# Consider the function Y = pXZ where X greater than 0 and Z greater than 0. Draw the contour lines...

## Question:

Consider the function {eq}Y = pXZ {/eq} where {eq}X > 0 {/eq} and {eq}Z > 0 {/eq}. Draw the contour lines (in the positive quadrant) for this function for {eq}Y = 4, Y = 5, {/eq} and {eq}Y = 10 {/eq}. What do we call the shape of these contour lines? Where does the line {eq}20X + 10Z = 200 {/eq} intersect with the contour line {eq}Y = 50 {/eq}?

## Indifference Curves:

Indifference curve is a type of level curves in economics. All consumption bundles on an indifference curve yields the same level of total utility, hence consumers are indifferent between those consumption bundles.

## Answer and Explanation: 1

Become a Study.com member to unlock this answer! Create your account

View this answerThese contour lines are plotted below (with p = 1):

These contour lines are convex.

For the case of p = 1, the point of intersection is the...

See full answer below.

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question#### Search Answers

#### Learn more about this topic:

from

Chapter 3 / Lesson 12In economics, indifference curves show which goods in the marketplace bring equal satisfaction to consumers, leaving them indifferent to which goods they purchase. Explore the definition, learn about their use and impact in economics, and review how they work.

#### Related to this Question

- Consider the function Y=\sqrt{XZ} where X is greater than 0 and Z is greater than 0. Draw the contour lines (in the positive quadrant) for this function for Y= 4, Y= 5, and Y= 10. What do we call th
- Consider the function f(x) = 2x^2 + 4. A) Calculate the area, A, under the function and above the horizontal axis between 1 and 2. B) Sketch your result indicating all relevant points.
- Consider the function f(x) = 2x^2 +4 . (a) Calculate the area, A, under the function and above the horizontal axis between 1 and 2. (b) Sketch your result and indicate all relevant points.
- Consider the function F given by the following expression: F(n,k)=min{2n,k} where n and k are numbers. Here min{2n,k} is the minimum of 2n and k. Draw the iso-level set of F(n,k)=2. This iso-level set
- Consider the multivariate function below:Y = 8X1 - X21+ 14X2 - 7X22, i) Find the extreme values of the given multivariate function, ii) Graph the extreme values of the given multivariate function
- Determine whether the following function has a maximum and/or a minimum point, and where they occur: y= -4x^3 + 10x^2 - 5x + 60 and sketch the shape of the function showing any maximum and minimum points.
- Consider the function y = -2.05 + 1.06x - 0.04x^2. Find all the critical points of y and use the first and second derivative tests to classify them.
- Suppose that the utility functions, 'u(x,y)' and 'v(x,y),' are related by 'v(x,y) = f(u(x,y)).' In each case below, determine whether the function 'f' is an increasing, monotonic transformation or not
- Part a Given the following multivariate function: 50 + 18X + 10Z - 5XZ - 2X 2 Determine the values of X and Z that maximize the function. Part b Given the following Total Revenue function: TR = $
- Find the function's relative maxima, relative minima, and saddle points, if they exist. If an answer does not exist, put DNE. z 3 x 2 y 2 relative maximum
- 1. Given some unknown function f(x,y), define the function G = g(x,y) = f(x,y) + x + y^2. Suppose that iso-G curves are drawn in (x,y)-space. Calculate the slope of the iso-G curve that passes throu
- Are the following functions monotonic transformations? You can determine it by drawing a graph or calculating their derivatives. Assume u \ge 0 throughout. (a) f(u) = ln(u+1) (b) f(u) = u^3 (c) f(u) = u^2/(u + 1)
- Find the extreme points for the following function: y = 6x^2 - 15x + 7 a. x = 30 b. x = 32 c. x = 54 d. x = 15
- Suppose that f(x) is a concave function and g(x) is a function that is both increasing and concave. See if you can show that the composite function y(x) = f(g(x)) is also concave.
- Find the first derivative of the function: Z = 20P^(1/4) (30P^(2/5)).
- Find the ?rst and second derivative of each function and determine whether each function is convex or concave. If it is both, ?nd the ranges for which it is convex and ranges for which it is concave:
- Consider the utility function U (X_1 Y) = X^2/3 Y^1/3 a) For the points x = 1, 5, 10, and 20, find the amount of Y such that the pair (X,Y) lies on the indifference curve associated with U = 10. b) C
