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PRIVATE EXERCISE Subject : Business Administration Trainee: Pham Thi Diep Anh Class: GaBA01.X03 Exercise 1: Internet service provider has two potential customer groups as follows: 10 Enterprises and 10 Universities * Demand function as per Enterprise: Q = 10 – P * Demand function as per University: Q = – P In which, Q is mil sec./month; maginal cost as per access unit is VND/s a) Assume that the company can separate between enterprises and universities • • • • Each enterprise has common demand line Q=10-P; thus, we have to calculate the subscription and access costs as per an enterprise and take the results to multiply with 10 E (Enterprise): To acquire the maximum surplus profit from the consumers, the company sets up the price based on maginal cost P=MC= ⇒Access time Q1=10-2=8 mil sec ⇒Access cost = mil sec x VND/ s = 16 mil VND ⇒ Subscription cost (F1) is the consumption surplus for each enterprise which uses the service of the company and this is company’s profit: Area of the triangle ABC = AB x AC/2 = 8x8/2=32 mil Thus, total cost of 10 universities will be: • Total subscription cost: 32x10DN=320 mil • Total access cost: 16x10=160 mil • Profit from 10 enterprises: π(dn)= 10(F1+ (P-MC)*Q1) = 10(32+ (2-2)*8) = 320 mil VND * University group: consists of 10 universities a Each university has the same demand line Q=8-P; thus, we have to calculate the Subscription cost and Access cost of each university, then multiply with that of 10 universities: • To have the maximum profit from the surplus of the customer, the company shall set the maginal cost P=MC= • ⇒Access time Q2=8-2=6 mil sec • ⇒Access cost = mil sec.x VND/ s = 12 mil VND • ⇒ Subscription cost (F2) is the consumption cost for each university which use the service of the company and this is company’s profit: Area of the triangle ABC = AB x AC/2 = 6x6/2=18 mil VND b Total cost of 10 universities will be • Total Subscription cost: 18x10DN=180 mil VND • Total Access cost: 12x10=120 mil • Profit from 10 universities: π(đh)= 10(F2+ (P-MC)*Q2) = 10(18+ (2-2)*6) = 180 mil VND *Total profit: π = π(dn)+π(đh) =320 + 180 = 500 mil VND P F1 C MC = P2 Q = 10 - P P 10 Q P (đ/s) B F2 Q=8-P A C MC=2 Q (Tr giây) b Assume that your company cannot separate customer groups and you are not going to calculate the Subscription cost (Subscription cost = 0) Calculate access cost to maximize profit? Figure out the profit of your company? Due to the fact that we cannot separate customer group, we cannot differentiate prices * For enterprise group: Q1 = 10*(10-P1)= 100-10P1 or P1= 10- Q1/10= 10-0,1Q1 => MR1=10-0,2Q1 * For university group: Q2=10*(8-P2)= 80-10P2 or P2= 8-Q2/10=8-0,1Q2 => MR2=8-0,2Q2 * Two customer groups share the same demand function We have: Q= Q1+Q2= 180 - 20P => P=9-Q/20= - 0,05Q Breakpoint A corresponds to Q=20 and P=8 Demand line equation encountered by the company is: P=10 - 0,1Q with Q < 20 P= 9-0,05Q with Q > 20 * The corresponding maginal income equation consists of phases: MR=10- 0,2Q with Q < 20 MR= 9-0,1Q with Q > 20 * Due to the fact that we cannot differentiate prices, the output of maximizing profit shall be specified based on the principle: MR=MC From the data, we have MC=2 If Q Q=40 (excluded due to Q20, we have: MR=MC ⌠9-0,1Q=2 => Q= 70 Then: P=(180-70)/20=5,5 * Company’s profit: π= (P-MC) * Q = (5,5-2)*70= 245 mil VND * Thus, with Access time Q=70 mil sec./month, Access cost is 5,5 VND/sthe company will have the maximal profit of 245 mil VND/month P P P 10 10 Q=100-10P1 Q=80-10P2 Q=180-20P 5,5 MC MC 2 MR1 MC MR2 MR Q 50 100 Q 40 80 20 70 90 c Assume that you apply the dual cost (in which you specify the common Subscription cost and Access cost for the two customer groups Calculate Subscription cost and Access cost, Profit of your company? Explain why price is not equal to the maginal cost - Subscription cost and Access cost is common for groups, but these groups have different demand line The Subscription cost will be figured out by the consumption surplus of the customer group with lower demand line