Consider the two scenarios for a small open economy based on the Mundell-Fleming IS-LM model with floating exchange rate and perfect capital mobility.
Where \( Y \) is aggregate income, \( C \) is aggregate consumption, \( I \) is investment, \( r^* \) is the world interest rate, \( G \) is government expenditure, \( T \) is taxes, \( NX \) is net exports, \( e \) is exchange rate, \( M \) is money supply, and \( P^* \) is general price level. Given the relationships:
\( I \) has a negative relationship with \( r^* \),
\( NX \) depends negatively on both \( e \) and \( Y \),
\( P^* \) is fixed.
Which of the following statements is/are CORRECT?
Consider the following Harrod-Domar growth equation: \[ \frac{s}{\theta} = g + \delta \] where \( s \) is the saving rate, \( \theta \) is the capital-output ratio, \( g \) is the overall growth rate, and \( \delta \) is the capital depreciation rate. If \( \delta = 0 \) and \( s = 20% \), then to achieve \( g = 10% \), the capital-output ratio will be ________ (in integer).
Let \( Y \) be income, \( r \) be the interest rate, \( G \) be government expenditure, and \( M_s \) be money supply. Consider the following closed economy IS-LM equations with a fixed general price level (\( \bar{P} \)):
IS equation: \[ Y = 490 + 0.6Y - 4r + G \] LM equation: \[ \frac{M_s}{\bar{P}} = 20 + 0.25Y - 10r \] If \( G = 330 \) and \( \frac{M_s}{\bar{P}} = 500 \), then the equilibrium \( Y \) is ________ (round off to one decimal place).
A simple Keynesian open economy model is given by: \[ S + T + M = G + I + X \] where \( S \), \( I \), \( G \), \( T \), \( X \), and \( M \) stand for saving, investment, government expenditure, taxes, exports, and imports, respectively. If the country has a trade surplus, which strategy/strategies among the following will reduce the trade imbalance?
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.