Chapter 10, Problem 1E

To determine

(a)

To find:

The missing values in the table.

Answer to Problem 1E

The missing values in the table are as shown below:

Output (Q)	Fixed Cost (FC)	Average Fixed Cost (AFC)	Variable Cost (VC)	Average Variable Cost (AVC)	Total Cost (TC)	Average Cost (ATC)	Marginal Cost (MC)
1	$50	$50	$30	$30	$80	$80	$80
2	$50	$25	$50	$25	$100	$50	$20
3	$50	$16.67	$80	$26.67	$130	$43.34	$30
4	$50	$12.50	$120	$30	$170	$42.50	$40
5	$50	$10	$170	$34	$220	$44	$50

Table (1)

Explanation of Solution

The missing values in the table are calculated by using the following formulas:

  $\begin{array}{l}1)Variable\text{C}ost(VC)=Totaloutput\times AverageVariable\text{C}ost\\ \Rightarrow \boxed{VC=Q\times AVC}\\ 2)TotalCost(TC)=Variable\text{C}ost+FixedCost\\ \Rightarrow \boxed{TC=VC+FC}\\ 3)AverageFixedCost(AFC)=\frac{FixedCost}{Totaloutput}\\ \Rightarrow \boxed{AFC=\frac{FC}{Q}}\\ 4)AverageVariableCost(AFC)=\frac{VariableCost}{Totaloutput}\\ \Rightarrow \boxed{AVC=\frac{VC}{Q}}\\ 5)AverageCost(AC)=\frac{TotalCost}{Totaloutput}\\ \Rightarrow \boxed{AC=\frac{TC}{Q}}\\ 6)MarginalCost(MC)=\frac{TotalCost}{Totaloutput}\\ \Rightarrow \boxed{MC=\frac{\Delta TC}{\Delta Q}}\\ or,\\ \boxed{M{C}_n=V{C}_n-V{C}_{n-1}}\end{array}$

Economics Concept Introduction

Perfect competition:

It is a market structure where large number of buyers and sellers exist, and products are homogeneous.

Total cost (TC):

The total outlay in production activity is referred to as total cost.

Fixed costs (FC):

The costs that once incurred remain same at all levels of output are called fixed costs.

Variable costs (VC):

The costs that vary with the level of output are regarded as variable costs.

Average total cost (ATC):

When, for any level of output, the total costs are divided by the level of output, it is called average cost or average total cost at that level of output.

Average fixed cost (AFC):

When, for any level of output, fixed costs are divided by the level of output, it is regarded as average fixed cost at that level of output.

Average variable cost (AVC):

Average variable cost is the variable cost divided by the level of output.

Marginal Cost (MC):

The additional cost of producing an extra unit of output is referred to as the marginal cost of producing that unit of output.

To determine

(b)

To find:

The minimum price for firms to break-even.

Answer to Problem 1E

The minimum price at which the firm breaks even is P = MC =80.

Explanation of Solution

Under perfect competition, the price is equal to marginal cost. That is, P=MC. In production activity, break-even point is the point where the firm is earning zero profits. That is, break-even point is the level of output at which the total revenue exactly matches total costs.

First, find out total revenue ( TR ) for each output level taking P = MC. Further, find out the profit (p) for each output level.

Total Product (Q)	Marginal Cost/ Price (P=MC)	Total Revenue (TR)	Total Cost (TC)	Profit (p)
1	80	80	80	0
2	20	40	100	-60
3	30	90	130	-40
4	40	160	170	-10
5	50	250	220	30

Table (2)

In the given case, the firm would break-even at Q=1. The price corresponding to Q=1 is $80. Therefore, the minimum price at which the firm breaks even is P = MC =80.

Economics Concept Introduction

Perfect competition:

It is a market structure where large number of buyers and sellers exist, and products are homogeneous.

Total cost (TC):

The total outlay in production activity is referred to as total cost.

Total Revenue (TR):

Total revenue is the total proceeds from sale of a given level of output.

Profit (p):

Profit is the difference between total revenue and total cost.

Break-even point:

In production activity, break-even point is the point where the firm is earning zero profits. That is, break-even point is the level of output at which the total revenue exactly matches total costs.

To determine

(c)

To find:

The shut-down price.

Answer to Problem 1E

The shut-down price for the firm is P = MC =$20.

Explanation of Solution

Shut-down point is the point where the firm fails to cover even the average variable costs of production ( AVC ). That is, shut down occurs where P

Total Product (Q)	Average Variable Cost (AVC)	Marginal Cost/ Price ( P = MC )
1	30	80
2	25	20
3	27	30
4	30	40
5	34	50

Table (3)

In the Table (3), it can be identified that at Q=2, the price of $20 does not cover the average variable cost (AVC) of $25. Therefore, the shut-down price for the firm is P=MC=$20.

Economics Concept Introduction

Perfect competition:

It is a market structure where large number of buyers and sellers exist, and products are homogeneous.

Total cost (TC):

The total outlay in production activity is referred to as total cost.

Variable costs (VC):

The costs that vary with the level of output are variable costs.

Average variable cost (AVC):

Average variable cost is the variable cost divided by the level of output.

Shut-down point:

Shut-down point is that point where the firm fails to cover even the average variable costs of production (AVC).

To determine

(d)

To find:

The output level the firm would produce at a price of $40 and the corresponding profit.

Answer to Problem 1E

The output level at P =$40 would be Q= 4. At P =$40 and Q= 4, the profits are negative -$10. It means a loss of $10.

Explanation of Solution

The table below shows output, price and profits:

Total Product (Q)	Marginal Cost/ Price (P=MC)	Total Revenue (TR)	Total Cost (TC)	Profit (p)
1	80	80	80	0
2	20	40	100	-60
3	30	90	130	-40
4	40	160	170	-10
5	50	250	220	30

Table (4)

It can be identified from the table that at P =$40, the output produced is Q=4. At P =$40 and Q= 4, the profits are negative which is -$10. It means a loss of $10.

Economics Concept Introduction

Perfect competition:

It is a market structure where large number of buyers and sellers exist, and products are homogeneous.

Total cost (TC):

Total costs are the total outlay in production activity.

Total Revenue (TR):

Total revenue is the total proceeds from sale of a given level of output.

Profit (p):

Profit is the difference between total revenue and total cost.