- Please define a function. How does one draw a line, y=ax+b? How does one draw a line, ax+by=c? What is quadratic function, and how many maximums and minimums does it have? What is the definition of a
- Consider the function f(x) = 5+2x-4x^3 (a) What is the derivative of f(x)? Use a sign diagram to determine where f(x) is (1) increasing and (2) decreasing.
- Find the first derivative of the following. Be sure to show intermediate work and do not simplify your answer. Z = -6X^5 + 3X^3 - 2X
- Consider the utility function U(X,Y)=30X^.8 Y^.2. For the points X = 1, 5, 10, and 20 find the Y such that the pair (X,Y) lies on the indifference curve associated with U = 10. Explain why these poi
- Draw graphs for the following linear functions: a). y = 2x - 3 b). y = 2x + 3 c). y = -2x + 3 d). y = -2x - 3
- Convert each of the following z intervals to raw score x intervals. (a) z less than or equal to -1 (b) 1 less than or equal to z less than or equal to 2 (c) z greater than or equal to 1.5
- If the two functions MB(q)=320-18q and MC(q)=20+6q were demand and supply functions: (a) Plot both functions on one graph. (b) Show (i.e., calculate algebraically, briefly showing your steps) what t
- What is the area under the standard normal curve corresponding to Z greater than 2.85? a) 0.0022 b) 0.4978 c) 0.9978 d) 0.6103
- Consider the following utility functions: 1. u(x1,x2) = x1 + 2x2 2. u(x1,x2) = 2x1^{0.25} x2^{0.75} 3. u(x1,x2) = 1/2x1^2 - x2 4. u(x1,x2) = min{x1,2x2} 5. u(x1,x2) = max{x1,2x2} Give the equation of
- Find the 95% z-interval or t-interval for the indicated parameter. \\ A.\ \mu\ \ \ \ \bar{x} = 152,\ s = 30,\ n = 32\\ B.\ p\ \ \ \ \hat{p} = 0.7,\ n = 43
- Given: TC= 120 + 50Q - 10Q^{2} + Q^{3} (a) Find the equations of TVC, AVC, and MC functions. (b) Find the level of output at which AVC and MC are minimum, and prove that AVC and MC curves are U-shap
- Given: TC = 100 + 60Q - 12Q^2 + Q^3. Find (a) the equations of the TVC, AVC, and MC functions and (b) the level of output at which AVC and MC are minimum, and prove that the AVC and MC curves are U-sh
- Determine whether the following utility function is a monotonic transformation of u(x,y) show work a(x,y)= 2/3u(x,y) b(x,y)=u(x,y)^3-93
- At which point in its positive domain (x > 0) does the tangent to the following curve have its greatest (positive) slope: f(x) = 1 + 6.7x^3 - 6.7x^5
- Find h'(x) for the following function: h(x) = frac{1 + x}{x - 2}. Draw a graph of h(x).
- Find the extreme value of the following functions and state whether they are a local maximum, minimum or saddle point. a) 2x^2+y^2+xy b) Delta Airlines has regular flights between Atlanta and NYC. It
- 1. Find the maximum or minimum of the following functions: y = 4x^2 - 2x y = x^1/2 - 2x (Hint: Find x* and y* such that the slope is 0) 2. Plot the following functions showing clearly at least two poi
- Consider the following utility function: U = U(x, y) If ? 2 U ? x 2 < 0 , ? 2 U ? y 2 < 0 , does it mean that the indifference curves are convex? Explain why or why not.
- Suppose you are optimizing a function with the highest power of 3, describe how you would determine whether a max, min, or inflection point. Provide an example.
- Consider the following function: y=f(x)= frac{1}{3}x^3- frac{5}{2} alpha x^2+6alpha^2x+delta alpha where alpha and delta are two fixed parameters and x is the choice variable. a) Using the F.O.C, find the critical value (s). b) Using the S.O.C,
- Determine for which values of x the following functions are continuous and explain why (a) \frac {y = x}{(1-1)} and (b) y = r^\frac{-1}{2} + \frac{2}{(x - 2)^2} .
- Show that Cobb-Douglas function with decreasing returns to scale is strictly concave using hessian of second derivatives and the definition of the concavity.
- The slope of the line containing points Y and Z is ____. a. -0.5 b. -1 c. -2 d. -4
- Suppose we can write the production function as follows Y = ZL^{beta} where Z is a constant (its value can be taken as given), L and Y are variables and the "exponent" (beta) is a parameter (so its va
- Consider the following utility function: U = U ( x , y ) . If ? 2 U ? x 2 less than 0 , ? 2 U ? y 2 less than 0 , does it mean that the indifference curve are convex? Explain why or why not?
- (a) Find the candidate extreme points of the function: f(x) = 4x^3- 6x^2 + 6\space \text{on}\space (-1,1). (b) Determine the global minimum and maximum values over (-1,1)
