## Long Run Average Cost

1.

The long run average cost curve is U-shaped. This means that initially firms realize economies of scale as they start producing more output. However, as the output increases beyond a certain point, at the bottom of the “U”, there are constant returns to scale for a while. Ultimately, as the output extends further, above the flat part of “U”, there are diseconomies of scale.

Therefore, initially as the output increases, there is proportionately less increase in inputs. After some time, the increase in cost of inputs equals the increase in revenue from outputs. Ultimately, expanding production becomes costly and loss generating event, as the increase in cost outweighs increase in revenue.

With Free entry and exit:

Initially, there are few firms in the market. As they extend production to make profits, and realize the economies of scale, they start making super normal profits. This means that there stock of wealth and capital accumulation increases. This leads to further increase in their scale of operations and also the entry of new firms in the long run. The entry of new firms happens because they see a market where they can make positive profits. This means that the size of industry increases. Hence, the scale of production increases. This leads to the beginning of diseconomies of scale. Few firms start losing money and they incur losses.

The losses made by few firms lead to exit of firms till the time the market returns to the place where no firm is making positive profits. This is the long run equilibrium and will be upset only if there is some technological advancement which increases the scale at which IRS or CRS are realized.

Restricted Entry:

Under restricted entry, the pre existing firms will operate on the downward sloping part of the cost curve. This will mean that they will make positive profits. However, as the entry is restricted, new firms can not enter the market, and hence, the old firms keep on making positive profits.

2.

The first degree price discriminating monopolist is also known as perfectly discriminating monopolist.

Under first degree price discrimination, the monopolist tries to capture the consumer surplus. This is done by selling different units of outputs at different prices. If implemented to success, the monopolist captures the entire consumer surplus.

Under perfect first degree price discrimination, there is no deadweight loss. The monopolist captures entire consumer surplus, along with the producers’ surplus. Therefore, there is no efficiency loss. Also, this outcome is Pareto Efficient, as the welfare of consumers or producers can not be increases without the decline in welfare of the other party.

3.

The utility function takes the form of:

U( c_{1}, c_{2}, p_{1}, p_{2}) = p_{1}u(c_{1}) + p_{2}u(c_{2}) = (1-p) u(w) + p u(y)

In state 1, wealth situation is:

C_{1} = w – πs

In state 2, wealth situation is:

C_{2} = y – πs + s

U( c_{1}, c_{2}, p_{1}, p_{2}) = (1-p) u(w – πs) + p u(y – πs + s)

The actuarially fair price insurance satisfies the following condition:

Δu(c_{1})/ Δc_{1 }= Δu(c_{2})/ Δc_{2}

This says that the marginal utility of an extra dollar of income if the loss materializes should be equal to the marginal utility of an extra dollar of income if the loss does not materialize.

Since, the marginal utility of money declines as the amount of money increase- for a risk averse person, the equality of marginal utility condition above means that, c_{1} = c_{2}.

Then, w – πs = y – πs + s => s = w –y = amount of loss.

Now, if price is above actuarially fair price, then,

Δu (c_{1})/ Δc_{1} < Δu (c_{2})/ Δc_{2} => c_{1} > c_{2}

Therefore, w – πs > y – πs + s => s < w- y = amount of loss

Now, if price is below actuarially fair price, then,

Δu (c_{1})/ Δc_{1} > Δu (c_{2})/ Δc_{2} => c_{1} > c_{2}

Therefore, w – πs < y – πs + s => s > w- y = amount of loss

4.

P(x) = a – bx

C (x_{i}) = cx_{i}

Therefore, firm i’s payoff function is:

Π = q_{i }(a – c – q_{1} – q_{2}– ……- q_{i-1 }– q_{i+1}-……- q_{n})

The best response function is:

B (i) = (a – c – q1 – q2- ……- qi-1 – q_{i+1}-……- q_{n})/2

The best response function for all the other firms is same.

In equilibrium,

Q_{1}* = ½( a – c – q_{2}*- ……- q_{n}*)

Q_{2}* = ½( a – c – q_{1}*- q_{3}* – ……- q_{n}*)

Q_{n}* = ½( a – c – q_{1}*- q_{2}* – ……- q_{n-1}*)

Solving this system of equations, we get,

Q_{1}* = Q_{2}* =…..= Q_{n}* = Q*

Then, each equation is,

A – c –(n+1)Q* = 0 => Q* = (a-c)/(n+1)

Price = a – n(a-c)/(n+1) = (a +nc)/(n+1)

Profits per firm,

[(a +nc)/(n+1)] [(a-c)/ (n+1)] – c (a-c)/(n+1) = (a-c)/(n+1){ (a +nc)/(n+1) – c}

P – MC = (a + nc)/ (n+1) – c = {a + nc –nc – c}/ (n+1}

As n tends to infinity,

Profits: tends to zero as the denominator of the term outside the curly brackets and inside the curly brackets, both tend to 0.

P- MC: Tends to 0, as denominator tends to infinity

These results shows that as the number of firm increases, and the marginal cost is fixed for all level of outputs, and if there are no fixed costs; the market tends towards a perfectly competitive market. This also implies implicitly that as number of firms increases to infinity, share of each firm in the market becomes negligible, and hence it loses market power, and hence, the competitive market comes into picture.