Thus, to gain the maximized profit, the company will not set the price P based on the MC (marginal cost), in which P>MC - Identify P: Objective is still to maximize the profit - Assume that there are customers (an enterprise and an university), each customer shall pay the subscription cost is Fc, lệ Access cost Pc VND/s With Pc>MC, the company’s profit will be: ∏ = 2Fc + (Pc-MC)*(Q1+Q2) (1) 180 We identify Access cost Pc in a way that the profit of the Company will have the maximal value π=> max - We have: Function demand of an Enterprise: Q1= 8- Pc Function demand of an university: Q2 = 10-Pc Common function demand of an Enterprise and an university: Qc=Q1+Q2 =182Pc MC=2 - Calculate Fc: Subscription cost Fc is the consumption surplus of the customer with low demand line (University) Fc= SABC= (8-Pc)*Q2/2=(8-Pc)*(8-Pc)/2 (see graph for reference) Replace (1) by Fc, Q2, Q1+Q2, MC=2 we have: π = 2(8-Pc)*(Q2)/2 + (Pc-2)(18-2Pc) ⇔ π = (8-Pc)(8-Pc) + (Pc-2)(18-2Pc)= Pc2 -16Pc+64+18Pc-2Pc2-36-4Pc = -Pc2+6Pc+28 (2) This is the quadric function and the maximal value hàm (Maximal profit π at Pc as derivative = 0) π max as (2) ⇒ max, (2) max as derivative (2)=0 We have: (-Pc2+6Pc+28)'=-2Pc+6=0 ⇒Pc= Therefore, at Access cost Pc=3 VND/s, company’s profit is maximized At P=3 ⇒ Q1=8-3 = (mil.sec.) Q2 =10-3=7 (mil.sec.) - Subscription cost will be: Fc= (8-3)*5/2 = 25/2 = 12,5 mil VND Therefore, the subscription cost of the company includes the subscription cost for 10 enterprises and 10 universities:12,5*20 = 250 mil VND - Internet service cost: 10 universities : 3*5* 10 = 150 mil VND 10 enterprises: 3*7*10 = 210 mil VND - Total service cost: 150+210 = 360 mil VND - Total service and subcription cost of the Company: 250+360 = 610 mil VND - Profit from an enterprise and an university: ∏ = 2Fc + (Pc-MC)*(Q1+Q2) ⇔ 2*12,5 + (3-1)(5+7) = 25 + 12 = 37 mil VND - Company’s profit: 37 *10 = 370 mil VND As a result, the Company shall set the Subscription cost of 12,5mil VND/month, Access cost of 3VND/s applied for all customers Then the company’s profit will be 370 mil VND - In this case, the company will have to set the Subscription cost equal to the consumption surplus of the customer group with lower demand line (university group) The company needs to this to maitain this customer group - If the company sets the access value equal to the maginal cost P=MC, the profit from service =); the highest profit will be only equal to consumption surplus of the university group with lower demand line (2 times the area of triangle AB’C’) Thus, the company will lose a part of their profit equal to the differrence between the consumption surplus of the enterprise group and university group - In order to maximize the profit, the company will set the Access cost greater than the maginal cost P>MC, the profit of the company will be greater than times of area of triangle AB’C’ (equal to times area of triangle AB’C’ plus the area of quadrangle MCC’N) - Thus, the company can set the Access cost equal to the maginal cost; however, the profit will be decreased To maximize the profit, the company must set Access cost greater than the maginal cost (P>MC) Exercise 2: a Based on the maginal cost, how much is the estimation of the average variable cost function of EverKleen? From function SMC = 125 –0,42Q + 0,0021Q2 we calculate the SMC function: VC = 125Q – 0.21Q2 + 0.0007Q3 AVC = VC/Q = 125 – 0.21Q + 0.0007Q2 b At which production cost will AVC have the minimal value? Calculate the value AVC at its lowest point? AVC has the minimum value as AVC’ = 0, replace and we have: - 0.21 + 0.0014 Q = => Q0 = 150 AVC value at its lowest point: AVC0 = 125 – 0.21Q0 + 0.0007Q02 = 109.25 ($) c Should managers of EverKleen go on with their business or if not, whether they should go on with their business or close down? Why? The estimation factor of the average variable cost function is 5%; therefore, the value of actual AVA at the lowest point will vary in range : 109.25 x 95% < AVC 0r < 109.25 x 105% 103.79 ($) < AVC0r < 114.75 ($) The market price for a sever covering summer