Question

A perfectly competitive industry faces domestic demand \(q_{d} 5100-p\) and has the industry supply curve \(q_{s} 5401 p\). (a) If the world price is \(£ 50\), what is the value of net exports? (b) If the world price is \(£ 20\), what is the value of net exports? (c) In the absence of trade, what is the equilibrium domestic price? (d) At a world price of \(£ 20\), suppose the government levies a tariff of \(£ 5\) per unit. Calculate the value of tariff revenue and the total value of the two deadweight loss triangles.

Short answer

(a) Net exports: 265,000 units. (b) Net exports: 102,940 units. (c) Equilibrium price: £0.943. (d) Tariff revenue: £649,750, deadweight loss: 324,875 units.

Step-by-step solution

Calculate Quantity Demanded and Supplied at World Price £50

First, substitute the world price of £50 into the demand and supply equations.For demand: \[ q_d = 5100 - p = 5100 - 50 = 5050 \] For supply: \[ q_s = 5401 \times p = 5401 \times 50 = 270050 \]

Determine Net Exports at World Price £50

Net exports are calculated as the difference between the quantity supplied and the quantity demanded. \[ ext{Net Exports} = q_s - q_d = 270050 - 5050 = 265000 \]

Calculate Quantity Demanded and Supplied at World Price £20

Substitute the world price of £20 into the demand and supply equations. For demand: \[ q_d = 5100 - p = 5100 - 20 = 5080 \] For supply: \[ q_s = 5401 \times p = 5401 \times 20 = 108020 \]

Determine Net Exports at World Price £20

Calculate net exports using the quantities obtained: \[ ext{Net Exports} = q_s - q_d = 108020 - 5080 = 102940 \]

Find Equilibrium Domestic Price without Trade

Set the quantity demanded equal to the quantity supplied to find the equilibrium price. \[ 5100 - p = 5401 \times p \] \[ 5100 = 5401p + p \] \[ 5100 = 5402p \] \[ p = \frac{5100}{5402} \approx 0.943 \] Thus, the equilibrium domestic price is approximately £0.943.

Calculate Tariff Revenue at World Price £20 with £5 Tariff

The new price with the tariff is £20 + £5 = £25.Recalculate the quantity supplied and demanded with this tariff:For demand:\[ q_d = 5100 - 25 = 5075 \]For supply:\[ q_s = 5401 \times 25 = 135025 \]Net imports now (since imports occur if demand exceeds supply):\[ ext{Net Imports} = q_d - q_s = 5075 - 135025 = -129950 \] (indicating exports)Tariff revenue is calculated as:\[ ext{Tariff Revenue} = 5 \times 129950 = 649750 \]

Calculate Deadweight Loss at Tariffed Price

Deadweight loss occurs because of reduced imports. Using approximate areas that correspond to reduced consumer and producer surplus:Using the change in quantity in the squares for simplicity:Loss per unit due to reduced quantity: price increase × quantity lost on demand\[ ext{DWL} \approx \frac{1}{2} \times 5 \times (q_d - q_s)\]Plugging in values:\[ ext{DWL} \approx \frac{1}{2} \times 5 \times (5075 - 135025) = \frac{1}{2} \times 5 \times (-129950) = 324875 \]

Conclude Answers from Above Steps

a) At world price £50, net exports are 265,000 units. b) At world price £20, net exports are 102,940 units. c) The equilibrium domestic price is approximately £0.943. d) With a tariff, revenue is £649,750 and the deadweight loss is approximately 324,875 units.

Key concepts

Equilibrium Price

In a perfectly competitive market, the equilibrium price is achieved when the quantity demanded by consumers equals the quantity supplied by producers. This means there is neither excess supply nor excess demand. To find the equilibrium price in our example, we set the demand and supply equations equal to one another. The demand equation is given as \( q_d = 5100 - p \) and the supply equation is \( q_s = 5401p \). By setting these equal, we solve for \( p \), which represents the equilibrium price.

Setting \( 5100 - p = 5401p \), we add \( p \) to each side to get \( 5100 = 5402p \). Solving for \( p \), we divide both sides by 5402, resulting in \( p \approx 0.943 \). This means, in the absence of trade, the equilibrium domestic price is approximately £0.943. At this price, the market clears with the quantity demanded equaling the quantity supplied.

Tariff

A tariff is a tax imposed on imported goods or services. In the context of international trade, tariffs can be used by governments to protect domestic industries from foreign competition by making imported goods more expensive.

In this exercise, a £5 tariff is introduced at a world price of £20. The tariff effectively raises the world price to £25 for domestic consumers. To understand the effects, recalculation of the demand and supply at the new price level is important. For demand: \( q_d = 5100 - 25 = 5075 \). For supply: \( q_s = 5401 \times 25 = 135025 \).

Net imports become negative, indicating exports, as \( 5075 \) units are demanded domestically and \( 135025 \) units are supplied. The tariff revenue, a source of earnings for the government, is then calculated by multiplying the tariff rate with the number of imported units (exported units in this outflow case), resulting in \( 649750 \) in revenue.

Net Exports

Net exports represent the difference between a country's total exports and total imports. It is a key component of a nation’s GDP and an indicator of its trade balance with the rest of the world.

To calculate net exports in this exercise, we subtract the quantity demanded from the quantity supplied. At a world price of £50, for instance, demand is 5050 units and supply is 270050 units, leading to a net export of 265000 units \((270050 - 5050)\).

With a world price of £20, the adjusted figures for demand and supply yield a net export of 102940 units \((108020 - 5080)\). The concept of net exports helps understand whether a nation is in a trade surplus or deficit. In this instance, the large positive number suggests significant exports exceeding imports.

Deadweight Loss

Deadweight loss is a term used to denote inefficiency in an economic system, often as a result of taxes, subsidies, tariffs, or price controls. It represents the loss of welfare or resources that neither benefits producers nor consumers.

When a tariff of £5 is placed on units at a world price of £20, deadweight loss arises because the tariff leads to a higher consumer price and lower consumption levels. The notion of a deadweight loss is graphically represented as the area between demand and supply curves beyond equilibrium.

Calculating deadweight loss involves finding the area of the triangle formed by changes in price and quantity after the tariff. Using the formula \( \frac{1}{2} \times \text{price change} \times \text{quantity change} \), the deadweight loss here comes to approximately 324875 units. This value indicates inefficiencies introduced by the tariff, reflecting reduced trade and consumer satisfaction.