GATE 2025 Economics XH – C1 Question Paper (Available)- Download Solution PDF with Answer Key

Here are two analogous groups, Group-I and Group-II, that list words in their decreasing order of intensity. Identify the missing word in Group-II.

Abuse  → Insult  → Ridicule
________  → Praise  → Appreciate

• (A) Extol
• (B) Prize
• (C) Appropriate
• (D) Espouse

Had I learnt acting as a child, I __________ a famous film star.

Select the most appropriate option to complete the above sentence.

• (A) will be
• (B) can be
• (C) am going to be
• (D) could have been

The 12 musical notes are given as \( C, C^\#, D, D^\#, E, F, F^\#, G, G^\#, A, A^\#, B \). Frequency of each note is \( \sqrt[12]{2} \) times the frequency of the previous note. If the frequency of the note C is 130.8 Hz, then the ratio of frequencies of notes F\# and C is:

• (A) \( \sqrt{6} \)
• (B) \( \sqrt{2} \)
• (C) \( 4\sqrt{2} \)
• (D) \( 2 \)

The following figures show three curves generated using an iterative algorithm. The total length of the curve generated after 'Iteration n' is:

• (A) \( \left( \frac{5}{3} \right)^{\frac{n}{2}} \)
• (B) \( \left( \frac{5}{3} \right)^n \)
• (C) \( 2n \)
• (D) \( \left( \frac{5}{3} \right)^n(2n - 1) \)

Which one of the following plots represents \( f(x) = -\frac{|x|}{x} \), where \( x \) is a non-zero real number?

Note: The figures shown are representative.

Identify the option that has the most appropriate sequence such that a coherent paragraph is formed:

P: Over time, such adaptations lead to significant evolutionary changes with the potential to shape the development of new species.

Q: In natural world, organisms constantly adapt to their environments in response to challenges and opportunities.

R: This process of adaptation is driven by the principle of natural selection, where favorable traits increase an organism’s chances of survival and reproduction.

S: As environments change, organisms that can adapt their behavior, structure, and physiology to such changes are more likely to survive.

• (A) P → Q → R → S
• (B) Q → S → R → P
• (C) R → S → Q → P
• (D) S → P → R → Q

A stick of length one meter is broken at two locations at distances of \( b_1 \) and \( b_2 \) from the origin (0), as shown in the figure. Note that \( 0 < b_1 < b_2 < 1 \). Which one of the following is NOT a necessary condition for forming a triangle using the three pieces?

Note: All lengths are in meter. The figure shown is representative.

• (A) \( b_1 < 0.5 \)
• (B) \( b_2 > 0.5 \)
• (C) \( b_2 < b_1 + 0.5 \)
• (D) \( b_1 + b_2 < 1 \)

Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure indicates their order of position at the start of the game. They play the game by moving forward in a circle in the clockwise direction.

After the 1^st round, 4^th student behind P leaves the game. After 2^nd round, 5^th student behind Q leaves the game. After 3^rd round, 3^rd student behind V leaves the game. After 4^th round, 4^th student behind U leaves the game. Who all are left in the game after the 4^th round?

• (A) P; T; Q; S
• (B) V; P; T; Q
• (C) W; R; Q; V
• (D) Q; T; V; W

The table lists the top 5 nations according to the number of gold medals won in a tournament; also included are the number of silver and the bronze medals won by them. Based only on the data provided in the table, which one of the following statements is INCORRECT?

• (A) France will occupy the third place if the list were made on the basis of the total number of medals won.
• (B) The order of the top two nations will not change even if the list is made on the basis of the total number of medals won.
• (C) USA and Canada together have less than 50% of the medals awarded to the nations in the above table.
• (D) Canada has won twice as many total medals as Japan.

An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee. The overhead is 20% of the consulting fee, if the fee is up to Rs. 5,00,000. For higher fees, the overhead is Rs. 1,00,000 plus 10% of the amount by which the fee exceeds Rs. 5,00,000. The government charges a Goods and Services Tax of 18% on the total amount (the consulting fee plus the overhead). An employee of the organization charges this entire amount, i.e., the consulting fee, overhead, and tax, to the client. If the client cannot pay more than Rs. 10,00,000, what is the maximum consulting fee that the employee can charge?

• (A) Rs. 7,01,438
• (B) Rs. 7,24,961
• (C) Rs. 7,51,232
• (D) Rs. 7,75,784

Which one of the following numbers is odd one out?

