2. In autarky, the domestic economy has a single producer of aluminum. Without t

Question

2. In autarky, the domestic economy has a single producer of aluminum. Without trade this firm can and does operate like a monopoly. Its operating conditions can be completely described by its total cost function: TC(O)-450+10Q+0.0625*o2 and the domestic demand for aluminum which is given by the (inverse) demand function P(Q) = 60-0.25"Q Here the Q represents pounds of aluminum and P represents pesos per pound. a) Graph the marginal [MC(Q)] and average total cost [ATC(Q)] functions for this firm along with the demand curve and marginal revenue [MR(Q)] function. Derive (using calculus, not the graph) the monopolists optimal output and price if the firm maximizes profits in autarky. Indicate both on your graph. What is the total profit available to the firm in autarky? If this country begins to trade with the rest of the world, this aluminum producer will no longer be a monopolist. Indeed, the domestic economy is so small relative to the rest of the world, that it can buy or sell as much aluminum as it wants when trading with the rest of the world at the current world price Pw-15. Under these conditions, how much aluminum will domestic consumers buy? How much will this domestic producer make in the short run? How much aluminum will be imported? Will this monopolist continue to produce in the long run? Explain. If instead of free trade, the aluminum producer lobbies, successfully, for a tariff of 10 pesos on each pound of imported aluminum the domestic price Pd Pw+10. Under this trade restriction, calculate domestic production, consumption and imports (with this tariff) preferred to free trade for either the producer or consumers? Is restricted trade (with this tariff) preferred to autarky for either the producer or b) e) How much tariff revenue would the government collect? Is restricted trade consumers d) If instead of a tariff, the aluminum producer lobbies, successfully for an import allows imports of exactly 20 pounds of aluminum, what will be produced, ed and imported by the domestic economy? What is the maximum revenue quota that the government could extract by auctioning off the right to import those 20 pounds under a quota? Do consumers prefer the tariff (above) or the import quota? Does the firm prefer the quota or the tariff? welfare higher with free trade, trade with the proposed tariff, trade with rt quota of 20 pounds or autarky? Please explain how you are able to rank e) Is aggregate an impo these alternatives.

Explanation / Answer

Answer 2

The Total Cost Function is given by

TC(Q) = 450 + 10Q + 0.0625Q2 --------------------------(i)

(a)

Therefore, Average Cost AC = TC/Q

= ( 450 + 10Q + 0.0625Q2 )/Q

= 450/Q + 10 + 0.0625Q -------------------------(ii)

and Marginal Cost MC = d(TC)/dQ

= 10 + 2x0.0625Q

= 10 + 0.125Q --------------------------(iii)

Price P(Q) = 60- 0.25Q -------------------------(iv)

From (iv we can derive the MR curve as

MR = 60 - 2x0.25Q

= 60 - 0.5Q ----------------------(v)

For Profit Maximization, MC = MR

Hence, 10 + 0.125Q = 60 - 0.5Q

=> 0.5Q + 0.125Q = 50

=> 0.625Q = 50

=> Q = 80

Hence, P = 60 - 0.25Q = 60 - 0.25x80

= 60 - 20

= 40

Hence, Price = 40.pesosand Q= 80 pounds in equilibrium

Now Total Profit of the Monopolist = TR (Total Revenue ) - Total Cost

= PxQ - (450+10Q + 0.0625Q2 )

= 40x80 -(450 +10x80 + 0.0625x80x80)

= 3200 - 1650

= 1550 pesos

Answer (b)

Pw = 15 pesos when Local Price = 40 pesos

At Pw = 15 pesos,the demand of consumers = 180 pounds(derived from the demand function)

The local firm will supply only 80 pounds. There will be import of 100 pounds.

In the long run, the domestic firm would reduce the cost of production in order to survive.

Answer (c)

If a tariff of 10 pesos is imposed ,the domestic price = 15+10 = 25

For this Price, the demand = 140 pounds

Of this amount, the local firms would supply 80 pounds; there would be import of 60 pounds.

The revenue government would earn = 60x10 = 600 pesos.

The restricted trade is good for the producer as this would make restricted import and the local firms would get an opportunity to reduce their cost.

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