Asked by labiba rabbi on May 12, 2024
Verified
A firm has the production function f(X, Y) X3/4 Y1/4, where X is the amount of factor x used and Y is the amount of factor y used.On a diagram we put X on the horizontal axis and Y on the vertical axis.We draw some isoquants.Now we draw a straight line on the graph and we notice that wherever this line meets an isoquant, the isoquant has a slope of 9.The straight line we drew
A) is horizontal.
B) is a ray through the origin with slope 3.
C) is vertical.
D) is a ray through the origin with slope 4.
E) has a negative slope.
Isoquants
Curves that represent combinations of different inputs that produce the same level of output in production theory.
Production Function
A production function describes the relationship between inputs (like labor and capital) and the output that can be achieved with those inputs, illustrating the maximum output possible.
Slope
A measure of the steepness or incline of a line, often representing the rate of change between two variables in mathematics and economics.
- Learn about the adaptability of substitution for inputs during production activities.
Verified Answer
GN
GLORIA NAA ODOFELEY TAWIAHMay 14, 2024
Final Answer :
B
Explanation :
The slope of an isoquant at any point represents the rate at which factors can be substituted for one another while keeping the same level of output. The fact that the isoquants have a slope of 9 wherever they meet the straight line indicates that the substitution rate between X and Y is constant along that line. Therefore, the line must be a ray through the origin with a slope equal to the constant substitution rate, which is 3 (9 = 3).
Learning Objectives
- Learn about the adaptability of substitution for inputs during production activities.