31541          42651          53791          64871          75981

• (A) 31541
• (B) 42651
• (C) 53791
• (D) 75981

Ankit, Arun, and Ankur have one apple each. Ankur also has one banana. Alam has one mango and one kiwi. Ankit has just bought one pineapple. Who has the least number of fruit(s)?

• (A) Ankit
• (B) Arun
• (C) Ankur
• (D) Alam

If each vowel in the word RESIDE is changed to its previous letter in the English alphabet and each consonant is changed to the next letter in the English alphabet, which one of the following options will be the third from the right?

• (A) T
• (B) D
• (C) S
• (D) H

Vipul, Ahmad, Santosh, and David are playing Carrom. Vipul and Ahmad are partners sitting opposite to each other. David faces towards South. If Vipul faces towards West, then who faces towards the North?

• (A) Alam
• (B) Santosh
• (C) David
• (D) Vipul

Consider the following sentence: "What the country needs ___\ accordingly."

First and last parts of the sentence are given. P, Q, R, and S are the remaining parts of the sentence, not necessarily in that order.

P: and change tactics

Q: who would encourage players

R: are coaches and officials

S: to read the game as it progresses

Which one of the following options is correct that gives the most appropriate order and meaning to the sentence?

• (A) QSPR
• (B) RQSP
• (C) RQPS
• (D) SPRQ

A car started from city P at 9:40 AM. The time taken for the car to reach city Q is 4 hours and 50 minutes. The time of arrival of the car at city Q is:

• (A) 15:10 Hours
• (B) 14:20 Hours
• (C) 14:30 Hours
• (D) 14:10 Hours

P is three years younger than R but one year older than S. S is one year older than Q but 4 years younger than R. R is 15 years old. The age of Q is ____ years.

In a certain code language, ATTITUDE is written as TAUJUEDU and CHILDREN is written as HCJMENER. How is LANGUAGE written in that code language?

• (A) ALOHVEGA
• (B) ALHOVAGA
• (C) LAVOHEGA
• (D) ALHOVGEA

The table shows the data of 450 candidates who appeared in the examination of three subjects – Social Science, Mathematics, and Science.
How many candidates have passed in at least one subject?

• (A) 48
• (B) 162
• (C) 390
• (D) 425

If \( \times \) means \( + \), \( + \) means \( \div \), \( - \) means \( \times \), and \( \div \) means \( - \), then evaluate:

8 \( \times \) 7 \( - \) 8 \( + \) 40 \( \div \) 2.

• (A) \( 3 \frac{8}{5} \)
• (B) \( 7 \frac{2}{5} \)
• (C) \( 2 \frac{7}{5} \)
• (D) \( 8 \frac{3}{5} \)

Given a series \( 5, 8, 11, 14, \dots \), if the \( n \)-th term of the given series is 320, then find \( n \) (where \( n \geq 1 \)):

• (A) 104
• (B) 105
• (C) 106
• (D) 107

Suppose, your last year taxable income was Rs. 22000. Due to hike in salary, your taxable income this year is Rs. 34200. The details for tax calculation are given in the table below.

• (A) 1970
• (B) 1060
• (C) 910
• (D) 420

Anand, Hari, and Chris are engaged in one of the three types of occupations – clerk, teacher, and plumber, not necessarily in that order. Each person is assigned only one type of occupation. No two or more persons can be assigned the same type of occupation. Clerk is Chris’s cousin. Hari lives next door to the plumber. Anand, who knows more facts than the teacher, has to drive more than 1 hour to reach Hari’s home. Identify each of the person’s correct type of occupation, and accordingly, which one of the following options is correct?

• (A) Anand is teacher and Chris is clerk.
• (B) Hari is clerk and Anand is plumber.
• (C) Chris is teacher and Hari is clerk.
• (D) Anand is clerk and Chris is plumber.

Many countries are facing water shortage crises in the past few years. A report of the United Nations has named India among the worst countries for poor quality of water. The report ranks 122 countries according to the quality of their water as well as their commitment to improve the situation. Some countries in Europe are considered the worst because of the quality of its groundwater. Rain failed in some parts of India in the past. The vast areas of Rajasthan, Madhya Pradesh, and Andhra Pradesh were affected by severe drought. People without water turn desperate and violent. Consequently, the food godowns were attacked in some of the states. Based on the details given in the passage, which of the following option(s) is/ are correct statement(s)?

• (A) There is no proof that India is affected by poor quality of water.
• (B) A few European countries are suffering due to the occurrence of drought.
• (C) Lack of access to water can lead to social unrest.
• (D) Intense shortage of water is visible in some states of India.

