Joint Juice produces a prepackaged joint support supplement for relief of joint pain with 180 tablets per bottle and operates in a perfectly competitive market. Basically, all the firms in this competitive market have technologies (production and cost conditions) that are the same as Joint Juice's. Suppose Joint Juice's total cost function is given by the following where q is Joint Juice's quantity of packages per day: C(q)=250+6q+0.1q The market demand function for the output in this market is given by: Q = 1,848 - 2P a. If there are 20 identical firms in this industry, find the market equilibrium price for the prepackaged supplements. b. Calculate Joint Juice's optimal output level and profits given the market price for the product. c. If Joint Juice is typical of the firms in this industry calculate the firm's long-run equilibrium output, price, and profit level. Suppose the situation changes. Joint Juice has its plant in Portland Oregon. The local government passes a new tax on businesses that raises Joint Juice's fixed cost by $25 per period. The cost function now becomes: C(q)=300+6q+0.1q All the other firms in the market are in other states/cities that are not subject to the laws or taxes of Portland. d. Calculate Joint Juice's optimal output level and profits if the market price for the product stays the same as for part a. What will the firm do in the long run? e. Is it reasonable to assume the market price prevailing today will remain the same in the long run? If so why? If not, why not? How about the number of firms in the market?