- A random variable has the following density function. f(x) = 1 - .5x 0 less than x less than 2 a. Graph the density function. b. Verify that f(x) is a density function. c. Find P(X greater than 1). d. Find P(X less than .5).
- Given y = ax^2 + bx + c (a greater than 0; b greater than 0). Determine if the function is: (a) Strictly increasing or strictly decreasing (b) convex, concave or linear
- Draw a fully labeled figure of the FE line, the LM curve and the IS curve. Label the point where all three curves intersect E. Show in the figure how the curves move in response to a positive supply s
- For a utility function for two goods to be strictly quasi-concave (i.e. convex rence curves), the following condition must hold: UxxU2x - 2UxyUxUy + UyyU2y < 0. Use this condition to check the conve
- Derive Hicksian Demand curve for good "y" for the following utility functions assuming a utility level of U bar and Px=1. a) U(x,y) = (x^a)(y) b) U(x,y) = Ln(x) + y c) U(x,y) = (x^a)(y^(1 - a))
- How do you find the Z score such that the area under the standard normal curve to the left is 0.93?
- Consider the utility function U = X^a + ay, where a = alpha. A) What is the optimal combination of x and y? B) Solve for the indirect utility function. C) Show that utility is increasing in I and decr
- You are given the following sample: a. Find the Least Squares estimate of and b. Draw a graph showing the above points and your estimated linear relationship between x and y.
- Consider the CES utility function: U(Qx, Qy) = (1/Qx+1/Qy)^-1 i. Plot the indifference curves for U = 0.5, U = 1, and U = 1.5. Based on your plot, would an individual with these preferences view X and
- (a) Let f(x) be a function having a second-order derivative f"(x). What is the condition for finding an inflection point of f(x)? (b) Suppose f(x) = 4x^3 -2x^2. Find any inflection points f(x) may have.
- Clearly demonstrate that the following function is globally convex when -\sqrt{12}< a< 0: f(x,y) = x^4+y^4+ax^2y^2
- A uniformly distributed random variable has a minimum and maximum value of 20 and 60, respectively. a. Draw the density function. b. Determine P(35 less than X less than 45). c. Draw the density function including the calculation of the probability in par
- If the two functions from questions 1( MB(q)=320-18q ) and 2 ( MC(q)=20+6q ) were demand and supply functions: (a) Plot both functions on one graph. (b) Show (i.e., calculate algebraically, brie y s
- Consider the utility function U=x^a+ay a=alpha I=Pxx+Pyy (a) What is the optimal combination of x and y? (b) Solve for the indirect utility function. (c) Show that utility is increasing in I and de
- 3. Suppose you have the following value function: v(x) = 2x for gains and v(x) = 3x for losses. a. Suppose your reference point is zero, represent the value function graphically. b. Suppose you have
- A uniformly distributed random variable has minimum and maximum values of 20 and 60, respectively. a. Draw the density function. b. Determine P(35 less than X less than 45). c. Draw the density function including the calculation of the probability in part
- Suppose you have the following value function: v(x) = 1x for gains and v(x) = 1.5x for losses. a)Suppose your reference point is zero, represent the value function graphically. b) Suppose you have a
- How do I use functions to draw indifference curves?
- Consider the numerical utility ranking U transformed into another set of numbers by the function F. Which of the following transformation is not monotonic? a. F(U) = U1/2 b. F(U) = U2 c. F(U) = ln(
- Consider the following multivariate function: Y = 6X_1 X_2^(1/2) i) Find the partial derivative of Y with respect to X_1 ii) Find the partial derivative of Y with respect to X_2
- Draw a graph of the consumption function. Then add the investment function to obtain C + I. ||Real GDP||Consumption Saving||Investment||C + I |$2,000|$2,200|$400| |$4,000|$4,000|$400| |$6,000|$5,800|$
- Suppose two Lorenz curves cross, would it be possible to tell which one indicates a lower level of inequality? Explain.
- Find the partial derivative. f(x, y, z) = ln ( x^(0.5) y^(0.5) )
- Use derivatives to determine whether the following function is concave or convex. u = - 4 ln (6).
- (a) Let f(x) be a function having a second-order derivative f"(x). What is the condition for finding an inflection point of f(x)? (b) Suppose f(1) = 4x^3 - 2x^2. Find any inflection points f(x) may have.
