Input Output Combination and Optimization

Input Output Combination

Choosing input and output combinations, referencing topic five about input-output relations and productivity measurements (marginal, physical, and total).

Optimal Input

Decision rule: MVP = MFC (Marginal Value Product equals Marginal Factor Cost) or MVP \geq MFC for efficient input use. Focus is on single input, single output scenarios initially.

Two Inputs, One Output

Considering two inputs to produce one output (ISO-quant). The decision of the combination depends on expenditure ability. ISO-cost line represents the farmer's spending ability.

• ISO-quant: A curve.

• ISO-cost line: A straight line.

Analogy to indifference curves and budget lines from topic two (demand section). Rate of substitution of inputs: increasing one input requires decreasing the other (diminishing rate of substitution). This substitution depends on input costs; the goal is to use cheaper inputs.

ISO-quant

Different input combinations yielding the same output level. Substitution is the marginal rate of substitution, or the slope of the ISO-quant curve. How to optimize input combination using ISO-cost line.

Scale Economies

Increasing, decreasing, or constant returns to scale. Proportional increase in all inputs and resulting output change. Limitations exist due to fixed inputs restricting output increases.

• Increasing returns of scale

• Decreasing returns to scale

• Constant returns to scale

Products and Possibilities

Products and possibilities curve illustrates optimizing output mix (e.g., beet and wool) given enterprises. Optimizing which mix of two enterprises you can produce depends on revenue expectations and output prices. The logic applies to both input use and output selection.

Optimal Input Output Selection

Choosing optimal input-output selection. ISO-quant, ISO-coast line, and optimal input choice explained via video clips in the online study module.

ISO Quant Details

Illustration of ISO-quant as a curve, representing combinations of capital and labor yielding the same output (e.g., 100 units).

• Units of capital per period of time

• Units of labor per period of time

Non-straight line curvature implies trade-offs between capital and labor. Straight line ISO-quant indicates perfect substitution. The diminishing rate shown in the downward curve. If you want to have one more you should have other one less than that. Different ISO-quants represent different output levels; moving to higher curves means producing more.

ISO Quant Characteristics

• Moving up means producing more.

• Along one ISO quant, it is assumed output will be the same at along any combination of inputs.

• At any point on a given ISO-quant, the output is the same, with different combinations of inputs.

• Going to a higher ISO-quant requires more of at least one input to produce more output.

ISO Costline

Different ranges of change between labor and capital along the ISO-quant. Change is capital by a level, the labor will change. As you move down the ISO-quant, the change in capital decreases for an equal change in labor. Different shapes of ISO-quants: perfect substitutes, imperfect substitutes, and complements.

ISO Quants Shapes

• Perfect substitutes are straight lines (e.g., two brands of chemicals). You can change equally.

• Imperfect substitutes are curved (e.g., capital and labor). The curve is not straight and is not equal to a straight line.

• Perfect complements are L-shaped (inputs must be used in fixed proportions, e.g., tractor and plow). Company management, they're a pair, you need to have at least an amount of one input with an amount of the other input.

Perfect Substitutes

Two chemicals or fertilizers where you can use one or the other. Choice depends on which is cheaper, assuming equal impact.

Imperfect Substitutes

Substitution is possible, but increasing one input requires decreasing the other input by a diminishing amount.

Perfect Complements

Combination is needed. Example: tractor and plow. One tractor can use many plows. There should be some combination.

Rate of Substitution

Rate of substitution is defined as change in input x1 over change in input x2 \frac{\Delta x1}{\Delta x2}, which equals the marginal physical product of x2 over x1 \frac{MPP{x2}}{MPP{x1}}. However, marginal rate of substitution (MRS) essentially the slope of the ISO-quant curve.

• If you want to see change means you have give it a tangent.

Budget Line : ISO Costline

ISO-cost line considers the cost of inputs.

Example: 1000 spent on capital or labor (capital = $100/hour, labor = $10/hour). Ten units of capital or 100 units of labor can be rented. It is either all spend on capital or all spend on labor. Combination are either 50 and 50 or any combination.

ISO-cost line is similar to a budget line. Firm with 10 units of capitale at $100 = $1000 budget. The firm got 100 units of labor at $10 = 1000 budget. If spending doubles, the ISO-cost line shifts up; if halved, it shifts down. Changes in wage rates or rental rates change the slope of the ISO-cost line. Slope of the curve reflects the ratio of prices or costs. Changes in budget cause parallel shifts. The curve change depend on what is the change in the wage rate.

Optimal Combination of Input

Optimal combination of inputs occurs where the slope of the ISO-quant equals the slope of the ISO-cost line (tangency). Only one combination will be optimal in terms of cost. At the equilibrium point, the ratio of prices of the inputs equals MRS. Because earlier look at what is MRS. Rate of change in the isoc one.

• Ratio of the price of inputs mean the slope of the budget line is equal to MRS.

• Because the optimal ratio of the input is the point where ISO one tangent to the ISO coastline.

Least cost or optimal combination on different levels of ISO-quants is where ISO-cost line is tangent to the ISO-quant. Budget limitations: cannot operate above a certain output level. Not spending the full budget is not optimal either. At some point it will equal.

The tangent shows different shifts and the cost of inputs stay the same throughout the lines.

If labor cost changes, the equilibrium point shifts to use less labor and more capital.
Earlier at point a, now be come tangent at point B for the ISO C won. A is a coast one for labour
Less labour and more capital

New Combinations

If there's an ISO one there can be a B which should be the point of G. If the labour cost is increase, the the tagent will be change. The d represent a parallel line for A P star parallel meaning is to show the slope.

• Optimal combination of input of ISO cost line and ISO quad.

Scale Economies Defined

Economies of scale refer to join productivity when increase by same proportion. If all the inputs increase by 10%, if the output increase by 10% it an increasing economic subscale.
If it is less than 10%, it's a decreasing economic sub scale.
If it equals the same it's a constant one

Constraint on Economies Of Scale

Cannot assume doubling inputs doubles output due to fixed inputs. Simply doubling of all the variable cannot mean that the output will be equal or more because they are fixed inputs. That will decrease.

Combining Enterprise. Producing Two Outputs

Farms often produce a mix of products to maximize profit. Combining enterprise to produce both outputs.

Example the harvest can be two outputs. Crop of livestock where both outputs have point Q and point R that are crops and livestock. What ever the resource is the same. Each combination either point Q or Q R you can combine output the resouce will be the same. That mean using the same resource. This graph shows that if you want one outputmore the other ouput will be less. The diminishing value that come down. For example you want 11 crop for the number 5 livestalk. And when switch. This is a hypothethical graph. Rate of the production and substitution.

ISO Revenue Line

Given products and possibilities curves, income is determined by the ISO revenue line. The products and possibilities curve has the ISO revenue line. So that is the optimal combination of two products the same logic is the same way. Price ratio of crops and livestock. The output is equal to the rate of the substitution so the slope show equal to the curve of