1.6.2 Costs

Question 1

What are explicit/implicit costs

Answer 1

Explicit - cost of acquiring inputs -> opportunity cost simply market price

Implicit - reflects foregone opportunities e.g. managerial time (what they could earn in another job)

Taking into account implicit costs essential for decision making, rarely shows up in accounting costs

Question 2

What is the opportunity cost of retnting capital?

Answer 2

• Rental price (similar to wage payments for labour)

Even if capital purcahsed, opportunity cost of using it is still there as can rent it out to someone else so market rate still there to measure opportunity cost of renting capital

Note that the implicit rental costs change over time - if the rent we could get for land we owng goes up, opportunity cost of using that land goes up - how much we paid for it in the past irrelevant as it is a sunk cost

Question 3

What if there is no market for a capital good

Answer 3

Compare to economic cost of alternatives

E.g. buying capital at $20k, use for a year and sell for $17k or keep the 20k and invest at 5%

Opportunity cost of 1 is difference after 1 year - depreciation of 3k vs foregone interest of 1k

Question 4

What are fixed costs, variable costs and total costs

Answer 4

Do not vary with level of output, q,

• Spending on land, office space, production facilities
• costs fixed in short run may be variable in long run e.g. rent

Variable costs vary with the level of output:
- Cost of variable inputs such as material and labour - labour not always fully variable

Total costs are the sum of fixed and variable costs

Question 5

What is the marginal cost?

Answer 5

Change in total cost if firm produces an additional unit of output

MC = dC(q)/dq = dVC(q)/dq

Question 6

How do you calculate the 3 average cost measures?

Answer 6

AFC = FC/q
(always falls as output increases, fixed costs spread over more units)

AVC = VC/q
(increase/decreases with output)

ATC = TC/q = FC/q + VC/q = AFC + AVC

Question 7

How are short run cost curves illustrated?

Answer 7

Example on page 18 and page 19

Question 8

What is the short run production function?

Answer 8

Determines shape of short run cost curve, assumptions:

• Amount of capital fixed in short run
• Price of labour (variable) fixed and equal to w, so variable costs:

VC = w*L

AVC = VC/q = (wL)/q = w(L/q)

Since we know that APL = q/L or 1/APL = L/q

We know AVC = w*(L/q) = w/APL

As a result,

MC = dVC/dq = d(w*L)/dq = w dL/dq

MPL = dq/dL
OR
1/MPL = dL/dq

Thus, MC =w * dL/dq = w/MPL

(Example on page 19 cos this make no darn sense)

Question 9

How do you calculate the marginal costs and MPL of the short run production function

Answer 9

We know AVC = w*(L/q)

APL = q/L can be rewritten as 1/APL = L/q

So, AVC = w*(APL)

Finding MC:

MC = dVC/dq = d(wL)/dq = wdL/dq

Finding MPL:
MPL = dq/dL
Rewrite as 1/MPL = dL/dQ

Thus, MC = w*(1/MPL) = w/MPL

There are 3 examples on page 19

Question 10

What is the shape of production function/cost curve

Answer 10

Illustrated on page 19

Quantity against cost per unit

MC curving upwards and diminishing

AC curves downwards, crosses MC and starts to slowly curve upwards

Question 11

What is optimal input choice

Answer 11

Short run amount of some factor is fixed, costs associated with the factor are fixed costs.

Long run all factors variable so no fixed costs

To produce a given quantity of output at minimum costs, firms use information about production functions and price of production factors:

• Short run only vary labour
  Long run vary both - long run costs never higher than short run costs

Question 12

What does an isoquant/isocost show? What is the equation

Answer 12

Isoquants show combinations of inputs that produce a specific level of output

Isocost lines show combinations of inputs that require the same total expenditure:

If firm hires L hours of labour at wage rate w per hour, total labour costs w*L

If firm rents K hours of machines at rent r per hour, capital costs r*K

total costs are wL + rL

For a fixed level of cost C (with line above):

C = wL + rK
OR
K = C/r - (w/r)L

(ILLUSTRATED PAGE 20)

Question 13

What are the properties of an isocost?

Answer 13

• Cost level, C and input prices determine where line hits the axes and Y intercept is C/r and x intercept is C/w
• Isocosts farther from origin have higher costs than those closer to origin
• Slope of each isocost the same, given by the relative price of the inputs (-w/r in the diagram)

Isocost similar to budget constraints but:
- Consumers have one budget constraint only - incomes and prices determine
- Firms have many isocost lines

Question 14

What is the optimal input choice

Answer 14

Firms choose the isocost with the lowest cost for a desired level of output

This will be where output (isoquant) = isocost line
- If you move along the isocost line you will produce less than q1

(Also illustarted page 20)

At point A, isocost line tangental to isoquant

So at A, dK/dL = -w/r

Recalling slope of an isoquant is the MRTS = dK/dL, at point A the MRTS = -w/r

Question 15

How can we use the property MRTS = -w/r to get MPL and MPK

Answer 15

Recall MRTS is equal to negative of the ratio of MPL/MPK

MRTS = -MPL/MPK

Thus MRTS= -w/r can be:

MPL / w = MPK / L

As such, costs are minimised if inputs are chosen so the last pound spent on labour yields as much additional output as the last pound spent on capital

(Example on page 20)

Question 16

What occurs when facto prices change?

Answer 16

Firms substitute away from the now relatively more expensive factor

e.g. if wages go down, isocost lines become flatter
- Firms substitute away from capital and towards labour

e.g. for q=1.52L^0.6K0.4

If wages fall from 24 to 8, but price of capital remains at 8

The optimal capital/labour ratio falls from 100/50 to 52/77

Cost of producing q=100 falls from 2000 to 1032

Question 17

How do we derive a firms long term expansion path and long run cost curve?

Answer 17

Repeating the process of finding cost minimising combination level of imputs allows us to find the long term expansion path and cost curve

Expansion path: curve through tangency points between isocost lines and isoquants for different output levels

L against K

Cost curves: derived from the long run expansion path, axis switch to Quantity of units per hour against Consumption

As with short run curves, the shape is determined by the production function

Question 18

What are economies/diseconomies of scale

Answer 18

EofS - average costs falling as output goes up

For fixed factor prices this happesn if underlying production function has increasing returns to scale (IRS)
- Then doubling all inputs will more than double output, so average costs fall

DofS - average costs rise as output goes up
- Happens if underlying production fucntion has decreasing returns to scale

Degree of returns to scale varies for the same firm as output goes up - first increases, then decreasing returns to scale

Question 19

What is the shape of the average cost curve?

Answer 19

Often find a U or L shaped pattern
- Shape of long run cost curve determined by shape of production function

U shape:
- First decreasing SRAS as on IRS part of production function, then increasing average costs as we move to DRS part

L shape:
- First dereasing, then constant average costs (i.e. production fnction first has IRS, then CRS)

Question 20

What are the properties of costs in the long run? How is this illustrated with short run costs?

Answer 20

Cannot be higher than in the short run:
- Cant vary capital in short run, so might have to produce with suboptimal levels of capital

Firms could always choose same capital stock level as in short run, so can never be worse off in the long run

(illustrated page 21 - long run horizontal line at optimal cost part, SRMC curves upwards, SRAC is U shaped)