Question

A publishing company faces the following total cost and demand schedules:

Books Price Total Cost $

0 - 10

1 10 12.5

2 8 14.5

3 7 16.0

4 6 17.0

5 5.2 19.0

6 3.5 21.5

7 2 25.0

a) Calculate the company’s fixed cost, average cost, and marginal cost.

b) Calculate the Total Revenue, average revenue and marginal revenue.

c) If the company wants to maximize profits, how many books should it sell? (Use MR = MC!) What is the total profit?

d) Explain in terms of marginal analysis why your result in “c” holds.

Please also explain how you calculated these answers

Answer 1

Find the calculated numbers in the table below:

A B C D E F G H I J K L M Books Price Total Cost Fixed Cost Variable Average Average Average Marginal Total Average Marginal Fixed Variable Total Revenue Revenue Cost Cost Revenue Cost = Price Profit 2.5 10 -2. 10 2 .5 100 2.5 12.5 104. 5 5 2.25 7.25 10 6 3.333333 25.333333 7 2.5 1.75 4.25 9 2 1.8 3.81 11.5 1.666667 1.916667 3.583333 15 1.428571 2.142857 3.571429 non -11)

The formula view of the calculations can be seen below:

A B C D E F G H м Books Price Total Cost Fixed Cost Variable Cost Average Average, Average Total Variable Fixed Cost Cost Cost Marginal Cost Total Revenue Average Revenue = Marginal Revenue Price Profit 1 2 0 10 12.5 14.5 10 10 10 =J3/A3 4 2 5 3 6 4 10 =C2-D2 =C3-D3 =D3/A3 =C4-D4 =D4/A4 =C5-D5 |=D5/A5 =C6-D6 |=D6/A6 =C7-D7 =D7/A7 =C8-D8 |=D8/A8 =C9-09 1=D9/A9 | =E3/A3 =E4/A4 =E5/A5 =E6/A6 =E7/A7 =E8/A8 =E9/A9 16 17 =SUM(F3:G3) =(C3-C2)/(A3-A2) |=B3*A3 ESUM(F4:G4) =(C4-C3)/(A4-A3) =B4*A4 -SUM(F5:65) 1=(C5-C4)/(A5-A4) |=B5*A5 =SUM(F6:46) 1=(C6-C5)/(A6-A5) |=B6*A6 =SUM(F7:67) =(C7-C6)/(A7-A6) |=B7*A7 =SUM(F8:48) =(C8-C7)/(A8-A7) =B8*A8 =SUM(F9:49) 1=(C9-C8)/(A9-A8) |=B9*A9 10 10 10 =(13-0)/(A3-A2) =(14-13)/(A4-A3) =(5-14)/(A5-A4) I=J6-J5)/(A6-A5) = (J7-J6)/(A7-A6) =(J8-J7)/(AS-A7) =(19-18)/(A9-A8) 15.2 = 3-C3 =14-C4 =35-C5 =J6-C6 =17-C7 =8-C8 |=J9-09 =J5/A5 =J6/A6 =J7/A7 = 8/A8 = 29/A9 19 3.5 21.5 97 25 10

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(a) Since at zero production of books, cost is 10, which must be the cost which needs to be incurred irrespective of the level of production, known as fixed cost. Hence, total fixed cost = 10.

Average cost can be derived by dividing total cost by the number of units of output (books).

Marginal cost is the cost incurred for the additional unit of output, which is derived as the ratio of change in cost due due to addition units of production to the change in production of additional units or the number of additional units.

(b) Total revenue = price multiplied by total number of units sold. Accordingly total revenue is calculated.

Average revenue is the revenue per unit of output, which is essentially same as the price.

Marginal revenue is the revenue that can be derived by selling extra unit of book (output). Hence, it is calculated as the change in total revenue due to change in output by 1 unit.

(c) Based on the marginal analysis, profit is maximized at MR = MC. From the table, it can be observed that MR = MC = 2, when output (number of books) = 5. Hence, 5 books should be sold to maximize profit.

(d) Marginal revenue is the revenue obtained from an additional unit of book and marginal cost is the cost incurred by producing an extra unit of book. Consider a case when MR>MC, i.e., if an additional unit of book generates more revenue than the cost incurred, then the company should continue to produce additional units of book. Other wise, it will loose potential profit because MR>MC. Hence, profit keeps on increasing as long as MR > MC. This situation case be observed till number of books = 4 in the present case.

When MR = MC, the revenue generated by an additional unit of book is just same as the cost incurred for it and hence at this level of output, profit does not increase, which means that profit is maximum at this level of output.

If the company continues to produce, MR < MC and hence, cost incurred for the additional unit exceeds the revenue generated by it and hence, profit starts falling.

So, based on marginal analysis, profit reaches its maximum when MR = MC. In our case MR = MC = 2 at books = 5.