Answer the following.
3. The market illustrated below has Inverse demand p(Q) = 130 - 30 and industry wide marginal cost MC(Q) = 10 + 2Q. If production is competitive, this is the market (inverse) supply curve. If production is consolidated under a monopolist, this is the monopolist's MC curve. a. Suppose there is a monopolist. Explain how marginal revenue for a monopolist is different than for a firm under perfect competition. Then derive the profit-maximizing market outcome (including the monopoly price and quantity @. and P.)- b. Now suppose the market operates under perfect competition, but with a per unit taxt = $30. Determine the market equilibrium and illustrate on a diagram. As a follow-up, determine the relationship Q (t) that gives the equilibrium market quantity as a function of the tax rate. c. If you invert the relationship from part (b), you have T(Q), the tax the government would need to set if it wishes the market quantity to be Q. Then total tax revenue is T(Q) = (Q) . Q. [This may be useful for the intuition that's requested below.I Determine whether total welfare in this market is higher (i) under a monopoly, or (fi) under perfect competition with an "empire-building" government that maximizes total tax revenue T'(Q). For (il), make the usual assumption that tax revenue is spent on something useful (le.. not wasted). Illustrate both cases on a single diagram, Do your best to explain why your comparison turns out as it does. [Applying intuition about the components of marginal revenue MR(Q) to the "marginal tax revenue" 7"(Q) might be helpful.] P P(Q) = 130 - 30 MC(Q) = 10 + 2Q (s(p) = 4p -5)Suppose you are estimating parameters of the following regression model: Where: I'm = average starting pay at graduation, in pounds. N'a = tuition fee in 2012, in pounds. X's = independent recruiter rating (maximum is 5.0). 1 = disturbance term. Using cross-section data on top 50 UK graduate business schools, you obtain the following results: Y, = 9941 + 0.25 X2 + 15125 X31 (6114) (0.121) (7349) R' = 0.87. RSS = 10310 The figures in parentheses are the estimated standard errors. RSS are residual sum of squares.) (i) Comment on the signs of the variables in the model. (2 Marks) (ii) Interpret and explain individual coefficients. (4 Marks] (iii) Suppose X's increases by 0.25; what is the expected impact of this change on Y? (2 Marks) (iv) Comment on the explanatory power of the regression. (2 Marks) (v) Using t-tests show whether individual coefficients are significantly different from zero at 5% level of significance. (4 Marks) (vi) Test whether the coefficient of X, is significantly different from 1 at 5% level of significance. (2 Marks) (vii) Carry out an appropriate test to check if coefficients are jointly significant. (5 Marks)1. Assume that the market for steel is competitive. The inverse demand curve for steel is P = 120 - Q and its inverse supply (i.e., industry marginal cost) curve is P = Q + 20, where P is price and Q is quantity. (a) Depict these inverse demand and supply curves in a diagram and use algebra to calculate the market equilibrium values of price, Pe, quantity, Qc, and price elasticity of demand, Ec. [10 points] (b) In the above context, also calculate consumer surplus, CS, producer surplus, PS, and social welfare, SWc. [10 points] 2. Suppose that the industry in Question I is taken over by a monopolist. (a) Depict the monopolist's profit maximization problem in a diagram and use algebra to solve for the values of price, Pm, quantity Om, and price elasticity of demand, Em. [10 points] (b) Calculate the impacts of monopolization in terms of the resulting changes in consumer surplus, producer surplus, and social welfare. [10 points] 3. (a) Return to the scenario in Question 1 and assume that the process of producing steel causes air and water pollution, which result in marginal external cost MEC = 20. Taking this externality into consideration, calculate the socially optimal level of steel production, Q, and illustrate its determination in a diagram like the one for Question 1(a) by using any additional curve that may be needed. Also calculate social welfare, SWs. [10 points] (b) If the competitive market fails to account for external costs and continues to produce at Q (from Question 1(a)), what would be the resulting loss in social welfare? Explain your calculation with the help of a diagram. [5 points] (c) Calculate a per unit tax that could correct the market failure in part (b). If this tax is implemented, what would be the resulting values of social welfare, consumer surplus, producer surplus, total external costs, and total tax revenue? Also illustrate these areas in a diagram. [15 points]MAT 166 -Pre-Calculus Writing Assignment | Students will be expected to answer all questions with the whole story. Perform each task on your paper, If you are asked to explain or define, be sure to use complete sentences. Sentence fragments are meaningless in technical writing The intent should be to inform the reader, and to convince the reader of the knowledge and competence of the author. Answer the following questions in the order they are given. Answers should be organized on a separate sheet of paper. Answers may be nped, hand written or a combination of both. If answers to questions are not numbered (or lettered), it will be assumed that question I was answered and no other. This assignment is intended as a condensed review of functions. There is a recommended video that may aid in the completion of this assignment, but you may use any resource to aid in the completion of this assignment. Be sure to use a trusted source, and cite any source that you used. If you quote a source, paraphrase the quote in your own words. I. Read all the directions for this assignment and copy the most important instruction as your answer to this question. 2. Watch the video https//www.yxstubs.com/waishiv HourscawWr and write your favorite color as the answer to this question. 3. Create or find a definition of a function. Include a definition of "domain" and "range" in the answer to this question. (It is recommended that the words "relation" or "pairing"be used in the definition.) (see page 137.138) Use the previous definition of function to explain the "vertical line test" and why it works. Note. A feat and a definition are not the same. 5. Tell why the trigonometric functions adhere to the algebraic definition of a function, and describe the "inputs" and "outputs" of any trigonometric function. 6. Create or find a definition of a "one-to one function". (p 357) 7. Use the previous definition to explain the "horizontal line test" and why it works. Note: A rest and a definition are not the same 8. Create or find a definition of inverse functions". (p 359) 9. Given that the function / (X) has an inverse function . (F) a. If f(2)=120 . find / (120) b. If the domain of /(x) ;, re[0,1000) . what is the range of S (F)? e, If the domain of / () represents time in years after 2010, and the domain of / (X) represents the population of Ourtown, write a sentence to interpret 1 / (2)=120 it. f (500) =7 /(x)=4+5 10. Let 7 and g(x)=7x-5 a Find ('9 (x) and (9-f)(x ) b. Come to a conclusion about the relationship between the functions f (x ) and glx] explain how you arrived at the conclusion. and 1 1. What is the most important concept you have learned/remembered by doing this assignment
