Chapter 8, Problem 1CACQ

1.

To determine

The level of output to be produced by the firm in the short-run.

Explanation of Solution

Every firm’s main objective is to maximize the profit. Firm’s usually decide the price and output which help them to maximize the output.

  $\text{Profit }= \text{Revenue }-\text{ Total cost}$

  $\text{Profit }=\text{ Price }\times \text{Quantity }-\text{ TC}\left(\text{q}\right)$

For profit maximization condition we will differentiate wr.t “q”

  $\frac{d\left(\text{Profit}\right)}{dq}=\frac{d}{dq}\left(\text{Price }\times \text{ quantity }\right)- \frac{d}{dq}\left(\text{TC}\left(q\right)\right)$

Applying the condition for “maxima”

  $0=P-\frac{d}{dq}\left(\text{TC}\left(q\right)\right)$

  $P=\frac{d}{dq}\left(\text{TC}\left(q\right)\right) (\text{ But}\frac{d}{dq} \left(\text{TC}\left(q\right)\right) \text{is equal to marginal cost)}$

So,

P = MC

Under perfect competition, firmprofit maximize the profit where “MC = P”.

So, the graph output in short run will be “3”

2

To determine

The change in pricing policy by the firm under short run.

Explanation of Solution

As firm try to operate at profit maximization output,under this output firm will charge the price which will help them to keep on the output level.

  $\text{Profit }= \text{Revenue }-\text{ Total cost}$

  $\text{Profit }=\text{ Price }\times \text{Quantity }-\text{ TC}\left(\text{q}\right)$

For profit maximization condition we will differentiate wr.t “q”

  $\frac{d\left(\text{Profit}\right)}{dq}=\frac{d}{dq}\left(\text{Price }\times \text{ quantity }\right)- \frac{d}{dq}\left(\text{TC}\left(q\right)\right)$

Applying the condition for “maxima”

  $0=P-\frac{d}{dq}\left(\text{TC}\left(q\right)\right)$

  $P=\frac{d}{dq}\left(\text{TC}\left(q\right)\right) (\text{ But}\frac{d}{dq} \left(\text{TC}\left(q\right)\right) \text{is equal to marginal cost)}$

So,

P = MC

Under perfect competition, firm profit maximize the profit where “MC = P”.

So, by the graph under profit maximization condition “MC = P”. Price will be “70”.

3.

To determine

To calculate: The total cost at given level of output.

Explanation of Solution

Total cost is the sum of variable cost and total fixed cost.

Here Total fixed cost = 100

Total Variable cost = 120

  $\begin{array}{l}\begin{array}{l}\text{Total cost = Total fixed cost + Total variable cost}\hfill \\ \text{ = 100 + 120}\hfill \end{array}\\ =\$220\end{array}$

As firm operate on the profit maximizing output, on this output level, the firm’s total cost will be “$220”.

4

To determine

To calculate: thevariable cost at given level of output.

Explanation of Solution

Variable cost is the cost which changes with change in the output.

Example − The raw material used for production. When firm wants to increase production the demand for raw material increases which lead to increase its cost. Whereas when firm wants to decrease production, it needsfewer raw materials which lead to decrease in the cost.

So, that’s why variable costvary according to level of production.

So, at the profit maximizing output level, firm’s variable cost will be “120”.

5

To determine

To calculate: Thefixed cost at given level of output.

Explanation of Solution

Fixed cost are the costs which does not change with the change in output level.

Example − The fixed cost can be utilities like electricity or rent. These costs are independent of production level and are termed as fixed.

As firm is operating at profit, maximum level of output at this output firm’s fixed cost will be “100”.

6

To determine

Firm’s profit level in short runwhen producing at given level of output.

Explanation of Solution

Profit is the amount a firm receive after compensating all the cost which it incurs for producing the output. At the profit maximization output, firm’s profit is

Firm’s profit will be “revenue − cost “which will be

  $\begin{array}{l}\text{Profit }=\text{ Revenue }–\text{ Total cost}\\ \text{Profit }=\text{ Price ×Quantity }–\left(\text{Variable cost + fixed cost}\right)\\ \text{Profit }=210-220\\ \text{Profit }=-\$10 \end{array}$

7

To determine

Firm’s profit at shut-down point.

Explanation of Solution

Shut down − When a firm cannot recover its variable cost, then this point is known as shut down point.

Example − If the variable cost of a firm is “$100” but it is making “$80” in revenue then for that firm, it is better to shut down than to be in business.

At shut down condition P = AVC

  $\begin{array}{l}\text{Here},AVC=40\\ \text{Profit }=\text{ Revenue }–\text{ cost}\\ \text{Profit }=40–\left(\text{Fixed cost + variable cost}\right)\\ \text{Profit }=40–\left(100+40\right)\\ \text{Profit }=40–140\\ \text{Profit }=-100\end{array}$

So,P should be 40 and profit will be -100. So, P = 40 will be firm’s shut down point.

8

To determine

Whether the firm will continue to operate or shut-down its operations in the long-run.

Explanation of Solution

As firm is not able to recover the variable cost which means that firm is unable to meetits day to day cost and is going under loss, that’s why firm will not work in the long run.