months is P = 115 ($) > AVC 0r the minimal average variable cost Therefore, EverKleen should run its services to compensate for losses d Managers of EverKleen realize that the two outputs turn out to be optimal What are such output and which output is absolutely optimal? As EverKleen provide profit-maximized servicesm MC = MR = P, replace we have: 125 – 0.42Q + 0.0021Q2 = 115 ; then 0.0021Q2 – 0.42Q + 10 = and the results are : Q1 = 29 Q2 = 172 e How much profit (loss) Managers of EverKleen expect to earn (or lose? Service provided with Q2 = 172 : + Total income : TR = P x Q2 = 115 x 172 = 19780 ($) VC = 125Q2 – 0.21Q22 + 0.0007Q23 = 18849.3 ($) + Conversion cost : + Total cost : TC = FC + VC = 22349.3 ($) + Loss : L = TR – TC = - 2569.3 ($) + Unit loss: LU = L/Q = - 14.94 ($) f Ssume fixed cost of EverKleen increases up to $4,000 How much impact is made on the optimal output? why? If fixed cost of EverKleen increases up to 4000 ($) : + Total cost: TC = FC + VC = 22849.3 ($) + Loss : L = TR – TC = - 3069.3 ($) + Unit loss : LU = L/Q = - 17.84 ($) The above results show that if the losses increase, EverKleen is still able to gon on its business Exercise 1: Internet service provider has two potential customer groups as follows: 10 Enterprises and 10 Universities * Demand function as per Enterprise: Q = 10 – P * Demand function as per University: Q = – P In which, Q is mil sec./month; maginal cost as per access unit is VND/s a) Assume that the company can separate between enterprises and universities • • • • Each enterprise has common demand line Q=10-P; thus, we have to calculate the subscription and access costs as per an enterprise and take the results to multiply with 10 E (Enterprise): To acquire the maximum surplus profit from the consumers, the company sets up the price based on maginal cost P=MC= ⇒Access time Q1=10-2=8 mil sec ⇒Access cost = mil sec x VND/ s = 16 mil VND ⇒ Subscription cost (F1) is the consumption surplus for each enterprise which uses the service of the company and this is company’s profit: Area of the triangle ABC = AB x AC/2 = 8x8/2=32 mil Thus, total cost of 10 universities will be: • Total subscription cost: 32x10DN=320 mil • Total access cost: 16x10=160 mil • Profit from 10 enterprises: π(dn)= 10(F1+ (P-MC)*Q1) = 10(32+ (2-2)*8) = 320 mil VND * University group: consists of 10 universities a Each university has the same demand line Q=8-P; thus, we have to calculate the Subscription cost and Access cost of each university, then multiply with that of 10 universities: • To have the maximum profit from the surplus of the customer, the company shall set the maginal cost P=MC= • ⇒Access time Q2=8-2=6 mil sec • ⇒Access cost = mil sec.x VND/ s = 12 mil VND • ⇒ Subscription cost (F2) is the consumption cost for each university which use the service of the company and this is company’s profit: Area of the triangle ABC = AB x AC/2 = 6x6/2=18 mil VND b Total cost of 10 universities will be • Total Subscription cost: 18x10DN=180 mil VND • Total Access cost: 12x10=120 mil • Profit from 10 universities: π(đh)= 10(F2+ (P-MC)*Q2) = 10(18+ (2-2)*6) = 180 mil VND *Total profit: π = π(dn)+π(đh) =320 + 180 = 500 mil VND F1 C MC = P2 Q = 10 - P P P (đ/s) Q 10 B F2 Q=8-P A C MC=2 Q (Tr giây) b Assume that your company cannot separate customer groups and you are not going to calculate the Subscription cost (Subscription cost = 0) Calculate access cost to maximize profit? Figure out the profit of your company? Due to the fact that we cannot separate customer group, we cannot differentiate prices * For enterprise group: Q1 = 10*(10-P1)= 100-10P1 or P1= 10- Q1/10= 10-0,1Q1 => MR1=10-0,2Q1 * For university group: Q2=10*(8-P2)= 80-10P2 or P2= 8-Q2/10=8-0,1Q2 => MR2=8-0,2Q2 * Two customer groups share the same demand function We have: Q= Q1+Q2= 180 - 20P => P=9-Q/20= - 0,05Q Breakpoint A corresponds to Q=20 and P=8 Demand line equation encountered by the company is: P=10 - 0,1Q with Q < 20 P= 9-0,05Q with Q > 20 * The corresponding maginal income equation consists of phases: MR=10- 0,2Q with Q < 20 MR= 9-0,1Q with Q > 20 * Due to the fact that we cannot differentiate prices, the output of maximizing profit shall be specified based on the principle: MR=MC From the data, we have MC=2 If Q Q=40 (excluded due to Q20, we have: MR=MC ⌠9-0,1Q=2 => Q= 70 Then: P=(180-70)/20=5,5 * Company’s profit: π= (P-MC) * Q = (5,5-2)*70= 245 mil VND * Therefore, With Access time Q=70 mil sec./month, the Access cost will be 5,5 VND/s, the maximal profit will be 245 mil VND/month c Assume that you apply the dual cost (in which you specify the common Subscription cost and Access cost for the two customer groups Calculate Subscription cost and Access cost, profit of your company? Explain why price is not equal to the maginal cost - Subscription cost and Access cost is common for groups, but these groups have different demand line The Subscription cost will be figured out by the consumption surplus of the customer group with lower demand line Thus, to gain the maximized profit, the company will not set the price P based on the MC (marginal cost), in which P>MC - Identify P: Objective is still to maximize the profit - Assume that there are customers (an enterprise and an university), each customer shall pay the subscription cost is Fc, lệ Access cost Pc VND/s With Pc>MC, the company’s profit will be: ∏ = 2Fc + (Pc-MC)*(Q1+Q2) (1) We have to find the Access cost Pc in oder to have the maximal profit π=> max for the company - We have: Demand line of an enterprise: Q1= 8- Pc Demand line of an university: Q2 = 10-Pc The command demand line for an enterprise and an university: Qc=Q1+Q2 =182Pc MC=2 - Calculate Fc: Subscription cost Fc is the consumption surplus of the customer with low demand line (University) Fc= SABC= (8-Pc)*Q2/2=(8-Pc)*(8-Pc)/2 (see the graph for reference) Replace (1) by Fc, Q2, Q1+Q2, MC=2, we have: π = 2(8-Pc)*(Q2)/2 + (Pc-2)(18-2Pc) ⇔ π = (8-Pc)(8-Pc) + (Pc-2)(18-2Pc)= Pc2 -16Pc+64+18Pc-2Pc2-36-4Pc = -Pc2+6Pc+28 (2) This is the quadric function Therefore, the function will have the maximal value (maximal profit π at Pc as the derivative= 0) π max as 2) ⇒ max, (2) max as derivative of (2)=0 We have: (-Pc2+6Pc+28)'=-2Pc+6=0 ⇒Pc= Therefore, at Access cost Pc=3 VNd/s, the profit of the company is maximal At P=3 ⇒ Q1=8-3 = (mil sec.) Q2 =10-3=7 (mil sec.) - Subscription cost will be: Fc= (8-3)*5/2 = 25/2 = 12,5 mil VND Therefore, Subscription cost of the company will include Subscription cost of 10 Enterprises and 10 universities: 12,5*20 = 250 mil VND - Internet service cost: 10 universities : 3*5* 10 = 150 mil VND 10 enterprises: 3*7*10 = 210 mil VND - Total service cost: 150+210 = 360 mil VND - Total service and subscription of the Compnay: 250+360 = 610 mil.VND - Profit from an university and en enterprise: ∏ = 2Fc + (Pc-MC)*(Q1+Q2) ⇔ 2*12,5 + (3-1)(5+7) = 25 + 12 = 37 mil VND - Company’s profit : 37 *10 = 370 mil VND As a result, the Company shall set the Subscription cost of 12,5mil VND/month, Access cost of 3VND/s applied for all customers Then the company’s profit will be 370 mil VND - In this case, the company will have to set the Subscription cost equal to the consumption surplus of the customer group with lower demand line (university group) The company needs to this to maitain this customer group - If the company sets the access value equal to the maginal cost P=MC, the profit from service =); the highest profit will be only equal to consumption surplus of the university group with lower demand line (2 times the area of triangle AB’C’) Thus, the company will lose a part of their profit equal to the differrence between the consumption surplus of the enterprise group and university group - In order to maximize the profit, the company will set the Access cost greater than the maginal cost P>MC, the profit of the company will be greater than times of area of triangle AB’C’ (equal to times area of triangle AB’C’ plus the area of quadrangle MCC’N) - Thus, the company can set the Access cost equal to the maginal cost; however, the profit will be decreased To maximize the profit, the company must set Access cost greater than the maginal cost (P>MC)