibrium price? Please explain with equations/models and your reasoning clearly. (8 points) c) If RestaurantAand 8 get into a competition by choosing their price level. what will he the equilibrium market price and equilibrium market quantity? [2 points) d) Given the answer from part cl. what will be the possible problemls} facing by Restaurant A and B? (4 points) e) Given the market demand and cost function stay the same as above. and if the number of restaurants increases to 5. li restaurants compete by choosing quantity produced. what will be the enuilibrium market (total) quantity and price? (4 points) Now. let the market demand come: Q. = a - up ['a" and 'b" are the unknown parameter}: the number of restaurants increases to 3 (Restaurant A. B. and Cl and Restaurant A's cost function is: TCA= F; + cam: Restaurant B's cost function is: TCB= Fa + can\": Restaurant B's cost function is: TCc= PC + ccqc. where FA. ca. F3. :3. Fc. cc are all positive numbers. f) Please nd the best response function of Restaurant A. B. and C in general form. respectively. 'Here. only the best response function of Restaurant A. B. and C would be enough. you don't need to solve the equilibrium. (10 points)