Isoquant and Isocost
9.d. Isoquants: An isoquant (equal quantity) is a curve that shows the combinations of certain inputs such as Labor (L) and Capital (K) that will produce a certain output Q. Mathematically, the data that an isoquant projects is expressed by the equation
f (K,L) = Q
This equation basically says that the output that this firm produces is a function of Labor and Capital, where each isoquant represents a fixed output produced with different combinations of inputs. A new isoquant emerges for every level of output (See Figure 9.1). Isoquants have certain properties that resemble that of indifference curves – convex to the origin, downward sloping, and nonintersecting curves.
The Marginal Rate of Technical Substitution (MRTS) equals the absolute value of the slope. The MRTS tells us how much of one input a firm can sacrifice while still maintaining a certain output level. The MRTS is also equal to the ratio of Marginal Productivity of Labor (MPL): Marginal Productivity of Capital (MPK). The mathematical form of how Labor (L) can be substituted for Capital (K) in production is given by:
MRTS (L for K)= -dK/dL = MPL/MPK
For Example: When going from point B to A in Figure 9.1, the Slope = (8 units of Capital)/(-6 units of Labor). The MRTS (L for K) = -(8/-6) = 4/3 between points B and A, which means that 4 units of Capital can substitute for 3 units of labor.
Isocosts: An isocost line (equal-cost line) is a Total Cost of production line that recognizes all combinations of two resources that a firm can use, given the Total Cost (TC). Moving up or down the line shows the rate at which one input could be substituted for another in the input market. For the case of Labor and Capital, the total cost of production would take on the form:
TC = (WL) + (RK)
TC= Total Cost, W= Wage, L= Labor, R= Cost of Capital, K= Capital
Example: A company producing widgets encounters the following costs- cost of capital is $25000, labor cost is $15000,
f (K,L) = Q
This equation basically says that the output that this firm produces is a function of Labor and Capital, where each isoquant represents a fixed output produced with different combinations of inputs. A new isoquant emerges for every level of output (See Figure 9.1). Isoquants have certain properties that resemble that of indifference curves – convex to the origin, downward sloping, and nonintersecting curves.
The Marginal Rate of Technical Substitution (MRTS) equals the absolute value of the slope. The MRTS tells us how much of one input a firm can sacrifice while still maintaining a certain output level. The MRTS is also equal to the ratio of Marginal Productivity of Labor (MPL): Marginal Productivity of Capital (MPK). The mathematical form of how Labor (L) can be substituted for Capital (K) in production is given by:
MRTS (L for K)= -dK/dL = MPL/MPK
For Example: When going from point B to A in Figure 9.1, the Slope = (8 units of Capital)/(-6 units of Labor). The MRTS (L for K) = -(8/-6) = 4/3 between points B and A, which means that 4 units of Capital can substitute for 3 units of labor.
Isocosts: An isocost line (equal-cost line) is a Total Cost of production line that recognizes all combinations of two resources that a firm can use, given the Total Cost (TC). Moving up or down the line shows the rate at which one input could be substituted for another in the input market. For the case of Labor and Capital, the total cost of production would take on the form:
TC = (WL) + (RK)
TC= Total Cost, W= Wage, L= Labor, R= Cost of Capital, K= Capital
Example: A company producing widgets encounters the following costs- cost of capital is $25000, labor cost is $15000,