A. The Isoquant curve contains all combinations of 2 inputs that produce the same total output.
B. All points on an isoquant curve are technically efficient.
C. The curve is bowed toward the origin because of the law of diminishing marginal productivity.
D. The slope of the isoquant is called the "Marginal Rate of Technical Substitution" (MRTS) or the "Marginal Rate of Substitution (MRS).
E. The absolute value of the MRS is equal to the Marginal Productivity of the input on the x-axis divided by the Marginal Productivity of the input on the y-axis.
MRS = MPx/MPy
F. As one moves down the isoquant, the MRS decreases. This is called the law of diminishing MRS. (It follows from the law of diminishing marginal productivity.)
G. For every possible combination of inputs, there is an isoquant. The whole set of isoquants is called the "isoquant map". The "isoquant map" is a picture of the state of technology.
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A. The isocost line represents all combination of two inputs which have the same total cost.
B. Total Cost is equal to the unit cost of factor X (Px) times the quantity of factor X (Qx) plus the unit cost of factor Y (Py) times the quantity of factor Y (Qy).
Total Cost = Px*Qx +Py*Qy
C. The y-axis intercept is equal to Total Cost divided by the price of factor y. The x-axis intercept is equal to Total Cost divided by the price of factor x.
D. The intercepts can be connected with a straight line.
E. The absolute value of the slope of the isocost is equal to the price of factor x divided by the price of factor y
Slope of isocost = -Px/Py
F. Shifts in the isocost line:
- If the firm decides to spend more, the new isocost will shift outward parallel to the old isocost.
- If the price of factor x rises, the curve will rotate inward and become steeper.
- If the price of factor y rises, the curve will rotate inward and become steeper.
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A. The problem is to
- Maximize output for a given level of total cost.
- Minimize cost for any given level of output
B. The optimal combination will be the one where the isoquant is just tangent to the isocost.
C. At the point of tangency, the slope of the isoquant will be equal to the slope of the isocost. Hence:
MPx/MPy = PX/Py
D. Hence, at the tangency point, the marginal product per dollar spent will be the same for all inputs:
MPx/Px = MPy/Py
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A. As a firm expands its output it will move to higher tangency points.
B. This determines the shape of the long-run total cost curve.
B. All points on the long run cost curve will be technically and economically efficient.
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