11-26-2018, 08:27 PM

ECO404 - Assignment 1 Solution

Semester: Autumn 2018

Case 1:

TC= XY+7Y2 – 100Y

Requirement:

Keeping in view the above information, find out profit maximizing output levels for both products [Butter (X) and Cheese (Y)] for Adam Milk & Foods (Pvt.) Ltd.

At Profit-Maximizing Output:

TC = TR

TR=100X-2X2

Profit =TR-TC

Profit = 100X-2X2-XY-7Y2+100Y

With respect to “X”

100-4X-Y

With respect to”Y”

-X-14Y+100

4X + Y = 100 (1)

X + 4Y = 100 (2)

Multiply equation (1) by”4”

16X + 4Y = 400 (3)

X +4Y = 100 (2)

Subtract equation (3) & (2)

16X + 4Y =400

_X _+ 4Y =_100

15X+ 0 = 300

X = 20

Putting the value of X in equation (2)

X+ 4Y = 100

20 + 4Y =100

4Y = 80

Y = 20

Case 2:

P = 400 - 4Q TC = 750 + 25Q

MR = dTR/dQ = 400 – 8Q MC = dTC/dQ = 25

Requirement:

From the information given above, calculate the:

A. Quantity, price and profit at the short-run revenue maximizing output level.

B. Quantity, price and profit at the short-run profit-maximizing level of output.

A. Quantity, price and profit at the short-run revenue maximizing output level.

MR=dTR/dQ=400-8Q

By taking second derivative of “MR”

d2TR/dQ2 = -8 < 0

Q = 50

P = 400-4Q

P = 400-4(50)

P = 400-200

P =200

TC=750 + 25Q

TC =750 + 25(50)

TC = 750+ 1250

TC = 2000

TR= 400Q-4Q2

TR = 400(50) – 4(50)2

TR = 20000 – 10000

TR = 10000

Profit = TR – TC

Profit = 10000 -2000

Profit = 8000

B. Quantity, price and profit at the short-run profit-maximizing level of output.

Profit = TR –TC

Profit = 400Q- 4Q2 -750-25Q

Profit = -4Q2 +375Q- 750

Taking first derivative

-8Q+375

Q = 46.875

Second derivative

-8 < 0

Putting the value of “Q” in P

P = 400 – 4Q

= 400 – 4(46.875)

= 400 -187.5

= 212.5

Putting the value of “Q” in Profit equation

Profit = -4Q2 + 375Q +750

= -4(46.875)2 + 375(46.875) +750

= -8789 + 17578 +750

= 9539

Note: Assignment is shared by another student, verify the correctness before submitting the solutions.

Semester: Autumn 2018

Case 1:

Adam Milk & Foods (Pvt.) Ltd. is Pakistan's largest selling cheese brand. Adam has developed its product portfolio over the years and now carries fresh milk, yoghurt, lassi, desi ghee and a wide variety of cheeses. Last year, there emerged some fluctuations in the demand of Butter (X) and Cheese (Y) of Adam’s. Taking into account these demand variations and summer season, the firm wants to maximize its profit by the optimal production of both products. Let the total cost and total revenue function of Adam Milk & Foods (Pvt.) Ltd in the year 2017 has been estimated as:

TR=100X-2X2TC= XY+7Y2 – 100Y

Requirement:

Keeping in view the above information, find out profit maximizing output levels for both products [Butter (X) and Cheese (Y)] for Adam Milk & Foods (Pvt.) Ltd.

At Profit-Maximizing Output:

TC = TR

TR=100X-2X2

Profit =TR-TC

Profit = 100X-2X2-XY-7Y2+100Y

With respect to “X”

100-4X-Y

With respect to”Y”

-X-14Y+100

4X + Y = 100 (1)

X + 4Y = 100 (2)

Multiply equation (1) by”4”

16X + 4Y = 400 (3)

X +4Y = 100 (2)

Subtract equation (3) & (2)

16X + 4Y =400

_X _+ 4Y =_100

15X+ 0 = 300

X = 20

Putting the value of X in equation (2)

X+ 4Y = 100

20 + 4Y =100

4Y = 80

Y = 20

Case 2:

Faisal mover travelers, Inc. offers special tour packages for Northern areas in the summer season to increase the revenue of its company. Although its passengers have grown rapidly during recent years, the company's management fears that a recent attack of new competitors may severely hinder future growth opportunities. Therefore, it believes that the time has come to make decisions for the company’s growth. The marketing and accounting departments have provided management with the following monthly demand and cost information:

P = 400 - 4Q TC = 750 + 25Q

MR = dTR/dQ = 400 – 8Q MC = dTC/dQ = 25

Requirement:

From the information given above, calculate the:

A. Quantity, price and profit at the short-run revenue maximizing output level.

B. Quantity, price and profit at the short-run profit-maximizing level of output.

A. Quantity, price and profit at the short-run revenue maximizing output level.

MR=dTR/dQ=400-8Q

By taking second derivative of “MR”

d2TR/dQ2 = -8 < 0

Q = 50

P = 400-4Q

P = 400-4(50)

P = 400-200

P =200

TC=750 + 25Q

TC =750 + 25(50)

TC = 750+ 1250

TC = 2000

TR= 400Q-4Q2

TR = 400(50) – 4(50)2

TR = 20000 – 10000

TR = 10000

Profit = TR – TC

Profit = 10000 -2000

Profit = 8000

B. Quantity, price and profit at the short-run profit-maximizing level of output.

Profit = TR –TC

Profit = 400Q- 4Q2 -750-25Q

Profit = -4Q2 +375Q- 750

Taking first derivative

-8Q+375

Q = 46.875

Second derivative

-8 < 0

Putting the value of “Q” in P

P = 400 – 4Q

= 400 – 4(46.875)

= 400 -187.5

= 212.5

Putting the value of “Q” in Profit equation

Profit = -4Q2 + 375Q +750

= -4(46.875)2 + 375(46.875) +750

= -8789 + 17578 +750

= 9539

Note: Assignment is shared by another student, verify the correctness before submitting the solutions.