EBK MICROECONOMIC THEORY: BASIC PRINCIP
EBK MICROECONOMIC THEORY: BASIC PRINCIP
12th Edition
ISBN: 8220103612135
Author: Snyder
Publisher: YUZU
Question
Book Icon
Chapter 2, Problem 2.1P

a.

To determine

The partial derivatives of the function f(x,y) .

a.

Expert Solution
Check Mark

Answer to Problem 2.1P

The partial derivatives of the function f(x,y) are

  fx=8x,fy=6y,2fx2=8,2fy2=6,2fxy=0

Explanation of Solution

Given information:

The function,

  f(x,y)=4x2+3y2

Since,

  f(x,y)=4x2+3y2

Partially differentiate with respect to x and y ,

  fx=x(4x2+3y2)=4×2x+0=8x

and

  fy=y(4x2+3y2)=0+3×2y=6y

Now

  2fx2=x(fx)=x(8x)=8×1=8

and

  2fy2=y(fy)=y(6y)=6×1=6

Also,

  2fxy=x(fy)=x(6y)=0

b.

To determine

The derivative dydx using the implicit function theorem.

b.

Expert Solution
Check Mark

Answer to Problem 2.1P

  dydx=8x6y

Explanation of Solution

Given information:

The function,

  f(x,y)=4x2+3y2

and

  f(x,y)=16

Since,

  f(x,y)=4x2+3y2

Then,

  16=4x2+3y2

Differentiate with respect to x ,

  0=4×2x+3×2ydydx8x+6ydydx=06ydydx=8xdydx=8x6y

c.

To determine

The value of dydx at x=1,y=2 .

c.

Expert Solution
Check Mark

Answer to Problem 2.1P

  dydx=23

Explanation of Solution

Since,

  dydx=8x6y

Substituting x=1,y=2 ,

  dydx=8×16×2

  dydx=812=23

d.

To determine

To draw:The graph of dydx=23 on the surface f(x,y)=4x2+3y2 .

d.

Expert Solution
Check Mark

Explanation of Solution

Since, dydx is the slope of the curve,

From the above part,

  dydx=83

So, draw the tangent plane on the surface

  f(x,y)=4x2+3y2

  EBK MICROECONOMIC THEORY: BASIC PRINCIP, Chapter 2, Problem 2.1P

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Describe the various measures used to assess poverty and economic inequality. Analyze the causes and consequences of poverty and inequality, and discuss potential policies and programs aimed at reducing them, assess the adequacy of current environmental regulations in addressing negative externalities. analyze the role of labor unions in labor markets. What is one benefit, and one challenge associated with labor unions.
Evaluate the effectiveness of supply and demand models in predicting labor market outcomes. Justify your assessment with specific examples from real-world labor markets.
Explain the difference between Microeconomics and Macroeconomics?  2.) Explain what fiscal policy is and then explain what Monetary Policy is? 3.) Why is opportunity cost and give one example from your own of opportunity cost. 4.) What are models and what model did we already discuss in class? 5.) What is meant by scarcity of resources?
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Microeconomic Theory
Economics
ISBN:9781337517942
Author:NICHOLSON
Publisher:Cengage
Text book image
Economics:
Economics
ISBN:9781285859460
Author:BOYES, William
Publisher:Cengage Learning
Text book image
MACROECONOMICS FOR TODAY
Economics
ISBN:9781337613057
Author:Tucker
Publisher:CENGAGE L
Text book image
Micro Economics For Today
Economics
ISBN:9781337613064
Author:Tucker, Irvin B.
Publisher:Cengage,
Text book image
Economics For Today
Economics
ISBN:9781337613040
Author:Tucker
Publisher:Cengage Learning
Text book image
Survey Of Economics
Economics
ISBN:9781337111522
Author:Tucker, Irvin B.
Publisher:Cengage,