Question

1. A publisher faces the following demand schedule for the next novel from one of its popular authors:

The author is paid $2 million to write the book,

Price 100 90 80 70 60 50 40 30 20 10 0

QD(1000s) 0 100 200 300 400 500 600 700 800 900 1000

and the marginal cost of publishing the book is a constant $10 per book.

a. Compute the total revenue, total cost, and profit at each quantity. What quantity would a profit-maximizing publisher choose? What price would it charge?

The total revenue at each level of production is given by the demand schedule above, using T R = P Q. The total cost is the constant fixed costs of $2 million plus the variable cost of ($10)Q. For convenience, the units of revenue, cost, and profit are given in millions. In the table below, we combine these equations with the calculation of marginal revenue. It turns out that the profit-maximizing level of output is 500,000 units, corresponding to a price of $50.

b. Compute marginal revenue. (Recall that MR = ∆T R/∆Q). How does marginal revenue compare to the price? Explain.

QD(1000s) 0 100 200 300 400 500 600 700 800 900 1000

TR ($ millions) 0 9 16 21 24 25 24 21 16 9 0

TC ($ millions) 2 3 4 5 6 7 8 9 10 11 12

Profit ($ millions) -2 6 12 16 18 18 16 12 6 -2 -12

Marginal Revenue ($) 90 70 50 30 10 -10 -30 -50 -70 -90

Marginal Cost ($) 10 10 10 10 10 10 10 10 10 10

c. Graph the marginal-revenue, marginal-cost, and demand curves. At what quantity do the marginal-revenue and marginal-cost curves cross? what does this signify?

The relevant information is given in the table above. In the table, we can see that marginal cost and marginal revenue are equal at Q = 50. That is MR(50) = MC(50) = 10. Not coincidentally, this is also the profit-maximizing level of output that we found earlier.

d. In your graph, shade in the deadweight loss. Explain in words what this means.

The social surplus maximizing level of output would set the price equal to marginal cost. In that case, P = 10 and then turning to the demand schedule this corresponds to output of Q(10) = 900, 000. The deadweight loss is the surplus that is lost because we do not makes the units from 500,000 to 900,000. In this case, the deadweight loss if represented with a triangle with base 900, 000− 500, 000 = 400, 000 and the height of 50 − 10 = 40. The area of this triangle is 0.5(400000)(40) = 2 million

e. If the author were paid $3 million instead of $2 million to write the book, how would this affect the publisher’s decision regarding what price to charge? Explain.

Recall that there are two questions for the firm — how much to produce, and how whether to stay in business. The first question — how much to produce — is based on comparing marginal costs and benefits (e.g. should I go from 3 to 4? From 4 to 5, and etc.). By definition, marginal costs are variable costs i.e. they are related to how much output is chosen. The increase in the fee to the author is a type of fixed cost. In the current exercise, the fee paid to the author has no affect on the market demand schedule or on the production costs of the book. Thus, there is no affect of the author’s fee on any of the MARGINAL factors in our exercise. The publisher’s profit will go down, but otherwise there is no effect on what choices it will want to make.

Answer 1

Price	Quantity (000's)	Total Revenue	Total Costs	Fixed Cost	Variable Cost	Marginal Cost	Marginal Revenue	PROFIT
P	Q	(P*Q)	FC+VC	FC	VC	(TCn-TCn-1)/Qn-Qn-1	(TRn-TRn-1)/Qn-Qn-1	TR-TC
100	0	0	2000	2000	0			-2000
90	100	9000	3000	2000	1000	10	90	6000
80	200	16000	4000	2000	2000	10	70	12000
70	300	21000	5000	2000	3000	10	50	16000
60	400	24000	6000	2000	4000	10	30	18000
50	500	25000	7000	2000	5000	10	10	18000
40	600	24000	8000	2000	6000	10	-10	16000
30	700	21000	9000	2000	7000	10	-30	12000
20	800	16000	10000	2000	8000	10	-50	6000
10	900	9000	11000	2000	9000	10	-70	-2000
0	1000	0	12000	2000	10000	10	-90	-12000

A. The profit-maximizing condition is MR(Marginal Revenue)= MC (Marginal Cost)

From the above it can be identified that MR=MC at quantity level 500 units(000's) and price is $50. So, ideally the price to be charged should be $50.

B. The marginal revenue is always lesser than the price. This situation can be observed in a monopoly market. This is because the monopolist to induce more demand must reduce the price of the product. However, only the price of the extra unit cannot be reduced. The price must be reduced for all the units to sell more units and hence, the MR is less than price and falls below the demand curve.

C.

From the graph it can identified that the MR and MC curves intersect at point 500 units(000's) . Before this point, the MR>MC hence, there was scope for the company to sell more books by reducing the price and earn higher a revenue and beyond this point MC>MR which means that cost incurred is higher than revenue generated so this means losses. Hence, the profit maximisation point is where MR=MC.

D.

Dead-Weight loss - Refers to loss of economic efficiency due to the inefficient allocation of resources.

The shaded portion refers to the dead -weight loss ( ABC triangle) . The area of ABC = 1/2*AB*AC= 1/2 *400,000*40 = 8 million