Question

Suppose there are two types of households in the economy: workers and retirees. Workers pay social security tax at rate τb on their labor incomes, revenues from which are distributed to retired people as retirement income. For simplicity, this is the only source income of retired people who are living hand to mouth (that is, they don’t save). The government decided to improve the lives of retired people by increasing the social security tax at time t∗ permanently. Write first-order condition with respect to labor. Derive IS and LM equations under this tax. What happens to IS and LM curves and aggregate demand in short run? What happens to long-run aggregate supply curve? What happens to unemployment in short run? Who will benefit from this policy in short run? Answer these questions under fixed and floating exchange regimes separately

Answer 1

The first order condition defines that an employment level is selected by the employer based on the marginal productivity of labour equalled to the wage rate.This equation reveals the labour demand function. L=L*(w,p)
The IS-LM stands for IS- investment savings, LM- Liquidity preferences money supply.This model states how economic goods market interact with the market for loanable funds or money market.The IS-LM graph establishes the relationship between output,GDP and also interest rates.Under Fixed Exchange Regime-when exchange rates are fixed government purchase more of government currencies and sell more foreign currency.This leads to dropping of the money supply.Under Floating Exchange Regime-when exchange rates are flexible especially in an open economy,the change in interest rates drive the mobility of capital and spending of the government also increases.
Aggregate supply curve in a long run is vertical, parallel to Y axis.It states that Aggregate Demand temporarily change the Total Outputs of the economy, whereas in a long run, capital and labour along with technology has an effect on Aggregate Supply because in the long run there is optimum use of resources in an economy.
Wages are sticky in the downward direction in a short run.The more supply of labour increase the more number of people in search for jobs also increases,but the availability of job is the same.This results in rise of unemployment by increase in the supply of labour in the short run.
Retired persons have the benefit of the policy in the short run.