Marginal Cost and Demand Curve
Economics 101
Summer 2012
Answers to Homework #5
Due 6/20/12
Directions: The homework will be collected in a box before the lecture. Please place your name, TA name and section number on top of the homework (legibly). Make sure you write your name as it appears on your ID so that you can receive the correct grade. Late homework will not be accepted so make plans ahead of time. Please show your work. Good luck!
Please realize that you are essentially creating “your brand” when you submit this homework. Do you want your homework to convey that you are competent, careful, professional? Or, do you want to convey the image that you are careless, sloppy, and less than professional. For the rest of your life you will be creating your brand: please think about what you are saying about yourself when you do any work for someone else!
1. Consider a monopolist where the market demand curve for the produce is given by P = 520 – 2Q. This monopolist has marginal costs that can be expressed as MC = 100 + 2Q and total costs that can be expressed as TC = 100Q + Q2 + 50.
a. Given the above information, what is this monopolist’s profit maximizing price and output if it charges a single price?
Answer:
MR = 520 – 4Q
MC = 100 + 2Q
520 – 4Q = 100 + 2Q
Q = 70 units of output
P = 520 – 2Q = 520 – 2(70) = $380 per unit of output
b. Given the above information, calculate this single price monopolist’s profit.
Answer:
Profit = TR – TC
TR = P*Q = ($380 per unit)(70 units) = $26,600
TC = 100Q + Q2 + 50 = 100(70) + (70)(70) + 50 = $11,950
Profit = $14650
c. At the profit maximizing quantity, what is this monopolist’s average total cost of production (ATC)?
Answer:
To answer this question we first need to write an expression for ATC.
ATC = TC/Q = 100 + Q + (50/Q)
Then replace Q with 70 to find the average total cost of producing 70 units of output.
ATC= 100 + 70 + (50/70) = $170.71 per unit
d. At the profit maximizing quantity, what is the profit per
Summer 2012
Answers to Homework #5
Due 6/20/12
Directions: The homework will be collected in a box before the lecture. Please place your name, TA name and section number on top of the homework (legibly). Make sure you write your name as it appears on your ID so that you can receive the correct grade. Late homework will not be accepted so make plans ahead of time. Please show your work. Good luck!
Please realize that you are essentially creating “your brand” when you submit this homework. Do you want your homework to convey that you are competent, careful, professional? Or, do you want to convey the image that you are careless, sloppy, and less than professional. For the rest of your life you will be creating your brand: please think about what you are saying about yourself when you do any work for someone else!
1. Consider a monopolist where the market demand curve for the produce is given by P = 520 – 2Q. This monopolist has marginal costs that can be expressed as MC = 100 + 2Q and total costs that can be expressed as TC = 100Q + Q2 + 50.
a. Given the above information, what is this monopolist’s profit maximizing price and output if it charges a single price?
Answer:
MR = 520 – 4Q
MC = 100 + 2Q
520 – 4Q = 100 + 2Q
Q = 70 units of output
P = 520 – 2Q = 520 – 2(70) = $380 per unit of output
b. Given the above information, calculate this single price monopolist’s profit.
Answer:
Profit = TR – TC
TR = P*Q = ($380 per unit)(70 units) = $26,600
TC = 100Q + Q2 + 50 = 100(70) + (70)(70) + 50 = $11,950
Profit = $14650
c. At the profit maximizing quantity, what is this monopolist’s average total cost of production (ATC)?
Answer:
To answer this question we first need to write an expression for ATC.
ATC = TC/Q = 100 + Q + (50/Q)
Then replace Q with 70 to find the average total cost of producing 70 units of output.
ATC= 100 + 70 + (50/70) = $170.71 per unit
d. At the profit maximizing quantity, what is the profit per