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2. (20 points) Suppose the total cost function of a monopoly firm is: TC(q)= q3 - 61.25q2 +1528.5q +2000 Suppose the revenue function for the firm is: R(q)= 1200q-2q2. With this information, answer the following questions: a. (5 points) Given the form of the revenue function, derive the inverse demand function for this monopolist. Also draw the graph for the demand function. b. (2 points) Form the firm's profit function for this monopolist. c. (10 points) Solve for the firm's profit maximizing output. For full credit it is absolutely necessary to show all the numerical work. d. (3 points) What is the profit at the profit maximizing output? 3. (15 points) Suppose the total cost function of a monopoly firm is: TC(q)= q3 - 61.25q2 +1528.5q +2000 a. (3 points) Derive the expression for the average variable cost (AVC) for this firm. b. (10 points) Solve for the firm's output where the AVC is minimum. For full credit it is absolutely necessary to show all the numerical work. c. (2 points) What is the AVC at this level of output?Consider the following function: f(x1, X2) = Ax1.5+x2 where x, 2 0, X2 2 0, A 2 0, 0 0 and faces prices p, and p2 respectively for goods x1 and X2. i) Derive and describe the demand of the consumer for goods x, and x2. [20 marks]2. Travis's demand for ice cream is Q1- =12 - 3F and Mays's is QM = 6 - P. [12 points} I} Find the market demand for ice cream if Travis and Maya are the ccnlyr hue cmsumers in the market. (3 points} 2} What is the price elasticity of demand when P = 2'? {3 points} 3} At this price, is demand elastic, unit elastic, er inelastic?I [3 points} 4} If this price were to increase by a little hit1 what would happen to the tents] revenues from ice cream sales? [3 points} In Problems 46-48, let C(n) be a city's cost, in millions of dollars, for plowing the roads, when n inches of snow have fallen. Let c(n) = C'(n). Evaluate the expressions and inter- pret your answers in terms of the cost of plowing snow, given 15 c (n)