- a) Write the equation of the linear function that passes through the point (4,2) and (-2, 4). b) Sketch and label the function.
- Determine the coordinate at which the maximum/or minimum occurs for the function f(x)=-3x^2+30x-30. Also find the coordinate of the vertex Show work
- Find h'(x) for the following function: h(x) = x^a
- Find h'(x) for the following function: h(x) = x^x
- Find h'(x) for the following function: h(x) = (x^2 - x)(5x^5 + x^2)
- If we have two utility functions, how can we say whether there is a monotonic transformation or not between the utility functions?
- Use derivatives to determine whether the following function is concave or convex. u = 4e^-v/2
- Show that the utility function of U = Aq^alpha_1 q^beta_2 and V = q^(alpha beta)_1 q_2 are monotonic transformations of each other, where A, alpha, and beta are positive.
- Suppose the supply function for product X is given by QXs = -30 + 2PX - 4PZ. Suppose PZ = $60. Graph the inverse supply function.
- Determine whether or not the following pair of utility functions are a monotonic transformation of each other. Justify your answer by calculating the MRS of each function. a) U1(x1, x2) = min{x1/2, 6x2} and U2(x1, x2) = max{x1/2, 6x2}
- Consider the estimate demand equation of: Qx =1000-3.3Px - 0.2Pz +0.001Y (3.5) (2.1) (0.5) t values in parenthesis, where Pz is the price of another good Z, and Y is income. Is good Z a substitute
- Consider the following utility function (referred as a quasi-linear utility function as it is linear in the second element): u(x,y)=ln(x)+y. with prices and income given by: p_x=1,p_y epsilon R_+ and
- Every line or curve has an equation ( or Function) to explain its shape. Based on the following supply and demand functions. Please graph each with their appropriate vertical intercepts and calculate
- Consider the utility function bW -W 2 , where b>W is a constant? (a) What is the Arrow-Pratt measure of absolute risk aversion for this utility function? (b) Does this utility function exhibit DARA,
- Consider a class of utility functions which are "additively separable," i.e., a. Find the first and second order conditions for utility maximization for these utility functions. Show that diminishing
- Graph the following functions with Y on the vertical axis and X on the horizontal axis: i) Y=X^{3} ii) Y=20-X^{2}
- Consider the equation Y=14-0.5X. With Y on the vertical axis and X on the horizontal axis, the slope of this line is a. -7 b. -2 c. -\frac{1}{2} d. -\frac{1}{7} e. 14
- Consider the equation Y=14-2X. With Y on the vertical axis and X on the horizontal axis, the slope of this line is a. -2 b. -7 c. -\frac{1}{7} d. 14 e. -\frac{1}{2}
- Using the Envelope theorem, find all local optimum and saddle points for the function f(x) = (x^2-1)^3.
- Apply Lagrange tools to consumer optimization. Objective function: Constrain: Step 1 (given): Construct Lagrange function: Obtain through the three first-order conditions to conduct the Lagrange anal
- Consider a sample with a mean of 30 and a standard deviation of 6. Use Chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number). 10
- Find the elasticities of y with respect to x for the two following functions: (a) y = x^a In xb (b) y = ae^{bx}.
- Consider the Function: y= f(x) = a + bx+ cx^2 What is dy/dx when x=25, a= 139, b = -13, c = 4? (nearest Integer) Given the same parameters as in A) at what value of x is y maximized? (Nearest .001)
- Consider a utility function U(x, y) = x^{1/3}y^{2/3}, what is the absolute value of MRS (x over y) at the point (x, y) = (5,10)?
- To find the value of x that maximizes f(x), first find the values of x that satisfies f^{\prime}(x) = 0 and f^{\prime\prime}(x) less than 0. If there is only one such value that is the value of x that
- Consider the following table. A. Draw the total product curve. B. Find the marginal product (MP) and average product (AP) for each quantity of labor. Draw the graphs for MP and AP curves on the same plane. C. What can be said about the relationship betwee
- Let f and g be two strictly concave functions and let function h be defined by = af + bg, where a is greater than 0 and b is greater than 0 are constants. Using the definition of strict concavity (
- Consider the function F given by the following expression: F(n,k)=min{2n,k} where n and k are numbers. Here min{2n,k} is the minimum of 2n and k. What is F(10,2)?