1.In an attempt to curb the problem of unemployment and win the forthcoming elections the government of the republic of zambia has decided to hire unemployed workers who had previously been receiving unemployment benefits as government employees and will now pay them to do nothing.

I. What will be the likely impact on zambia's natoinal income and GDP?
II. To what extent does the level of national income influence the level of personal income?
2. What are the types and causes of inflation?
3. Derive the IS and LM curves graphically and mathematically showing clearly solving their respective slopes.

I. The likely impact on Zambia's national income and GDP resulting from the government hiring unemployed workers and paying them to do nothing would depend on several factors.

National income refers to the total value of goods and services produced by a country's residents over a specific time period, usually a year. GDP (Gross Domestic Product) is a measure of the total value of goods and services produced within a country's borders.

If the government hires unemployed workers and pays them to do nothing, it could potentially increase the government's expenditure. This increased spending could indirectly boost the national income and GDP. However, it is essential to bear in mind that the impact will depend on the overall economic situation, such as the size of the government's expenditure relative to the country's GDP, the efficiency of the payment scheme, and other macroeconomic factors.

II. The level of national income can have a significant influence on the level of personal income. When the national income of a country rises, it creates business and job opportunities, leading to increased employment and income generation. As people earn more from these opportunities, it leads to an increase in personal income.

However, the relationship between national income and personal income is not linear. Various factors such as income distribution, taxation policies, and government spending affect how the increase in national income translates into personal income. For example, if income distribution is unequal, a rise in national income may not result in an equivalent increase in personal income for everyone in society.

--------------------------------------------------------------------------------------------------------------------------

Inflation is a sustained increase in the general price level of goods and services in an economy over time. It erodes the purchasing power of money and affects the overall economy.

There are different types and causes of inflation:

1. Demand-Pull Inflation: This occurs when the demand for goods and services in an economy exceeds its supply. When demand increases, businesses may raise prices to maximize their profits, leading to an upward pressure on the general price level.

2. Cost-Push Inflation: This type of inflation occurs when there is an increase in the production costs for businesses. Factors such as rising wages, increased raw material prices, or higher taxes can lead to a rise in prices as businesses pass on these additional costs to consumers.

3. Built-In Inflation: Also known as "inflationary expectations," this type of inflation occurs when workers and businesses expect prices to rise in the future. These expectations can influence wage contracts and pricing decisions, leading to a self-reinforcing cycle of inflation.

4. Imported Inflation: When the price of imported goods or raw materials increases, it can lead to inflationary pressures within an economy. Changes in exchange rates, trade policies, or global commodity prices are some factors that can contribute to imported inflation.

It is important to note that inflation is influenced by a combination of these factors, and the specific causes can vary across different countries and economic conditions.

--------------------------------------------------------------------------------------------------------------------------

To derive the IS (Investment-Saving) and LM (Liquidity Preference-Money Supply) curves graphically and mathematically, we need to understand the underlying economic models.

The IS-LM model is a framework of analysis used in macroeconomics to examine the relationship between interest rates, real income (output), and the demand for goods and services. It is based on the assumption that the goods market and the money market are in equilibrium.

Graphically:
1. The IS curve represents combinations of interest rates and output levels where the goods market is in equilibrium, i.e., total desired investment equals total desired saving.
2. The LM curve represents combinations of interest rates and output levels where the money market is in equilibrium, i.e., the demand for money equals money supply.

Mathematically:
1. The IS curve can be derived by setting total desired investment equal to total desired saving, where the investment function depends on the interest rate, and the saving function depends on income.
2. The LM curve can be derived by equating the money demand function (based on the interest rate and income) to the money supply.

The slopes of the IS and LM curves can be determined by taking the derivatives of their respective equations. The slope of the IS curve represents the sensitivity of investment and saving to changes in interest rates, while the slope of the LM curve represents the sensitivity of money demand to changes in income or interest rates.

The specific mathematical derivation of the IS and LM curves depends on the model's assumptions and equations used, which may vary. It is recommended to refer to macroeconomic textbooks or academic resources for detailed mathematical derivations applicable to a specific model.