Question

Suppose there exists two inputs. At a cost minimizing bundle of inputs, the slope of the isoquant must be the ratio of the factor prices.Is this statement true, false or uncertain?

Answer 1

The statement is true.

The slope of the isoquant is given by = Marginal product of input 1 / Marginal product of input 2

At the cost minimization level, this has to be equal to the ratio of the price of input 1 / price of input 2

If for instance, the slope is higher than the price ratio, the marginal product per dollar of input 1 is higher and the firm should use more of input 1 to produce the same output at a cheaper rate. The equilibrium is only achieved when the two ratios are indeed equal.