Question

A firm has the production function f(X, Y) = X^1/2 Y^1/2 , 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 3. The straight line we drew is:

Answer is - a ray through the origin with slope 3

Need step by step explanation please

Answer 1

The question is suggesting us to draw few isquants with production function Q = X^0.5 Y^0.5 . Let these be 100 = X^0.5 Y^0.5, 200 = X^0.5 Y^0.5, 300 = X^0.5 Y^0.5

Now we should draw isocost lines parallel to each other at these isoquants so that the slope of all the budget lines is 3. This is because at the tangency point, slope of budget line = slope of isoquant. Next we join these tangency points. This line that emerges from origin is the expansion path and it joins points of tangency. Since all points of tangency have a slope of 3, the expansion path connects points where slope of isoquant is 3.