In the following figure, four overlapping shapes (rectangle, triangle, circle, and hexagon) are given. The sum of the numbers which belong to only two overlapping shapes is ______.

Consider a square field ABCD. The diagonal AC is 50 meter. The cost of laying grass in the field is Rs. 5 per square-meter. The total cost for laying grass in the field ABCD is Rs. ________ (rounded off to two decimal places).

In the context of a perfectly competitive market, identify the statement that is NOT CORRECT.

• (A) Producing less than the competitive output lowers welfare.
• (B) Producing more than the competitive output lowers welfare.
• (C) The welfare is dependent on both price and the competitive output.
• (D) If a consumer values the last unit more than its marginal cost of production, producing an additional unit shall lower welfare.

The demand function is given as \( \log Q = \log A + 0.5 \log P \), where \( Q \) is quantity, \( P \) is the unit price of the good and \( A \) is a positive real number. The own price elasticity of demand is:

• (A) Perfectly elastic
• (B) Perfectly inelastic
• (C) Elastic
• (D) Inelastic

Which one of the following is part of the unconventional monetary policy?

• (A) Repo rate
• (B) Quantitative easing
• (C) Fractional banking
• (D) Reverse Repo rate

Which one of the following statements is NOT CORRECT in the context of Keynesian Absolute Income Hypothesis?

• (A) Average Propensity to Consume (APC) plus Average Propensity to Save (APS) is equal to one.
• (B) Marginal Propensity to Consume (MPC) is constant.
• (C) Average Propensity to Consume (APC) increases as income increases.
• (D) Marginal Propensity to Consume (MPC) plus Marginal Propensity to Save (MPS) is equal to one.

Let \( f(x, y, z) = x^2 y^3 z \). Then, what is the value of \[ x \frac{\partial f}{\partial x}(x, y, z) + y \frac{\partial f}{\partial y}(x, y, z) + z \frac{\partial f}{\partial z}(x, y, z)? \]

• (A) \( f(x, y, z) \)
• (B) \( 2f(x, y, z) \)
• (C) \( 3f(x, y, z) \)
• (D) \( 6f(x, y, z) \)

Let \( f(x) = -3x^2(1 - x) - 3x(1 - x)^2 - (1 - x)^3 \).

Then, \( \frac{df(x)}{dx} = \)

• (A) \( 3x^2 \)
• (B) \( 3(1 - x)^2 \)
• (C) \( 3x(1 - x) \)
• (D) \( x \)

In the context of environmental cost-benefit analysis, which of the following statements is/are NOT CORRECT?

• (A) The discount rates do not impact the fixed and variable costs of the project but does impact the perceived benefits in monetary terms.
• (B) The analysis does not incorporate people’s preferences for a policy.
• (C) The analysis is dependent on the choice of the discount rates.
• (D) The discount rates are not easily observable and choice is often subject to value judgements

Which of the following statements is/are CORRECT in the context of National Income Accounting?

• (A) Gross Domestic Product (GDP) is the sum of all factor payments.
• (B) Net Domestic Product (NDP) is equal to Gross Domestic Product (GDP) minus depreciation.
• (C) Gross National Product (GNP) is equal to Gross Domestic Product (GDP) plus net income from abroad.
• (D) Net National Product (NNP) is equal to Gross National Product (GNP) minus Gross Domestic Product (GDP).

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:

• (A) \( p = 1 \)
• (B) \( p = 2 \)
• (C) \( p = 6 \)
• (D) \( p = 12 \)

Which of the following statements is/are CORRECT?

• (A) The difference between Human Poverty Index and the Human Development Index is that the former measure focuses on deprivations.
• (B) The Human Development Index is insensitive to inequalities in the distribution of human development in the population.
• (C) Income-based poverty lines are sufficient to capture the well-being of a country’s citizens.
• (D) Multi-dimensional Poverty Index considers differences in intra-household distribution of resources.
• (B) The Human Development Index is insensitive to inequalities in the distribution of human development in the population.

Which of the following statements is/are the key feature(s) of India’s New Economic Reforms (1991)?

