Figure

Production Isoquants in Linear Programming

Each point along an isoquant represents the output level resulting from a given combination of inputs. For example, point X depicts the production of four units of Q by using 25 units of L and 16 units of K.

Units of L employed

Production Isoquants in Linear Programming

Each point along an isoquant represents the output level resulting from a given combination of inputs. For example, point X depicts the production of four units of Q by using 25 units of L and 16 units of K.

Units of L employed

Units of ^employed per time period

relative distance method

Graphic technique used to solve linear programming problems

One method of determining the quantity to be produced by each production process at varying points along the isoquant is called the relative distance method. The relative distance method is based on the fact that the location of a point along an isoquant determines the relative shares of production for the adjacent processes. If point X in Figure 9.2 were on process ray C, all output would be produced using process C. Similarly, if X were on process ray D, all output would be produced using process D. Because point X lies between process rays C and D, both processes C and D will be used to produce this output. Process C will be used relatively more than process D if X is closer to process ray C than to process ray D. Similarly, process D will be used relatively more than process C if X is closer to process ray D than to process ray C. Because point X in Figure 9.2 lies at the midpoint of the Q = 4 isoquant segment between C4 and D4, it implies production using processes C and D in equal proportions. Thus, at point X, Q = 4, QC = 2, and QD = 2.

The relative proportions of process A and process B used to produce Q = 3 at Point Y can be determined in a similar manner. Because Y lies closer to process ray A than to process ray B, point Y entails relatively more output from process A than from process B. The share of total output produced using process A is calculated by considering the distance B3Y relative to B3A3. The share of total output produced using process B is calculated by considering the distance A3Y relative to A3B3. Starting from point B3, the segment B3Y covers 56.6 percent of the total distance B3A3. This means that at point Y, about 56.6 percent of total output is produced using process A (QA = 0.566 X 3 = 1.7) and 43.4 percent (= 1.0 - 0.566) using process B (Qb = 0.434 X 3 = 1.3). Alternatively, starting from point A3, note that the segment A3Y covers 43.4 percent of the total distance A3B3. At point Y, 43.4 percent of total output is produced using process B and 56.6 percent using process A. Extreme accuracy would require painstaking graphic detail, but in many instances the relative distance method can adequately approximate production intensities along isoquants.

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