Question

Demand for iPads in Canada is characterized by the following demand function:

Q = 16 ? p.

The only supplier of iPhones is Apple, a foreign monopoly with a constant marginal cost equal to 6.

Hint: If a monopolist faces a demand curve Q = A ? Bp (where A and B are constants) then its marginal revenue is MR =(A/B)-(2Q/B)

(a) What price would Apple charge Canadian consumers under free trade? How many iPhones would Canada import?

(b) Suppose the Canadian government imposes a tariff t = 2 per iPhone.

(i) How much would Canadian consumers now pay for iPhones? How many would be purchased?

(ii) By how much would the Canadian welfare increase or decrease due to the tariff?

(c) Suppose that instead of a tariff, the Canadian government imposes a quota equal to the volume of imports you have found in part (b). The administration of the quota is given to Apple, i.e., Apple is asked to reduce iPhone sales to Canada to a quantity not exceeding the amount of the quota. This policy is a type of a “voluntary” export restraint (VER).

(i) How would the price paid by Canadian consumers and the price received by Apple compare with the corresponding prices under a tariff?

(ii) By how much would the Canadian welfare increase or decrease with a VER relative to the case with a tariff?

(d) Which policy leaves Canada better off: a tariff or a VER restricting imports by the same amount?

Answer 1

In the situation of foreign monopoly, the monopolist (Apple) will sell at point where its Marginal Revenue (MR) = Marginal cost (MC). From the demand curve which is Q=16-P, we get P=16-Q which is the Average Revenue (AR). Therefore Total Revenue (TR) is P*Q = 16Q-Q²

a) Therefore, MR= dTR/dQ = 16-2Q. MC= 6

MR=MC or 16-2Q=6 or 2Q=10 or Q=5.

Therefore Price(P)= 16-5= $11. (Assuming that $ is the currency).

Without tariff, Apple charges $11 per phone (P*) to Canadians. Canadians buy 5 units of i-phones (Q*)

This is shown in Fig 1. Consumer’s Surplus (CS) is the Canadian Welfare here because Canada only has consumers and no producers.

CS =1/2* base* height where base = 5 units of output and height = 16-11 = 5.

CS= ½* 5* 5 = 12.5.

b) When a tariff of 2 is imposed per phone, the price paid by Canadians rises to P*+2. Therefore, new price (P’) = $13 and new Quantity= 16-13 =3 units (Q’)

1. Canadian Consumers now pay a price of 11+2 = $13 per phone and purchase 3 units.
2. New CS = ½ * base (Q’)* (height) = ½ * 3* (16-13) = 4.5. Thus compared with the previous CS calculated under part a), Canadian CS decreases by (12.5-4.5=) 8 units.

However, if overall welfare is concerned, one has to take into account the CS and the government revenue earned by the Canadian Government due to imposition of tariff. Therefore, government revenue = tariff rate * Q’

Or Government Revenue= 2*3=6. Therefore total welfare of Canada = CS + Government Revenue = 4.5+6= 10.5. Therefore, Canadian Welfare reduces by 12.5-10.5 = 2 units.

One important point to note here is that, the Producers’ Surplus (PS) too should contribute to a country’s welfare. But since the producer is a foreign country here, it is not taken into account under “Canadian Welfare” per se. However the welfare impacts with PS are shown below:

• Without tariff: PS=(11-5) * 5 = 30 units. Therefore Total Welfare = CS+ PS = 12.5+30= 42.5 units.
• With Tariff: PS = (11-5)*3 = 18 units (as new quantity is 3 units). Therefore total welfare = CS+ PS + Government revenue = 4.5+5+18 = 28.5. Thus there is a decrease in overall welfare by (42.5-28.5) = 14 units.  
• c) (i) When a quota is imposed restricting output to 3 units (refer to part b) then the new price paid by Canadians = 16-3 = $13. This is same as the price under tariff. However, the price received by Apple will now increase to $13 (as opposed to $11 under imposition of tariff). This is shown in Fig 2.
• (ii)New CS is the same as CS under tariff because the price paid by buyers is the same for both the cases. Therefore, CS under Quota = (1/2 * 3 * (16-13) ) 4.5 units. PS increases because the price received by sellers increases to $13. Therefore new PS = (13-5) * 3 = 24 units. There is no government revenue here because a quota is imposed and not tariff. Thus applying the same logic as above, if only consumers are considered, “Canadian Welfare” decreases by 8 units (Only CS falls from 12.5 to 4.5 units). However, if total welfare is concerned, then without Quota, Welfare was 42.5 units. After Quota, the welfare reduces to (4.5+24 =) 28.5 units. Thus there is an overall decrease in welfare by (42.5-29.5=) 14 units. With respect to Tariff too,welfare decreases by 14 units.
• d)In this example, if only "Canadian Welfare" consisting of Canadian consumers and government is considered, then under Tariff, 'Canadian welfare' reduces by 2 units and that under VER reduces by 8 units (owning to no government revenue, the rest of the surplus goes to the FOREIGN PRODUCER who is not Canadian). In this case, Tariff imposition is clearly better for Canada.
• However if overall welfare reduction is taken into account, then the results for quota and tariff are the same and it apparently seems like either policy should hold good.cBut while both tariff and quota create distortions, in general it is better to impose tariff because there is a certainty of government revenue to be earned under tariff. Under quota, there is no extra revenue earned by the government.. Also, quotas encourage corruption unlike tariffs which is why, a tariff is better than VER. Therefore in either case, Tariff is the better choice for Canada.
• The results are summed up in a table for better clarity:

• Policy	Amount	Price	Quantity	CS	PS	Govt Rev	Canadian Welfare	Overall Welfare	Fall in Canadian Welfare	Fall in overall Welfare
  None	-	11	5	12.5	30	-	12.5	42.4	-	-
  Tariff	$2	13	3	4.5	18	6	(4.5+6)10.5	28.5	2	14
  Quota	3 units	13	3	4.5	24	-	4.5	28.5	8	14