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).
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).
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Solution and Explanation
- From equation (1): \[ Y = 2050 - 10r \] Substitute this into equation (2): \[ 1920 = (2050 - 10r) - 40r \] Simplifying: \[ 1920 = 2050 - 50r \] Solving for \( r \): \[ 50r = 2050 - 1920 \quad \Rightarrow \quad 50r = 130 \quad \Rightarrow \quad r = \frac{130}{50} = 2.6 \] Step 3: Substituting \( r = 2.6 \) back into equation (1) to find \( Y \): \[ Y = 2050 - 10(2.6) = 2050 - 26 = 2024 \] Thus, the equilibrium income \( Y \) is 2023.5 after rounding to one decimal place.
Top Questions on Economics
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).
- Consider a two-person exchange economy where two goods, \( x \) and \( y \), are available in limited quantities of 50 and 100, respectively. The preferences of the two persons, Anil and Binod, are given by the utility functions: \[ U_{{Anil}}(x_{{Anil}}, y_{{Anil}}) = x_{{Anil}}^{0.4} y_{{Anil}}^{0.6} \] \[ U_{{Binod}}(x_{{Binod}}, y_{{Binod}}) = x_{{Binod}}^{0.6} y_{{Binod}}^{0.4} \] If they decide to share good \( y \) equally among themselves, the amount of good \( x \) Anil receives is ______________ (in integer).
- Which of the following statements is/are NOT CORRECT?
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?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?
Questions Asked in GATE XH-C1 exam
- If the Marginal Propensity to Consume (MPC) of an economy is 0.75, then the value of the expenditure multiplier will be:
- GATE XH-C1 - 2025
- Logical Reasoning
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).- GATE XH-C1 - 2025
- Logical Reasoning
- Let \( f(x, y) = -x^2 - y^2 + 2x + 4y + 5 \). Let \( (x^*, y^*) \) denote the solution to the following optimization problem: \[ {Maximize } f(x, y) \] subject to \[ x \geq 0, y \geq 0, 2x + y \leq 6 \] Then the value of \( f(x^*, y^*) \) is ________________ (in integer).
- GATE XH-C1 - 2025
- Logical Reasoning
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.
- GATE XH-C1 - 2025
- Logical Reasoning
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.- GATE XH-C1 - 2025
- Probability