This question asks two things at once: how the value of a floating currency is set, and what happens when that value falls. The answer first builds the foreign exchange market, then traces a depreciation through net exports, growth, employment, the current account and the price level, before weighing the net effect.
How a floating exchange rate is determined
A floating exchange rate is the price of one currency in terms of another, set with no central bank target by the interaction of demand for the currency and supply of the currency in the foreign exchange market. On a diagram the vertical axis is the exchange rate (say US dollars per pound) and the horizontal axis is the quantity of pounds traded. The demand curve for pounds slopes down: a weaker pound makes British exports cheaper for foreigners, so they buy more pounds to pay for them. The supply of pounds slopes up: a stronger pound makes foreign goods cheaper for British buyers, so more pounds are offered to buy foreign currency. The equilibrium rate sits where the two curves cross, the rate at which the quantity of pounds demanded equals the quantity supplied.
Anything that changes that demand or supply moves the rate. Demand for a currency rises with foreign demand for the country's exports, inward foreign direct and portfolio investment, remittances sent home, and speculation that the currency will rise. Supply of the currency rises with domestic demand for imports and outward investment. Three relative variables are decisive. Relative interest rates: if a country's central bank raises rates above those abroad, hot money flows in chasing the higher return, demand for the currency rises and it appreciates. Relative inflation rates: higher domestic inflation makes exports less competitive, demand for the currency falls and it tends to depreciate. Relative growth rates: faster growth sucks in imports, raising the supply of the currency on the market. A depreciation is simply a fall in this market-determined rate, for instance a fall in demand for exports or a loss of investor confidence shifting demand for the currency to the left.
The likely effects of a depreciation
Net exports, aggregate demand, growth and employment
A depreciation lowers the foreign-currency price of exports and raises the domestic-currency price of imports. Exports become more competitive abroad while imports become dearer at home, so foreigners buy more of the country's goods and domestic buyers switch towards home-produced substitutes. Net exports (X minus M) tend to rise, and since net exports are a component of aggregate demand, the AD curve shifts to the right. On an AD to AS diagram with a vertical long-run aggregate supply at potential output, a rightward shift of AD raises real output and the price level. If the economy has spare capacity, most of the effect is a rise in real GDP and a fall in cyclical unemployment, because firms expand output and hire to meet the extra export and import-substituting demand. The size of this gain depends on how large the trade sector is and how much slack there is: near full employment the same AD shift mostly raises prices rather than output.
The Marshall-Lerner condition and the J-curve
The claim that net exports rise is not automatic. Whether the current account improves turns on the Marshall-Lerner condition: a depreciation improves the current account only if the sum of the price elasticities of demand for exports and for imports is greater than one. The logic is a trade-off between volume and value. A cheaper currency raises the volume of exports and cuts the volume of imports, which helps the balance, but it also raises the price paid for each unit of imports, which hurts it. If demand is elastic enough, the volume gains dominate and the balance improves; if demand is too inelastic, the dearer import bill dominates and the balance worsens. Many imports, such as essential fuel, food or capital equipment, are price-inelastic in the short run, which is why the condition can fail initially.
This feeds straight into the J-curve. In the short run, trade volumes are slow to respond because contracts are already signed and buyers take time to switch suppliers, so elasticities are low and the Marshall-Lerner condition often fails. The country pays more for the same volume of imports while export volumes have not yet grown, so the current account first worsens, tracing the downward dip of the J. As months pass, buyers respond to the new relative prices, export and import volumes adjust, elasticities rise above the critical value, and the balance improves beyond its starting point, tracing the upward arm of the J. The net effect on the current account therefore depends heavily on the time horizon.
Imported inflation, the central trade-off
The same dearer imports that threaten the current account also push up the price level. A depreciation raises the domestic price of imported finished goods and, more seriously, of imported inputs and energy. Higher input costs raise firms' costs of production, shifting short-run aggregate supply to the left and adding cost-push inflation on top of the demand-pull pressure from rising AD. This is imported inflation, and it is the key trade-off against the gain in net exports. For an economy that imports most of its food and fuel, the inflation cost can be severe, eroding real incomes and potentially forcing the central bank to raise interest rates, which would choke off the very growth the depreciation was meant to deliver.
A developed real-world example
The fall in sterling after the United Kingdom's 2016 referendum shows the pattern clearly. The pound dropped by around 10 per cent against the US dollar in the days after the vote and stayed well below its previous level, as investors marked down expected UK growth and investment, shifting demand for the currency to the left. The cheaper pound did make UK exports and tourism more competitive, supporting exporters and the manufacturing sector. But the much-anticipated improvement in the current account was muted and slow, exactly as the J-curve predicts, because UK demand for imported components and consumer goods proved fairly inelastic. The clearer effect was imported inflation: dearer imported food, fuel and inputs pushed UK consumer price inflation above 3 per cent in 2017, squeezing real wages while the trade balance was slow to respond. The episode shows that a depreciation can deliver competitiveness and a higher price level at the same time, with the current account improving only later if at all.
Judgement
A depreciation is neither a simple boost nor a simple cost; the net effect depends on conditions that must be weighed rather than listed. Over time horizon, the J-curve means the current account usually worsens before it improves, so a depreciation that looks harmful at six months can look helpful at two years. On elasticities, the gain in net exports only materialises if the Marshall-Lerner condition holds, which it often does not for an economy reliant on inelastic imported essentials. On capacity, the growth and employment benefit is large when there is spare capacity and small near full employment, where the AD shift mostly raises prices. The most reliable short-run effect is imported inflation, which is why a depreciation tends to help an economy with spare capacity, elastic traded goods and a small import-content of consumption, but can hurt one running near capacity and dependent on imported food and energy. On balance a moderate depreciation supports growth and employment in the medium term for an economy with slack and reasonably elastic trade, but the judgement must respect the timing of the J-curve and the standing risk that imported inflation offsets the competitiveness gain.