Question

Draw a production isoquant given that

y=500 for the following production functions:
a. y(K,L)=5K+2L
b. y(K,L)=K²L
c. y(K,L)=K¹/²L¹/²
d. y(K,L)=min(2K,L)

Answer 1

The student's question pertains to drawing production isoquants for a given output level using different production functions. The answer explains how to plot an isoquant for each provided production function and notes the differing shapes of isoquant curves due to differences in input substitutability and complementarity.

Step-by-step explanation:

The question asks for the drawing of production isoquants for a given level of output, specifically y=500, for different production functions. A production isoquant shows all the combinations of inputs that can produce the same level of output. We can sketch these as follows:

1. For the linear production function y(K,L) = 5K + 2L to yield y=500, we can plot the combinations of K and L that satisfy 500 = 5K + 2L. It will be a straight line with a negative slope.
2. The production function y(K,L) = K²L is a Cobb-Douglas production function, which yields contour lines of an isoquant that are curved. Setting it to 500, we solve for L in terms of K or vice versa.
3. The Cobb-Douglas production function y(K,L) = K¹/²L¹/² also produces curved isoquants, and by setting y=500, we can plot various combinations of K and L that satisfy the equation.
4. The Leontief production function y(K,L) = min(2K, L) will yield y=500 at points along the minimum of the two inputs (either 2K or L). The isoquant will look like a right angle, reflecting perfect complementarity between inputs.

These sketches represent the level of output when the quantity of capital (K) and labor (L) are varied. It is important to note that for the isoquant for the Leontief production function, inputs are used in fixed proportions.