Consider the following Cobb-Douglas production function. Q=10 K1/2L1/2 a. Find the first, second, and cross partial derivatives. b. Determine their signs. c. What is the economic interpretation of the signs of these derivatives?
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Consider the following Cobb-Douglas production function.
Q=10 K1/2L1/2
a. Find the first, second, and cross partial derivatives.
b. Determine their signs.
c. What is the economic interpretation of the signs of these derivatives?
The Cobb-Douglas production function shows the technological relationship between the amount of two or more input and the output produced.
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- Consider the following Cobb-Douglas production function. Q=10 K1/2L1/2a. Find the first, second, and cross partial derivatives. b. Determine their signs.c. What is the economic interpretation of the signs of these derivatives?DERIVATIVE In the following the symbol for the first derivative is dy/dx or Y’ and the symbol for the second derivative is d2y/dx2 or Y”, all of which are standard symbols. Y = X3 -2X2 +1 X -.333 0 .333 .667 1 1.333 1.667 Y dy/dx d2y/dx2 A function is given above. The table gives several pre-selected values of the independent variable (X). Use all of these to have enough to answer questions for this assignment. Calculate the Y value corresponding to each X value in the table. Write the Y value and its sign (+ or -) calculated in the cell below its X value. Pick any three of the X values and on a separate worksheet, show how you calculated its Y value. Use these X,Y pairs also if you chose to do the bonus option. Find the critical values among the given X values…Compute the first and second derivatives of the following functions of x. In each case, determine whether the function has any local extremes (maxima or minima) on the domain of nonnegative real numbers – i.e. for x E [0, 0). a. f(x) = 4 + 3x? b. f(x) = x (4x – 3) (9 - 5x) с. f(x) — x2 d. f(x) = In(x) -
- Hello. May I ask how did you get the values? Were those only assumed values? Can you also explain how did you make the normal form thoroughly?Find the derivative of ln(2x2)+ln(2x)+13 where x=1 Select one: a. None of the above b. 1/3 c. 3 d. 1Find the derivative of f(x)=32x3+14x2+2x+1 where x=2 . Select one: a. 24 b. 21 c. 6 d. 18
- Graph the function C=50+0.8Y and give economic interpretations of the elements of the equation.6). Compute the directional derivative of function f(x,y) = xy³ + 2.x²y at the point (2, 1) in the direction (,, ).The first order, and the second order, partial derivatives of the following function are, respectively z = r°y² + 15ye* Select one: = 2r*y O a. 2x3 + 15e" and Ob. 3x + 15e* and 2x * = 2y + 15e" and = 2x Oc. Od. = 2x®y+ 15e* and * = 3.x?y+ 15e" and 6ry e. Clear my choice
- Define the strict gradient series?A rental car company has a special deal on one of the available rentals. Let C be the cost, in dollars, of the rental car as a function of the distance d, in miles, it is driven in one day. A. What would the value C(75) represent in this context? B. Is function Cincreasing or decreasing? What are the units of the slope in this situation? C. Identify any maximum or minimum values of the function. What do they represent in this situation? State any assumptions that you make. D. Would the graph of C have any intercepts? What would they represent in this situation? E. Write a rule for C(d), and sketch a graph of the function.Consider the two period consumption savings problem faced by an individual whose utility is defined on period consumption. This utility function u(c) has the properties that it is strictly increasing and concave, u'(c) > 0, u"(c) < 0 (where u'(c) denotes the first derivative while u"(c) represents the second derivative) and satisfies the Inada condition lim.-→0 u'(c) approaches zero). The individual's lifetime utility is give by u(cı) + Bu(c2). In the first period of life, the individual has y1 units of income that can be either consumed or saved. In order to save, the individual must purchase bonds at a price of q units of the consumption good per bond. Each of these bonds returns a single unit of the consumption good in period 2. Total savings through bond purchases is s1 so that total expenditures on purchasing bonds is qs1. Let c1 denote the amount of consumption in period 1 chosen by the individual. In the second period of life, consumption in the amount c2 is financed out of the…
