Cost & Return Analysis

Farm & Ranch Business ManagementChapter #5

Farm & Ranch Business ManagementChapter #5

Production Function

As inputs are changed, outputs are changed also

Example: fertilizing wheat

Where is the maximum profit?

Lbs. Of Fertilizer Yield0 2020 2540 3260 4080 45100 48120 45

Law of Diminishing Returns

As an input is added in production, the output will increase at an increasing rate, then at a decreasing rate, and finally decline

English Translation: if you were to increase the amount of fertilizer on wheat, your yield in bu./acre would increase dramatically for the first few units, until you added enough fertilizer that the rate of yield increase would slow down, and may even become negative

Law of Diminishing Returns

Lbs. Of Fertilizer Yield Added0 20 020 25 540 32 760 40 880 45 5100 48 3120 45 -3

Stages of the Production Function

Stage #1: increasing average return for each added unit of input

Average Product = Total Yield divided by number of units added

Stage #1 Example

Lbs. Of Fert. Yield Added Avg Prod.0 20 0 2020 25 5 2540 32 7 1660 40 8 13.380 45 5 11.1100 48 3 9.2120 45 -3 7.5

Stages of the Production Function

Stage #2: begins when the marginal product equals the average product.

Diminishing returns begin to develop in stage #2

Stage #3: begins when the marginal product becomes 0.– Total product decreases if input is increased

Stage #3 of the Production Function

Lbs. Of Fert. Yield Added Avg Prod.0 20 0 2020 25 5 2540 32 7 1660 40 8 13.380 45 5 11.1100 48 3 9.2120 45 -3 7.5

How much fertilizer?

Lbs. Of Fert. Yield Added Avg Prod.0 20 0 2020 25 5 2540 32 7 1660 40 8 13.380 45 5 11.1100 48 3 9.2120 45 -3 7.5

Profit Maximizing Rule

Add the variable input (fertilizer) to the point where the value of the marginal product equals the value of the added input.

Profit Maximizing RuleFert. Total Yield

Lbs. Cost Yield Added Val.Add Avg Prod.0 20 0 2020 $10 25 5 $15 2540 $10 32 7 $21 1660 $10 40 8 $24 13.380 $10 45 5 $15 11.1100 $10 48 3 $9 9.2120 $10 45 -3 $-9 7.5

Profit Maximizing RuleFert. Total Yield

Lbs. Cost Yield Added Val.Add Avg Prod.0 20 0 2020 $15 25 5 $12.50 2540 $15 32 7 $17.50 1660 $15 40 8 $20 13.380 $15 45 5 $12.50 11.1100 $15 48 3 $7.50 9.2120 $15 45 -3 $-7.50 7.5

Fixed Costs

Not used in profit maximizing rule Must be considered to determine if you will

make a profit or not

Opportunity Cost

Cost of using a resource in one way based on the return that could be obtained from using the resource in another way

Ex: labor, what is your labor worth if not farming?

Ex: interest, your money could sit in a bank and earn interest, or be used to invest in your business (farm)

Least Cost: Mathematical Approach

If one input (soybean meal) can be substituted for another (corn)

Usually don’t substitute at equal ratesChange in corn = Price of SBMChange in SBM Price of Corn Corn = $.05 and SBM = $.13, ratio = .13/.05 = 2.6 Now divide changes and find a ratio of 2.6 Page 5-11