Question

Draw a picture of a cost-minimizing bundle of inputs to produce quantity q1 for a typical Cobb-Douglas production function. Be sure to label all your lines and each of the axes. Identify and label the cost-minimizing bundle of inputs as point A (i.e. lA and kA). Additionally, draw and label a bundle of inputs as point B (i.e. lB and kB) that will produce q1 but is not cost-minimizing.

Answer 1

Isoquant is represented by q1. All the points of the isoquant q1 indicate same output. We have considered two isocost lines, such as CD and C'D'. As observed, the isocost CD is tangent to the isoquant q1 at point A, where cost is minimized. At the cost minimization level, the input bundles used are (La, Ka).

Conside point B which lies on q1, but it does not represent cost minimizing bundle. It can be observed that point B lies above the isocost line CD. For example, it shares a point with the isocost line C'D' which lies above CD. Hence, point B is associated with higher cost even though the output level is same.