Question

3. (a) "A firm's cost- minimizing choice of inputs to produce a given output level depends on the relative cost ween its inputs in the production process. of the inputs and the extent to which the firm can substitute bet Discuss the above quote with the aid of a diagram. s $5 per hour for servers and $50 per hour to rent ovens and other (b) A fast food restaurant currently pay ine whether the restaurant is minimizing its cost of production when the ratio is 12. If not, what adjustments are called for to improve the efficiency in kitchen machinery. Determ of marginal pr o e N MPL resource use?

Answer 1

(a)

Relative cost of inputs is the slope of the isocost line for a firm which shows the budget available for production. The ratio of substitutability of inputs is the Marginal rate of substitution (MRS), which is the slope of the isoquant which reflects the total output produced. A firm minimizes cost at the point where the isoquant is tangent to isocost line, therefore at this point, slope of isoquant equals the slope of isocost line, signifying relative cost must be equal to the MRS.

In following graph, cost is minimized at point X where the isoquant Q0 is tangent to isocost line AB with cost-minimizing input bundle being L0 and K0.

(b)

Cost is minimized when (MPL / w) = (MPK / r), i.e. (MPK / MPL) = r/w

In this case, (r/w) = $50/$5 = 10, which is higher than (MPK/MPL). Therefore cost is not being minimized.

Since (MPK/MPL) > (r/w), resource usage will be efficient if the firm uses more labor and less capital until the ratios are equalized.