Question 2 (problem-set) In a small town, called Neverhood, there existed only one producer and supplier of natural gas. This rm, Gas-Hood, has a cost function that looked like this: C(yGH) = 2315,, + 20316,, + 250, where c is the cost (in E), and y is the quantity of natural gas (in cubic metres) produced by the rm. Neverhood's economy is dependent on natural gas, and it has a market demand for it shown as: Y(p) = 150 0.5;), where Y is the quantity of gas demanded in the market, and p is its unit price. (a) If Gas-Hood is a prot maximizing rm, what are the optimal levels of: [show every step of your calculation] i. Production of natural gas ii. Price of natural gas iii. Profit gained by Gas-Hood After a few years of having only one producer in town, a start-up energy company, called GreenGas, launches its production in Neverhood. Natural gas demand seems to be stable and not affected by emergence of the new factory. The natural gas supplied by the two rms are identical with respect to the quality and chemical features. GreenGas also is a profit maximizing company with a cost function of (30/55) = 373:6 \" 63'60 + 300- The two suppliers started to compete with one another to gain the larger share of the market. (b) If the two competitors act simultaneously, nd the optimal value of the following variables for both rms: i. Prod uction level ii. Price iii. Profit (c) After a while, Gas-Hood, as it had been around for some time and knew the market better, acted as the leader and decided about its production level rst. Under such arrangement, nd the optimal value of the following variables for both firms: i. Prod uction level ii. Price iii. Profit (d) Ten years of this competition passed, and while the market demand stayed the same, the two rms' cost arrangements evolved, and they converged to an identical simple linear cost function: 501,-) = 170yi ,where i = GH, 66 . Therefore, the firms came to an agreement to collaborate. They started making decision about the production level together. Under this collusion, what are the optimal values of the following variables for both rms: 2 i. Production level ii. Price iii. Profit (e) Compare the industry's output and price under the three phases of the market structure in part b, c, and d. Argue which model guarantees a higher welfare from the Neverhood oonsumers' point of view? In answering the above, show all math work. Explain the steps of your calculation and give reason. Feel free to round up numbers if they do not look nice and tidy