Microeconomics 2

John Hey

Plan for today1. We look at the Homework I set at the end of Lecture

11.2. We will quickly revise the relationships between the

total, average and marginal cost curves.3. We look at the optimal supply (“how much?”) decision

of the competitive firm (one who takes all prices as given).

4. We will show that the supply curve is the marginal cost curve (if upward sloping) and...

5. ... that the firms’ profit is the area between the supply curve and the price of output.

(which is the parallel of the result for the consumer surplus)

Homework• CES technology with parameters c1=0.4, c2=0.5,

ρ=0.9 and s=1.0. (Note: constant returns to scale.)

• The production function:• y = ((0.4q1

-0.9)+(0.5q2-0.9))-1/0.9

• I have inserted the isoquant for output = 40 (and also that for output = 60).

• I have inserted the lowest isocost at the prices w1 = 1 and w2 = 1 for the inputs.

• The optimal combination: q1 = 33.38, q2 = 37.54• and the cost = 33.58 + 37.54 = 70.92.

What you should do• Find the optimal combination (either graphically or

otherwise) and the (minimum) cost to produce the output for the following:

• w1 = 2 w2 = 1 y=40• w1 = 3 w2 = 1 y=40• w1 = 1 w2 = 1 y=60• w1 = 2 w2 = 1 y=60• w1 = 3 w2 = 1 y=60• Put the results in a table.

You can do this graphically or algebraically

• Algebraically

• The formulae (in the Maple file) are:• q1=y1/s(c1/w1)1/(1+ρ)[(c1w1

ρ) 1/(1+ρ) )+(c2w2 ρ) 1/(1+ρ)]1/ρ

• q2=y1/s(c2/w2)1/(1+ρ)[(c1w1 ρ) 1/(1+ρ) )+(c2w2

ρ) 1/(1+ρ)]1/ρ

• where y is the desired output.

Results

y w1 w2 q1 q2 cost

40 1 1 33.4 37.5 70.9

40 2 1 27.9 45.2 101.1

40 3 1 25.5 51.2 127.7

60 1 1 50.1 56.3 106.4

60 2 1 41.9 67.9 151.7

60 3 1 38.3 76.7 191.6

Chapter 12

• The total cost C(y) is the minimum cost to produce a given level of output y.

• It is always upward-sloping (in the long period passes through the origin) and its shape depends upon the returns to scale:

• decreasing ↔ convex• constant ↔ linear• increasing ↔ concave

Chapter 12

• The total cost C(y) is the minimum cost to produce a given level of output y.

• The average cost, C(y)/y, is the slope of the line from the origin to the total cost curve.

• The marginal cost, the rate at which total cost increases with output, is equal to the slope of the total cost curve.

Constant returns to scale: total cost

Constant returns to scale: marginal and average costs

Total cost: decreasing returns to scale

Two examples (of average and marginal costs) with decreasing returns

Average cost at an output of 40

Average cost at the output of 80

The average cost curve

Marginal cost at the output 40

Marginal cost at the output 80

The marginal cost curve

From the total cost curve to the marginal cost curve and back.

• The marginal cost curve is the slope of the total cost curve...

• ... hence the total cost curve is the area under the marginal cost curve.

• The marginal cost curve is the derivative of the total cost curve...

• ... hence the total cost curve is the integral of the marginal cost curve.

Chapter 13• Today we find the optimal output for a perfectly

competitive firm...• ...that takes the price of its output as given.• We will assume to begin with that the firm has

decreasing returns to scale.• We will see later that there are problems if the firm

has increasing or constant returns to scale.• Let us go to the Maple html file...• ... in which we assume to begin with that the output

price is 30 (per unit).

Chapter 13: summary

• The condition for the optimal output:• price = marginal cost...• ... where marginal cost is rising.

• It follows that the supply curve of the firm is simply its marginal cost curve.

• The profit/surplus of the firm is the area between the price and its supply curve.

Chapter 13

• Goodbye!