term 2 lecture 3 - cost minimisation

Question 1

how can you break down profit maximisation as a two step procedure?

Answer 1

first find the minimum cost to produce a given output, and then find the output that gives maximum profit

Question 2

what costs vary with output?

Answer 2

variable costs

Question 3

what costsdont change with respect to output?

Answer 3

fixed costs

Question 4

what are sunk costs?

Answer 4

costs that cannot be recovered if the firm exits the market, such as contractual obligations or selling of firms physical assets(only partial amount is recoverable)

Question 5

what are the simplifications for costs?

Answer 5

all fixed costs are due to time constraints on availing certain inputs
if there is enough time all costs can be freely adjusted - in the long run all costs are variable; there are no fixed or sunk costs
short run; all fixed costs are also sunk costs

Question 6

what is the aim of cost minimisation?

Answer 6

to minimise a cost function subject to some constraint ie hold output fixed at some specific value

Question 7

what are some important properties of the cost function?

Answer 7

1) short run cost is never smaller than the long run cost
2) both short and long run cost functions are increasing functions of (y,w1,w2)
3) if w1 and w2 are doubled, then cost will also be doubled[ cost functions are homogenous of degree 1 in w1 and w2]
4) derivative of C with respect to wi gives the conditional input demand function xi

Question 8

why is the case of fixed coefficient technology a special case?

Answer 8

it does not allow substitution between inputs the constional input demand is insensitive to input prices

Question 9

what is shown from the graphical representation of short and long run total costs and output expansion paths?

Answer 9

1. Short run cost is greater than the long-run cost at all y except at one point where they are equal.
2. As output is increased how the cost will increase depends on:
   * Returns to factor of the variable input in the short-run case, and
   * Returns to scale in the long-run case.
3. Two inputs are gross substitutes. If w1 increases x2 must rise,and if w2 rises x1 must rise.
4. If w1 and w2 are increased by the same rate à conditional input demands do not change.But the total cost will increase by the same rate.
5. Long-run AC curve is an envelope of short-run AC curves

Question 10

what are the properties of the conditional input demand functions and the long run cost function?

Answer 10

if w1 and w2 are increased by the same rate then the conditional input demands don’t change but the total cost will increase by the same rate
if y=A * x1^a * x2^b then C=By^(1/[a+b]) where B is an expression that includes w1 and w2

Question 11

what is the minimum efficient scale?

Answer 11

the output for which the marginal cost is equal to the average cost