# Consider a coin toss experiment and the following assets. Asset A gives £200 if the first is heads, £50 for tails. Asset B gives £200 if the second is heads and £50 for tails. Asset C is half of A plus half of B. Assets A and B are independent. Show that the expected value of each asset is the same and C reduces risk. Explain why C reduces risk?

**Math/Physic/Economic/Statistic Problems**

1. a) Calculate the equilibrium GDP of a Keynesian demand driven closed economy with autonomous investment and government expenditure. Derive the Balanced Budget Multiplier.

b) Now relax the assumption on autonomous investment. Introduce the investment function , where is the real interest rate. Derive the IS curve. If the LM curve in this economy is then derive the equilibrium output. Derive the multiplier effect and explain. Would there be a crowding out?

2. Consider a coin toss experiment and the following assets. Asset A gives £200 if the first is heads, £50 for tails. Asset B gives £200 if the second is heads and £50 for tails. Asset C is half of A plus half of B. Assets A and B are independent. Show that the expected value of each asset is the same and C reduces risk. Explain why C reduces risk?

The post Consider a coin toss experiment and the following assets. Asset A gives £200 if the first is heads, £50 for tails. Asset B gives £200 if the second is heads and £50 for tails. Asset C is half of A plus half of B. Assets A and B are independent. Show that the expected value of each asset is the same and C reduces risk. Explain why C reduces risk? appeared first on .