Step 1: Understand what transfer payments are.
Transfer payments are payments made by the government to individuals without any exchange of goods or services. Examples include unemployment benefits, pensions, and subsidies. These payments do not directly relate to the production of goods or services.
Step 2: Interpret the economic classification.
Transfer payments are termed "negative taxes" because they are payments from the government to individuals, essentially reversing the usual flow of taxes. Rather than collecting revenue, the government is disbursing funds.
Consider the following system of linear equations:
x + 2y + 3z = 0
2x + py = 0
3x + 2y + pz = 0
The value(s) of \( p \) for which the system of equations have infinitely many solutions is/are:
The following is a system of linear equations
x - 2y + z = 34 (1)
2x + y + z = 102 (2)
x + y - 3z = 17 (3)
The value of \( x + y + z \) is ________. (rounded off to two decimal places)
Two players \( A \) and \( B \) are playing a game. Player \( A \) has two available actions \( a_1 \) and \( a_2 \). Player \( B \) has two available actions \( b_1 \) and \( b_2 \). The payoff matrix arising from their actions is presented below:
Let \( p \) be the probability that player \( A \) plays action \( a_1 \) in the mixed strategy Nash equilibrium of the game.
Then the value of p is (round off to one decimal place).
The installation cost (IC) of a solar power plant is INR 89,000. The plant shall be operational for 5 years. The recurring costs for maintenance of the solar plant per year is INR 5,000 but the benefits it creates including reduction in emissions amounts to INR 25,000 per year. These are the only costs and benefits associated with this project. The social discount rate (r) considered is 4% per year. The yearwise information is presented below.
A coin has a true probability \( \mu \) of turning up Heads. This coin is tossed 100 times and shows up Heads 60 times. The following hypothesis is tested:
\[ H_0: \mu = 0.5 \quad ({Null Hypothesis}), \quad H_1: \mu>0.5 \quad ({Alternative Hypothesis}) \]
Using the Central Limit Theorem, the \( p \)-value of the above test is ________ (round off to three decimal places).
Hint: If Z is a random variable that follows a standard normal distribution, then P (Z ≤ 2) = 0.977.