Provide solutions to the following questions

1. Define the limit of a function by using the concepts of existence and neighborhoods. 2-a) Find: lim (1 - x3) xa1 1-x 2-b) Find lim 2+1 x a co (x + 1) 3. Find the price elasticity of the following nonlinear demand function: Q = ap-b Where Q is quantity demanded, p is the price of its own. (Show your work. This means that no work no credit.) 4. . Find the derivative of the quotient of the following U and V functions: Y = U / V, where U = X and V = 2X + 3 5. Find (1) the different quotient and derivative when tax rate increases from 15% to 20% and (2) the maximum tax revenuebased on the following quadratic tax revenue function: R = 200t - 200+2 6. Find (i) the marginal revenue, (ii) the marginal cost, and (iii) marginal profit of the following functions: TR = 41.50 - 1.102 TC = 150 + 10Q -0.502+ 0.02031. (8 Points) Consider the quadratic regression problem: Yi = Bo + BIXi+ B2X? + ci. Suppose that we have 4 observations (Y1, X1), (Y2, X2), (Y3, X3), (Y4, X4) and they take values (1, 1), (0, 2), (6, 3), (7, 4). The matrix representation of this model is Y = XB + E. Then Y = (1, 0, 6, 7)T, B = (Bo, B1, B2)], and E = (61, (2, (3, EA) T. Answer the following questions with your explanation. (a) What is X in this case? (b) Calculate 3 = (XTX)-1XTY. (c) Find all the eigenvalues of XTX. (d) Is XX positive definite?AUECO/AUENV 341 Assignment #2 Winter 2020 Work in groups of 2 Due: Monday, March 09 Total Marks: 55 Assume there are two firms in an industry with similar emissions but different Marginal Abatement Costs (MACs). The MAC for firm 1 is MAC, = 100 - 10E and the MAC for firm 2 is MAC2= 50 - 10E, where E the quantity of emissions. a) IfMD=30E, where MD =Marginal Damage and E = Emission, compute the socially efficient equilibrium for each firm. (5 marks) b) Now graph each MAC and draw the aggregate (industry) MAC. Assume MD is still MD = 30E, compute the socially efficient equilibrium for the industry. (5 marks) c) Suppose the government sets the pollution level for the industry at 4 units, calculate the net social cost of the policy