Hi could you please help me to solve those ?

KMA ANSWER ALL QUESTIONS 1. An industry of price-taking profit-maximising firms in perfect competition all produce using the same technology, and each has a total cost function given by: TC = 2q3 -4q2 + 3q Where TC is measured in thousands of pounds per week, and q is measured in thousands of units per week. Then: a) If the market price of output is p = $4.5 what is each firm's output and profit (or loss)? [10 marks] b) If the market price of output is p = fl1 what is each firm's output and profit (or loss)? [8 marks] c) Show that each firm's long-run output is 1000 unit per week (i.e. 1 thousands of units per week). [8 marks] d) What is the price of output when the industry is in equilibrium? [6 marks] e) if the market demand is given by P = 11 - 0.01Q, where Q is the industry output in thousands of units per week, what is the industry's equilibrium output and how many firms are in the industry in equilibrium? [10 marks] f) If the market demand shifts to P = 12 - .01Q, what is the industry's equilibrium output and how many firms are in the industry in the new equilibrium? [8 marks] Page 12' A rm called Shanghai Housing Limited has won a tender to build housing units within _ _ , , _ . _ . Quantitative Methods Formative, Summgy Answer Sheet for Question 1: the Durham city council. As part of its initial planning, it found out that the demand and supply functions for houses in Durham are given by the following: 1. Price Prot-maximising Prot/Loss Ps=a+BQsande=a_ Pd . quantity a) Represent the above functions on a suitable graph, properly labeling all the axes and 4 5 curves [3 marks] 1 1 b) Find the equilibrium values of quantity and price [10 marks] long-run equilibrium price c) In order to increase housing units, Durham local council is thinking to offer a subsidy of 29k per housing unit. Discuss, using post-subsidy expressions, the With demandas in(e): possible effects on equilibrium house prices and quantities if this decision is industry output implemented. [10 marks] number of rms d) Write expressions for the price elasticities of demand and supply of housing after the granting of the subsidy. [10 marks] With demand as m (1): industry output e) Write appropriate expression showing the projected total expenditure of Durham county council that is related to the subsidy [3 marks] number of rms Information available to Shanghai Housing Limited also indicated that the total variable cost for such a project is given by: TVC(Q) = 5Q2 + HQ Where Q is quantity of housing units produced and 8 and are Positive constants You also know that the total costs is approximated to be 9 if no housing units are produced. f (i) Using appropriate equations, w1ite the estimated housing prot function for this rm [4 marks] f (ii) Using your information from f(i) or otherwise, work out an expression for the number of housing quantity that will maximize prot. [10 marks] Page 2 Page 3