A firm has the production function f(x, y) = x + min{x, y}. The isoquants for the firm
A) are L-shaped with the corners of the L's on the line y = x.
B) are L-shaped with the corners of the L's on the line y = x + 1.
C) consist of two line segments, one vertical and the other with a slope of -1.
D) consist of two line segments, one horizontal and the other with a slope of -1.
E) are upside down L-shaped.

Question

Quizplus · Accepted Answer

The production function f(x,y) = x + min{x,y} implies that the firm uses both inputs x and y in production and the amount of output produced depends on the minimum value of x and y. 
To derive the isoquants, we set f(x,y) equal to a constant level of output (e.g. Q=1) and solve for y in terms of x:
y = Q - x + min{x,y}
y = 1 - x + min{x,y}
If x is less than y, the minimum value is x so we have y = 1. If x is greater than or equal to y, the minimum value is y so we have y = 1 - x + y, which simplifies to y = 1/2. 
Therefore, the isoquant for Q=1 consists of two line segments, one vertical at x=1/2 and the other with a slope of -1 passing through the point (1,0). The isoquants for higher levels of output will have the same two line segments but with different vertical positions. Thus, the answer is C.

A Firm Has the Production Function F(x, Y) = X