Multiple Input Cost Relationships. Output is identical along an isoquant Output is identical along an isoquant Isoquant means “equal quantity” Two inputs.

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Presentation transcript:

Multiple Input Cost Relationships

Output is identical along an isoquant Output is identical along an isoquant Isoquant means “equal quantity” Two inputs

Slope of an Isoquant The slope of an isoquant is referred to as the Marginal Rate of Technical Substitution, or MRTS. The value of the MRTS in our example is given by: MRTS =  Capital ÷  labor If output remains unchanged along an isoquant, the loss in output from decreasing labor must be identical to the gain in output from adding capital.

Plotting the Iso-Cost Line Capital Labor Firm can afford 100 units of labor at a wage rate of $10 for a budget of $1,000 Firm can afford 100 units of labor at a wage rate of $10 for a budget of $1, Firm can afford 10 units of capital at a rental rate of $100 for a budget of $1,000 Firm can afford 10 units of capital at a rental rate of $100 for a budget of $1,000

Slope of an Iso-cost Line The slope of an iso-cost in our example is given by: Slope = - (wage rate ÷ rental rate) or the negative of the ratio of the price of the two Inputs. The slope is based upon the budget constraint and can be obtained from the following equation: ($10 × use of labor)+($100 × use of capital)

Least Cost Decision Rule The least cost combination of two inputs (labor and capital in our example) occurs where the slope of the iso-cost line is tangent to isoquant: MPP LABOR ÷ MPP CAPITAL = -(wage rate ÷ rental rate) Slope of an isoquant Slope of an isoquant Slope of iso- cost line Slope of iso- cost line

Least Cost Decision Rule The least cost combination of labor and capital in out example also occurs where: MPP LABOR ÷ wage rate = MPP CAPITAL ÷ rental rate MPP per dollar spent on labor MPP per dollar spent on labor MPP per dollar spent on capital MPP per dollar spent on capital =

Least Cost Decision Rule The least cost combination of labor and capital in out example also occurs where: MPP LABOR ÷ wage rate = MPP CAPITAL ÷ rental rate MPP per dollar spent on labor MPP per dollar spent on labor MPP per dollar spent on capital MPP per dollar spent on capital = This decision rule holds for a larger number of inputs as well…

Least Cost Input Choice for 100 Units At the point of tangency, we know that: slope of isoquant = slope of iso-cost line, or… MPP LABOR ÷ MPP CAPITAL = - (wage rate ÷ rental rate) At the point of tangency, we know that: slope of isoquant = slope of iso-cost line, or… MPP LABOR ÷ MPP CAPITAL = - (wage rate ÷ rental rate)

Firm can afford to produce only 75 units of output using C 3 units of capital and L 3 units of labor Firm can afford to produce only 75 units of output using C 3 units of capital and L 3 units of labor What Inputs to Use for a Specific Budget?

The Planning Curve The long run average cost (LAC) curve reflects points of tangency with a series of short run average total cost (SAC) curves. The point on the LAC where the following holds is the long run equilibrium position (Q LR ) of the firm: SAC = LAC = P LR where MC represents marginal cost and P LR represents the long run price, respectively.

What can we say about the four firm sizes in this graph? What can we say about the four firm sizes in this graph?

Size 1 would lose money at price P Size 1 would lose money at price P

Q3Q3 Firm size 2, 3 and 4 would earn a profit at price P…. Firm size 2, 3 and 4 would earn a profit at price P….

Q3Q3 Firm size #2’s profit would be the area shown below…

Q3Q3 Firm size #3’s profit would be the area shown below…

Q3Q3 Firm size #4’s profit would be the area shown below…

If price were to fall to down size P LR, only size 3 would not lose money; it would break-even. Size 4 would have to down size its operations! If price were to fall to down size P LR, only size 3 would not lose money; it would break-even. Size 4 would have to down size its operations!

Optimal input combination for output=10 Optimal input combination for output=10 How to Expand Firm’s Capacity

Two options: 1. Point B ? Two options: 1. Point B ?

How to Expand Firm’s Capacity Two options: 1. Point B? 2. Point C? Two options: 1. Point B? 2. Point C?

Optimal input combination for output=10 with budget DE Optimal input combination for output=10 with budget DE Optimal input combination for output=20 with budget FG Optimal input combination for output=20 with budget FG Expanding Firm’s Capacity

This combination costs more to produce 20 units of output since budget HI exceeds budget FG This combination costs more to produce 20 units of output since budget HI exceeds budget FG Expanding Firm’s Capacity