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ef2452_B07_PS8

ef2452_B07_PS8 - What is the value of the elasticity of...

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Mathematics for Economics & Finance (EF 2452) Problem Set#8 Due: Week 10 Tutorial Class Please write your name, student ID and tutorial number on top of your answer sheet. Q1. The demand function for Revive, a monopoly supplier of water filtration equipment, is given by: Q = 31 - 2 P and its total costs (TC) are given by: TC = 6 + 16 Q - 4 Q 2 + 6 Q 3 where Q is in millions of units and price is in dollars per millions of unit. (a) Derive the profit function for the monopolist and find all the stationary points of the profit function using the first order condition. (b) Using the second order condition, identify the profit maximizing output for the monopolist from amongst the stationary points. (c) Find the elasticity of demand at the profit-maximizing level of output. Is the demand elastic or inelastic at the profit maximizing output? Comment on this elasticity level in general for all monopoly profit maximizing output. (d) What output level would the monopolist choose if it were a revenue maximizer?

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Unformatted text preview: What is the value of the elasticity of demand at the revenue maximizing level of output? Q2. A Frm’s total costs (TC) are given by the following expression: TC = 1 3 Q 3-5 Q 2 + 30 Q (a) Derive an expression for the Frm’s average cost (AC) function. (b) Find the output level at which the frm’s average cost is at a minimum. Use the second order condition to veri±y that it is a minimum. (c) What is the value o± average costs at this level o± output? (d) Derive an expression ±or the frm’s marginal cost (MC) ±unction. What is the value o± marginal costs at the output where average costs were minimized above? Q3. Assume the above frm operates in a per±ectly competitive market and is able to sell its output at a price o± \$14 per unit. Determine its proft-maximising level o± output using the frst order and second order conditions ±or a maximum....
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