CHAPTER PROGRESS EXERCISES 6.9 Maximum/Minimum Economic Applications l. A firm\'

ID: 1126756 • Letter: C

Question

CHAPTER PROGRESS EXERCISES 6.9 Maximum/Minimum Economic Applications l. A firm's total revenue function is given by the equation T-902-3 (a) Find the valuc of for which TR is maximised, hence calculate the maximum (b) Write down the equations of the average revenue and marginal revenue funct how AR and MR change before and after maximum TR. (c) Sketch TR, mph, writedownhhevale,of and MR when TR is zero and when TR is a maximum. 2. Given the demand functions, 45 i) Q-150-05P (ii) P-8-2C) (iii) P (a) Write down the cquations for TR. (b) Calculare the number of units which must be sold to maximise TR. Calcu late the maximum TR. (c) State the valucs of Q at which MR and AR are zero. 3. A shup which sell T-shirts las a demand function and a total cost function given by the equations P 240 10Q and TC 120+80 (a) Write down the equations for TR and proft. b) Calculate the number of T-shirts which must be sold to maximise (i) profit, (ii) total (c) Write down the equations for MR and MC. Show that MR- MC when profit is maximised (d) Plot the graphs of. (i) TR and TC on the same diagram. From the graph estimate the break-even poins (i) MR and MC on the same diagrami What is the significance of the point of intersection cost and average revenue functions for a particular brand of mobile phone are giver (oonfirm your answer algehraically). of these two graphs 4·The average by the equations AC5and A 25 8000 (a) Write down the equations for TR, TC, MR, MC. must be made and sold to break even? b) How many mf the profit: finction. Show, by differentiation, that neithe mobile phones ) Write dewn the equation of th profit nor revenuc ever reach a maximum. Use MR and MC to explain why there is (d) Piot the graphs T of TR, TC and the proft function on one diagram. Plot MR and MC on a R, TC and the senarate diagram. Comment on the relatioushiph 1:P=2374 II:p= 5504-0.BQ The total cost function is T-608 580+ 120Q 5. A company supplying ftted kitchens is considering t n the two diagra fterent pricing strategies:

Explanation / Answer

Answer 2 a : There are three demand function

MR =300-4Q =0

Q= 75 UNITS

MR =80-4Q

Q= 20 UNITS

MR=0

Q= N.D

AR= 300-2Q /AR=0

Q=150 UNITS

AR = 80-2Q

Q=40UNITS

AR= 45

AR =N.D

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Answer 3. a . P = 240-10Q

PQ / TR = 240Q-10Q2

PROFIT = TR- TC

PROFIT = 240Q-10Q2- 120-8Q

PROFIT = 232Q-10Q2-120

PROFIT =0

10Q2-232Q+120 =0

Q=11.6 /12 UNITS

TR= 240Q-10Q2

TR=0

240Q- 10Q2=0

Q=24 UNITS

240-20Q =8

232 =20Q

Q=11.6 UNITS/ 12 UNITS

Particulars Q= 150-0.5P/ P= 300-2Q P=80-2Q P=45 (A)TR =P*Q 300Q-2Q2 80Q-2Q2 45Q (B) Maximum TR where derviate of TR=0 300-4Q=0 80-4Q=0 45=0 Number of unit sold where TR is maximum Q=75 UNITS Q=20 UNITS 0 (C) When MR =0