ECS3708 Assignment 01
1.1 Suppose that the firm’s profit function is given as:
𝜋(𝑄) = 1000 − 5𝑄2
where 𝑄 is quantity produced and 𝜋 is profits. Which of the following statements is/are
correct?
a The optimal quantity the firm can produce to maximize its profit is 50.
b The optimal quantity the firm can produce to maximize its profit is 30.
c The optimal quantity the firm can produce to maximize its profit is 20.
d The optimal quantity the firm can produce to maximize its profit is 100.
e None of the above
1.2 Suppose that the firm’s production possibility frontier for good X and Y is given by:
1
𝑋 2 + 𝑌 2 = 100
4
𝑑𝑌
Which of the following statements explains 𝑑𝑋 ?
a 0.
4
b 𝑌
4𝑋
c − 𝑌
4𝑋
d 𝑌
e 𝑋⁄
𝑌
1.3 Suppose that utility function is given by 𝑈(𝑋, 𝑌) = 4𝑋 2 + 3𝑌 2. If X=1 and Y=2, which of
the following statements is correct about utility.
a Utility is 16
b Utility is 3
c Utility is 18
d Utility is 0
e None of the above.
1.4 Suppose that we have the following function:
𝑓 (𝑋, 𝑌) = −𝑋 2 + 2𝑋 − 𝑌 2 + 4𝑌 + 5
And we want to maximize the 1st order condition of X. Which of the following statements
is/are correct?
a 0
b 2
c 1
d 5
e None of the above.
1.5 From the function in question 1.4, which of the following statements explains 1 st order
conditions for maximization of Y?
2
1.1 Suppose that the firm’s profit function is given as:
𝜋(𝑄) = 1000 − 5𝑄2
where 𝑄 is quantity produced and 𝜋 is profits. Which of the following statements is/are
correct?
a The optimal quantity the firm can produce to maximize its profit is 50.
b The optimal quantity the firm can produce to maximize its profit is 30.
c The optimal quantity the firm can produce to maximize its profit is 20.
d The optimal quantity the firm can produce to maximize its profit is 100.
e None of the above
1.2 Suppose that the firm’s production possibility frontier for good X and Y is given by:
1
𝑋 2 + 𝑌 2 = 100
4
𝑑𝑌
Which of the following statements explains 𝑑𝑋 ?
a 0.
4
b 𝑌
4𝑋
c − 𝑌
4𝑋
d 𝑌
e 𝑋⁄
𝑌
1.3 Suppose that utility function is given by 𝑈(𝑋, 𝑌) = 4𝑋 2 + 3𝑌 2. If X=1 and Y=2, which of
the following statements is correct about utility.
a Utility is 16
b Utility is 3
c Utility is 18
d Utility is 0
e None of the above.
1.4 Suppose that we have the following function:
𝑓 (𝑋, 𝑌) = −𝑋 2 + 2𝑋 − 𝑌 2 + 4𝑌 + 5
And we want to maximize the 1st order condition of X. Which of the following statements
is/are correct?
a 0
b 2
c 1
d 5
e None of the above.
1.5 From the function in question 1.4, which of the following statements explains 1 st order
conditions for maximization of Y?
2
