Explain the following questions.This question is complete

IS-LM Model (Based on Mankiw Ch. 12 #3). Use the information about the following economy to build the IS-LM model. a. The consumption function is given by C = 300 + 0.6(Y - ). The investment function is / = 700 - 80r. Government spending and taxes are both 500. Graph the IS curve for this economy. Be sure to label the x- and y-axes. b. The money demand function is (M/p) = Y - 200r. The money supply M is 3,000 and the price level P is 3. On the same graph as in part a.), graph the LM curve. c. Find the equilibrium interest rate r and the equilibrium level of income Y. Label the equilibrium values on your graph. d. Suppose that government spending is increased from 500 to 700. How does the IS curve shift? What are the new equilibrium interest rate and level of income? Show the shift and the new equilibrium on your graph. e. Suppose instead that the money supply is increased from 3,000 to 4,500. How does the LM curve shift? What are the new equilibrium and level of income? On a new graph, show the original IS and LM curves and then show the shift and the new equilibrium. f. With the initial values for monetary and fiscal policy, suppose that the price level rises from 3 to 5. What happens? What are the new equilibrium interest rate and level of income? On a new graph, show the original IS and LM curves and then show the shift and the new equilibrium. g. . For the initial values of monetary and fiscal policy, derive and graph an equation for the aggregate demand curve (Hint: Solve the IS and LM curves in terms of r. Then combine them and solve for Y in terms of P.). What happens to this aggregate demand curve if fiscal or monetary policy changes, as in parts d.) and e.) (simply state which direction the aggregate demand curve shifts in each case)?1. (25 points) Consider two firms, 1 and 2, producing an identical good simul- taneously. This good has market demand given by the demand function y = (12 - p)/3, where p is price, and y = y1 + y2 is market quantity. yi represents the amount produced by firm i. Suppose production cost is 2yi + 1 for each firms. (a) Solve algebraically for these firms' reaction functions, expressing each firm's optimal output level given the level of its competitor's out- put.(5 pts) (b) Graph these reaction functions and show the equilibrium point. In- clude isoprofit contours through the equilibrium point for both firms. (5 pts) (c) Solve algebraically for the equilibrium: Determine the equilibrium market price, as well as each firm's equilibrium quantity and profit. (5 pts) (d) Solve for the collusive outcome in which two firms split monopoly profits. Is the profit for each firm in the collusive outcome larger than in the non-collusive outcome? Do you think firms will choose the quantities in the collusive equilibrium? Why? (5 pts) (e) Now consider that the marginal cost for each firm has increased to 3 while the fixed cost decreases to zero. Imagine that firms choose prices rather than quantities. Consumers split themselves evenly across the firms if the firms set the same prices, otherwise all con- sumers shop at the lower-priced firm. (5 pts) (1) Define a Nash equilibrium in prices p1 and p2. (2) Explain why the prices p, and p2 you propose is an equilibrium.Simple linear regression is a statistical method that allows us to summarize and study relationships between two continuous (quantitative) variables: One variable, denoted X, is regarded as the predictor, explanatory, or independent variable. The other variable, denoted Y, is regarded as the response, outcome, or dependent variable. Suppose that we are given n-i.i.d observations { (x;, y;)}"_, from the assumed simple linear regression model Y = BIX + Bo + . Answer the following questions on simple linear regression. 5-a. Denote 1 and Bo as the point estimators of B, and Bo, respectively, that are obtained through the least squares method. Show, step by step, that the two point estimators are unbiased. Derive the least squares estimator of of and determine whether it is unbiased or not. Show your work step by step. 5-b. Calculate _'_1(yi - Bix; - Bo) (Bix, + Bo). Determine whether the point (X, Y) is on the line Y = 1X + Bo. Explain your reasoning mathematically. 5-c. Using the maximum likelihood estimation (MLE) technique, derive a point estimator for the coefficient B1 and the intercept Bo, respectively. Determine whether the point estimators that you obtained via MLE are unbiased or not. Justify your conclusion mathematically. 5-d. Calculate the variance of the four estimators from Questions 5-a and 5-c, respectively. Show your work step by step. 5-e. Suppose that we are using the simple linear regression model Y = B1 X + Bo + 1 while the true model is Y = 1X1 + B2X2 + Bo + 82 where Bo, B1, and B2 are constants. We assume that the distributions of &, and e2 are both N(0,02), i.e., normal distribution with variance o?. We further assume that the two noise variables are uncorrelated. Find the least squares estimator of B, in this case and determine whether the point estimator that you obtain is biased or not. If it is biased, calculate the bias.(b) Assume these firms behave like price takers, how much will they produce and what price will they charge? Draw the outcome on a graph. What is the individual firms producer surplus? What is the total producer surplus of the market? (3 marks) (c) Suppose the four firms join together to form a single firm monopoly. What price will the cartel charge and how much output does the cartel produce? What is producer surplus for the cartel? (Hint: the marginal cost curve for the cartel firm is the supply curve found in part (a) with MC replacing P in this equation and MR = 200 -Q). What happens to consumer surplus and total welfare? (4 marks) 4. Calculate the own price elasticity of demand in the following situations (a) A price rise from po = 2 to p1 = 5 causes quantity demand to fall from go = 30 to q1 = 15 (1 mark) (b) The demand curve is given by q = 1/p with the slope of the demand curve given by $ = -1/p2. What is the own price elasticity of demand at any point?(2 marks) (c) The demand curve is given by q = 4 - 2p with the slope of the demand curve given by dp = -2. What is the own price clasticity of demand at: (i) p = 4; and (ii) p = 10? (2 marks) 5. Suppose the cost of producing q cars and q2 trucks is 45000 +80q1 + 10092. Calculate the measure of economies of scope when (1 mark each): (a) q1 = 100 and q2 = 200 (b) q1 = 500 and q2 = 800 6. Answer the following questions True, False, or Uncertain. Give a brief explanation of your answer. 1 mark for correctly identifying T, F. or U. 4 marks for explanation. (a) If a single price monopoly is instituted in what was a competitive market, consumer surplus will decrease more than producers gain. (b) If a firm's marginal cost is less than the firm's marginal revenue then the firm should decrease output and increase price. (c) If price is less than average cost then a firm will shut down. (d) A monopolist does not make a shutdown decision in the short-run and an exit decision in the long run since only competitive firms make these decisions