Production Function Analysis

Topic 5. Production and cost

(3) The long run: Isoquant and Isocost analysis

November 1st 2004

Lecture slides available from Nancy’s website:

The aim of today’s lecture is to:

• Introduce you to Isoquant and Isocost analysis.

This enables us to show how the firm will choose the optimal combination of inputs (when all inputs are variable) to produce a given output

Essential reading:

• Sloman chapter 5, especially Sections 5.3 and 5.4.

1. Production function analysis

Two inputs are used to produce output: L (workers) and K (machines).

X = Production of 500,000 units of output per week, by 4 workers using 5 machines

2. Isoquants

Iso = same Isoquant = same quantity

The slope of the isoquant is the Marginal rate of technical substitution (MRTS).

• MRTS = ΔK/ΔL

• MRTS = MPL/MPK

• MRTS is falling as you move down the isoquant.
• Why?

2a. Isoquant map

I1 = 400,000 units of output

I2 = 500,000 units of output

I3 = 600,000 units of output

2b. Technical efficiency

Production is technically efficient if output cannot be raised without using more of at least one input.

• The isoquant summarises all technically efficient points

• Production of 500,000 units of output at X would be technically inefficient.

2c. Demonstrating returns to scale using isoquants

I2 uses twice as many inputs as I1. I1 produces 400, 000 sausages.

2d. Marginal product of one variable factor (SR)

K is fixed; Lis variable. The marginal product (MP) of L is the extra output from one extra worker.

I1 produces 400,000

I2 produces 450,000

I3 produces 480,000

MP is 50,000 for the 5th worker and 30,000 for the 6th worker.

MPmay be increasing, constant or diminishing.

3. Isocost lines

Input possibilities

1The total amount available to be spent on workers and machines is £1,000 per week.

2The rental cost of a machine is £200 per week.

3The weekly wage of a worker is £100.

Therefore, the employer can hire 5 machines and no workers or 10 workers and no machines or some combination of workers and machines.

All possible input possibilities form the isocost line.

3a. Isocost line

• slope of the isocost line = PL/PK
  

3b. Isocost lines at different input prices

3c. Isocost lines at different levels of Total Cost

Show the effects on the isocost line of:

• higher total cost
• lower total cost

4. Minimising the costs of producing a given output

• at X, MRTS = PL/PK
• MRTS = ΔK/ΔL
• MRTS = MPL/MPK

So at X

MPL/MPK =PL/PK

And

MPL/PL = MPK/PK

5. Maximising output for a given cost

6. The distinction between technical and economic efficiency.

Both X and Y are technically efficient ways of producing 500,000 units of output.

X is also an economically efficient (cost-effective) way to produce 500,000 units of output.

Yis technically efficient, but is not economically efficient.

7. Derivation of long-run costs from an isoquant map.

• Expansion path: the tangency points of the isoquant and isocost curves.
• Shows the minimum cost combinations of L and K to produce each level of output; the LRTC are shown by the isocost.