Isoquant and Isocost

Isoquant is just an alternative way of representing the production function. Consider a production function with two inputs factor 1 and factor 2. An isoquant is the set of all possible combinations of the two inputs that yield the same maximum possible level of output. Each isoquant represents a particular level of output and is labelled with that amount of output. Cobb-Douglas Isoquants

An isoquant plots all the combinations of two inputs that will produce a given output level. A point on the isoquant curve is technically efficient.

In general, isoquants are downward sloping – the more labor we use, the less capital we need. It is bowed inward because of the law of diminishing marginal productivity. In the case of Cobb-Douglas Isoquants inputs are not perfectly substitutable.

The slope of an isoquant shows the rate at which L can be substituted for K.

- slope = marginal rate of technical substitution (MRTS). RTS > 0 and is diminishing for increasing inputs of labor. The marginal rate of technical substitution (RTS) shows the rate at which labor can be substituted for capital while holding output constant along an isoquant:

or

Isoquant map – a set of isoquant curves that show technically efficient combinations of inputs that can produce different levels of output. Higher levels of production are shown by isoquants that are further from the origin (see the graph 1).

Linear isoquantsmean that capital and labor are perfect substitutes	Leontief Isoquantsmean that capital and labor are perfect complements
Q = aK + bL MRTSKL = b/a Linear isoquants imply that inputs are substituted at a constant rate, independent of the input levels employed	Capital and labor are used in fixed-proportions. Q = min {bK, cL} Since capital and labor are consumed in fixed proportions there is no input substitution along isoquants (hence, no MRTSKL).

Isocost line– a line that represents alternative combinations of factors of production that have the same costs. Or in other words, the combinations of inputs (K, L) that yield the producer the same level of output.

The shape of an isoquant reflects the ease with which a producer can substitute among inputs while maintaining the same level of output.

The combinations of inputs that produce a given level of output at the same cost can be expressed as:

wL + rK = C

Rearranging, K= (1/r)C - (w/r)L

For given input prices, isocosts farther from the origin are associated with higher costs

Changes in input prices change the slope of the isocost line

4.2. Cost minimization (Producer’s choice optimisation)

The least cost combination of inputs for a given output occurs where the isocost curve is tangent to the isoquant curve for that output.

The slopes of the two curves are equal at that point of tangency.

The firm is operating efficiently when an additional output per dollar spent on labor equals the additional output per dollar spent on machines. So that marginal product per dollar spent should be equal for all inputs:

We define marginal physical product as the additional output that can be produced by employing one more unit of that input while holding other inputs constant:

And

Choosing the Economically Efficient Point of Production can be shown in the graph:

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