A firm has the production function f(X, Y)= X^3/4 Y^1/4, 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.

Question

Quizplus · Accepted Answer

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 F1F1F1S1F1F1F109 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 (F1F1F1S1F1F1F109 = 3).

A Firm Has the Production Function F(X, Y)= X3/4 Y1/4

A Firm Has the Production Function F(X, Y)= X^3/4 Y^1/4