Question

1. Consider a monopolist with a fixed cost of 500 and MC = 10 per unit. Demand in the market is P = 110 − q.

a. If the monopolist charges a linear price (the same price to all consumers) what is its price, quantity and profit? What is the DWL?

b. If the demand curve represents the demand for an individual consumer, if the monopolist can engage in first-degree price discrimination, what is the two-part tariff it charges? What is the resulting DWL?

c. Now again reconsider the monopolist charges a linear price (no price discrim- ination). The government decides to impose a per-unit tax of $20. What is the resulting output and price the consumers pay? What is the monopolist’s profit now that there is the tax imposed in the industry, and what is the DWL? Explain your answer, relative to part a. What is the tax revenue generated?

d. Can you suggest an alternative way the government can raise the same tax revenue in which there is less DWL than in part (c)?

Answer 1

Answer a :-

In the given question The marginal cost of producing each unit is $10/ unit .

Thus if a firm has to charge same price from all then the price will be equal to its marginal cost = $10

At price 10 the equilibrium quantity sold will be

Q =110-P

Q =110-10=100 units

Total Revenue at 100 units = 10*100=1000

Total cost at 100 units = Fixed cost + Variables cost

= 500+ 10(100)

=1500

Dead weight loss to the producers =1000-1500= 500

Answer b :-

When different prices are charged at different quantities , following table is derived :-

Quantity	MC	TC	AC	AR	TR	MR
45	10	950	21.11	65	2925	21
46	10	960	20.87	64	2944	19
47	10	970	20.63	63	2961	17
48	10	980	20.42	62	2976	15
49	10	990	20.20	61	2989	13
50	10	1000	20	60	3000	11
51	10	1010	19.80	59	3009	9
52	10	1020	19.60	58	3016	7
53	10	1030	19.40	57	3021	5
54	10	1040	19.25	56	3024	3
55	10	1050	19.10	55	3025	1
56	10	1060	18.90	54	3024	-1

Graphically representing the above table :-

In the above case the firm will continue to price until it's

MR> = MC

Thus till 50 units the firm will incur profits .

However after 50 units say 100 units

Price = 110-100=$10

Total revenue =10*100=1000

Total cost = 500+(10*100)=1500

Dead weight loss = 1500-1000=500

Answer c :-

If the government Imposes a tax of $20/unit

The price will increase to $30

Now if at this price , old quantity is sold , then it will create a dead weight loss to consumers

Total revenue = 100*30=3000

Total cost = 500+(10*100)=1500

Dead weight loss to consumers =3000-1500=1500

Dead weight loss to producers =2000-1500=500

Government revenue = (20*100)=$2000

Answer d :-

Now if at 100 units the government gets a revenue of $2000

This means that the government has imposed 200% tax on the manufacturing as excise duty .

This means the marginal cost will rise to $30

And thus the government will be able to generate same tax revenue.