Suppose the federal government increases spending without also increasing taxes. In the short run, how will this action affect real GDP and the price level in a closed economy? How will the effects of this action differ in an open economy?

Understanding the impact of government spending on a closed economy is crucial for macroeconomic analysis. In this scenario, there are no international trades such as exports and imports to consider. When the government decides to increase spending without a rise in taxes, it directly injects funds into the economy, leading to increased aggregate demand.

How does this happen? The formula for calculating a country's GDP in a closed economy is given by: \( GDP = C + I + G \), where \(C\) stands for consumer spending, \(I\) denotes investment, and \(G\) represents government spending. An uptick in \(G\) drives the aggregate demand upward, prompting businesses to bolster their production to meet the higher demand, thus, boosting the real GDP. The downside is that this surge in spending also presses on the economy's capacity, potentially causing prices to rise – a phenomenon termed demand-pull inflation.

Contrastingly, in an open economy where international trade plays a role, the effects of increased government spending unfold differently. Initially, the spike in government expenditure fuels aggregate demand, as it does in a closed economy. This is where factors unique to an open economy come into play: interest rates usually rise due to heightened demand for money and loanable funds.

The increase in interest rates begins to cause ripples across the global financial markets. Attractive interest rates pull in foreign capital, leading to the appreciation of the local currency. A stronger currency makes exports costlier and imports relatively cheaper, tipping the balance of trade and potentially decreasing net exports. This, in turn, could partially offset the initial boost in aggregate demand caused by government spending. Remarkably, the overall influence on real GDP might not be as stark as in a closed economy due to the interplay of international markets.

Aggregate demand is the total amount of goods and services demanded across all levels of the economy at a given overall price level and in a given time period. It is represented by the equation \( AD = C + I + G + (X – M) \), where \(X – M\) stands for net exports. A hike in government spending, \(G\), contributes to a rise in AD.

This increment can lead to an increase in production and employment to satisfy the heightened demand. However, if the economy is already near or at full capacity, the increased demand might not result in a significant surge in output but rather an escalation in the general price level, laying the groundwork for inflation.

Demand-pull inflation emerges when the aggregate demand in an economy outweighs the aggregate supply, leading to an upsurge in the general price level. It's akin to having 'too much money chasing too few goods'.

When the government enhances its spending, it can intensify demand to such an extent that prices begin to climb. The higher prices often stem from the increased competition for goods, as more individuals and the government itself vie for the same products. It is a core concept in understanding inflation, and it underpins the rationale behind certain monetary policies aimed at controlling inflation by managing the levels of demand in the economy.

Interest rates are a cornerstone of economic policy and have widespread implications across the economy. They are the cost of borrowing money, essentially the price tag on loanable funds.

With an increment in government spending without a corresponding tax increase, the government may need to borrow money, particularly if the spending leads to a budget deficit. Borrowing money increases the demand for loanable funds, which typically pushes the interest rates up. For individual consumers and businesses, higher interest rates might mean less borrowing for consumption and investment, which could temper the initial increase in aggregate demand that comes from higher government spending.

Currency appreciation refers to the increase in the value of one currency relative to another in the foreign exchange markets. When a government ramps up its spending, and as interest rates ascend in response, investors often view the currency as more attractive, leading to increased demand for the currency.

Appreciation has mixed effects: it can help to contain inflation by making imports less expensive, which can be advantageous for consumers. On the flip side, it can present challenges for domestic exporters, as their goods become less competitive abroad. The strength of a currency is, therefore, a double-edged sword in global trade and economic dynamics.

Net exports describe the difference between what a country sells abroad (exports) and what it buys from abroad (imports). It's a critical component of a nation's GDP, particularly in an open economy.

In the context of increased government spending, if it results in a stronger domestic currency due to higher interest rates, the price of exports will rise, potentially diminishing foreign demand. Conversely, imports become cheaper, possibly leading to an increased import volume. The interplay between higher exports' prices and cheaper imports can result in negative net exports, which may dampen the positive impact government spending has on aggregate demand and, by extension, on real GDP.