Solve the following questions.
Q2 = Output sold in market 2 Q1 = Price charged in market 1 Q2 = Price charged in market 2 The total cost of production is given by C = 50 + 40Q Where C = total cost of producing a unit of bread. Required: (a) The total output that the firm must produce in order to maximize profits. (4 marks) (b) What price must be charged in each market in order to maximize profits. (2 marks) (c) How much profit would the firm carn if it sold the output at a single price, and if the discriminates? (5 marks) (d) () The price elasticity of demand for the two markets at the equilibrium price quantity. (5 marks) (1) Comment on how the price elasticity of demand may be used in making economic decisions. (3 marks) (e) Under what conditions is price discrimination possible? (2 marks) (Total: 20 marks)You have been hired as a consultant by a firm producing bread to advise on a price strategy that would enable the firm to maximize profits. The firm is a monopolist which sells in two distinct markets, one of which is completely sealed off from the other. As part of the analysis, you establish that the total demand for the firm's output is given by the following equation: Q =50-5.0P And the demand for the firm's output in the two markets is given by the following equations: Q1= 32 -0.4P, and Q2 = 18-0.1P2 Where Q = total output Price Q1 = Output sold in market 1(i) (a) Describe the general form of the polynomial formula used to graduate the most recent standard tables produced for use by UK life insurance companies. (b) Show how the Gompertz and Makeham formulae arise as special cases of this formula. [3] (ii) An investigation was undertaken of the mortality of persons aged between 40 and 75 years who are known to be suffering from a degenerative disease. It is suggested that the crude estimates be graduated using the formula: 1 1 = exp both x+ + by x+ (a) Explain why this might be a sensible formula to choose for this class of lives. (b) Suggest two techniques which can be used to perform the graduation. [3] [Total 6]An insurer has initial capital of # and receives premium income continuously at the rate of e per annum. Let S() denote the total claim amount up to time /. (i) Describe a model that would allow the insurer to estimate its probability of ruin (ie the probability that its claims outgo is more than its available funds). State any assumptions that you make. [3] (1i) Write down an expression for the probability of ruin in terms of u , c and S(!). [1] [Total 4]
