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Question 1Each additional unit a company produces costs £45 to manufacture and it can sell each unit it produces for a fixed price of £72. The firm also has fixed costs of £8,100.(a) Find the break-even output and draw a break-even chart to illustrate this solution.(b) Write profit π as a function of output q and use this function to predict the profit when 450 units are sold.(c) What output level would generate a profit of £2,025?
2. A demand function is specified as P = 380 - 2.5Q where P is price (in £) and Q is quantity demanded.
(a) Draw a sketch graph of this demand function, identifying where it cuts the P and Q axes, and say what its slope is.(b) Derive the inverse function, Q = f (P) , and use it to find Q when P is £125.(c) What is arc elasticity of demand over the range of the demand schedule between the prices of £125 and £150?(d) Derive the total revenue function (TR) corresponding to this demand function and then find the output levels at which TR equals £13,000 by solving the relevant quadratic equation.(e) If this is a competitive market with the supply function P = 20 + 5Q what are equilibrium price and quantity?(f) If the government imposes a per unit sales tax t, derive a reduced form function for equilibrium quantity in terms of the tax t.(g) Using the function you have just derived, explain what happens to equilibrium quantity and price if a per unit sales tax of £30 is imposed.
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