Question 3-4

SESSION 13 The marginal revenue is the rate of change in total revenue per unit increase in output, Q The marginal cost is the rate of change in total cost per unit increase in output, Q AR is defined as average revenue per unit for the first Q su ccessive units sold. AR is determined by dividing total reven ue by the quantity sold, Q The AR function is equal to price, P. where Pis given by the demand function. P AR for any demand function, whether it is horizontal or downward sloping. AC is total cost divided by the level of output produced. Applications of Differentiation: MR, AR, MC, AC 1) The demand function for a monopolist is Q = 120-3P (a)Find expressions for TR, MR and AR. Evaluate TR, MR and AR at Q = 15. Hence explain in words the meaning of each function at Q 15 (b)Calculate the value of Q for which AR - 0.Calculate the value of MR when AR 0. Is it sensible for a monopolist to sell this value of o (c)Graph TR, MR and AR on the same diagram. 2) The demand function for a good is P 125 - Q (a)Find expressions for TR, MR and AR. Is the slope of the MR curve twice the slope of the AR curve? (b)Evaluate TR, MR and AR at Q 10 and at Q = 25. Hence, explain in words the meaning of each function at Q- 10, Q 25 (c)Calculate the value of Q for which MR 0. Calculate the value of Q for which AR 0 At what point (value of Q) does the sale of further units first start to reduce total revenue? Explain (d)Graph TR, MR and AR on the same diagram 3) A fim's fixed costs are 1000 and variable costs are given by 30 (a)Write down the equation for TC. Calculate the value of TC when Q = 20. (bWrite down the equation for MC. Calculate the value of MC when Q 20. Describe, in words, the meaning of MC for this function. 4) A fim has the following average cost function: 10 AC 50 (a)Show by differentiation that AC decreases indefinitely as Q increases. (b)Write down the equation for total cost. Hence, write down the equation for total variable cost and average variable costs. State the value of foxed costs (c)Write down the equation for marginal costs. Comment on the relationship between TC and MC in this example. 5) A fim has an average cost function, 150 AC Q-90+ +75 (a)Find an expression for the TC function and calculate TC when Q 15. (b)Write down the equations for FC and TVC. (c)Find an expression for the MC function. Show that MC 0 for all Q. Plot the MC and AC curves on the same diagram