2. The town of Springfield has two types of resident: high- and low- types. There are 5 of each type in Springfield. The high-type residents place a high value on firefighters and have the following marginal benefit from firefighters where Xt is the total number of firefighters in Springfield: MBpgp =20 Xr. The low-type residents place a low value on firefighters and have the following marginal benefit from firefighters: MBj, =20 -2X7. The town currently funds its fire department solely from the individual contributions of these residents. Assume the marginal cost of firefighters is: MC =20+ 3Xy. where 20 represents each firefighter's wages and 3X7 represents training costs. (a) Solve for and graph the total marginal benefit for firefighters among Springfield residents. Be sure to label intercepts and any \"kink points\" in this relationship. (b) What is the socially optimal number of firefighters? Add the marginal cost curve to your graph and indicate the socially optimal number of firefighters. (c) It turns out that disaster insurance companies will only operate in Springfield if there are 14 firefighters, a fact that residents do not incorporate into their marginal benefit curves. The federal government, in an attempt to encourage Springfield to reach at least 14 firefighters, has enacted a policy through which it will subsidize 50% of the wages of each firefighter in Springfield. i. Graph the new marginal benefit and cost of firefighters in Springfield. Solve for the new equilibrium quantity. Is this policy effective? ii. At what subsidization level (give a percent) will Springfield choose to hire exactly 14 firefighters