• (A) Liberalization of the economy
• (B) Privatization of public sector enterprises
• (C) Complete nationalization of all industries
• (D) Globalization and increased foreign direct investment

A Constant Elasticity of Substitution (CES) utility function is given as: \[ U_{CES}(z_1, z_2) = \frac{1}{\delta} \left( z_1^\delta + z_2^\delta \right) \]
where \( z_1 \) and \( z_2 \) are two goods, and \( \delta \leq 1, \delta \neq 0 \). A Quasi-linear (QL) utility function is given as: \[ U_{QL}(z_1, z_2) = 2z_1 + \log z_2 \]
where \( z_1 \) and \( z_2 \) are two goods. Which of the following statements is/are NOT CORRECT?

• (A) The CES utility function is homothetic but the QL utility function is nonhomothetic.
• (B) For \( \delta = 1 \), the CES utility function is not strictly convex.
• (C) The Marginal Rate of Substitution (MRS\( z_1, z_2 \)) for the CES utility function and the QL utility function are dependent on both \( z_1 \) and \( z_2 \).
• (D) If \( z_1 = z_2 \), the Marginal Rate of Substitution (MRS\( z_1, z_2 \)) is 2 for both the CES and the QL utility functions.
• Correct Answer:

Consider a lottery with three possible outcomes:





The maximum amount that a risk-neutral person would be willing to pay to play the above lottery is INR ____________.

For a closed economy with no government expenditure and taxes, the aggregate consumption function (\(C\)) is given by: \[ C = 100 + 0.75 \, Y_d \]
where \( Y_d \) is the disposable income. If the total investment is 80, the equilibrium output is _____________ (in integer).

If \( X \) is a continuous random variable whose probability density function is given by \[ f_X(x) = \begin{cases} \frac{1}{x^2}, & for 1 < x < \infty
0, & elsewhere \end{cases} \]
Then the median of \( X \) is __________ (in integer).

The inverse demand function for a monopolist is given by \( P = 100 - kQ \), where \( P \) is the unit price of the good, \( Q \) is the quantity and \( k \) is a constant. The cost function facing the monopolist is given as \( C(Q) = 50 + 2Q(1 + Q) \). If the profit maximizing output is 7, the maximum profit is __________ (in integer).

Consider a simple Keynesian closed economy model with the following information:

The Marginal Propensity to Consume (MPC) is 0.9 and the initial level of saving is INR 120. When income rises by INR 100, then the new level of saving will be INR _____________ (in integer).

If \( X \) is a continuous random variable whose probability density function is given by \[ f_X(x) = \begin{cases} cx^3 + 0.25, & for 0 \leq x \leq 1,\ c \in \mathbb{R}
0, & elsewhere \end{cases} \]
Then the value of \( c \) is __________ (in integer).

Consider a three-firms oligopoly market with a linear demand function given by \( P = 25 - Q \), where \( P \) is the unit price and \( Q \) is the total quantity supplied. The total quantity \( Q = q_1 + q_2 + q_3 \), where \( q_i \) is the output from the \( i^th \) firm with \( i = 1,2,3 \). The total cost (TC) curve of firm \( i \) is given by \( TC_i = \alpha_i + 5q_i \), where \( \alpha_i \)'s are positive real numbers. Assuming a Cournot solution exists, the value of \( Q \) is:

• (A) 9
• (B) 15
• (C) 12
• (D) 21

Transfer payments by governments are viewed as

• (A) Negative taxes
• (B) Indirect taxes
• (C) Non-tax revenues
• (D) Transfer of wealth

Match Column I with Column II.

• (A) (P → 3), (Q → 4), (R → 2), (S → 1)
• (B) (P → 3), (Q → 1), (R → 2), (S → 4)
• (C) (P → 2), (Q → 1), (R → 3), (S → 4)
• (D) (P → 2), (Q → 3), (R → 4), (S → 1)

Consider the following statements:


Statement 1: The new classical policy ineffectiveness proposition asserts that, systematic monetary policy and fiscal policy actions that change aggregate demand will not affect output and employment even in short run.

Statement 2: According to Real Business Cycle (RBC) model, the aggregate economic variables are the outcomes of the decisions made by many individual agents acting to maximize their utility subject to production possibilities and resource constraints.

• (A) ONLY Statement 1 is TRUE
• (B) ONLY Statement 2 is TRUE
• (C) BOTH Statements are TRUE
• (D) BOTH Statements are FALSE

Consider a two-variables (��, ��) linear regression model \[ y = \alpha + \beta x + \epsilon \]
where �� and �� are the parameters, and �� is the error term. The parameters are estimated using the Ordinary Least Squares (OLS) method. Let �� denote the estimated value of ��. If �� = 0, then which one of the following statements is CORRECT?

• (A) \( R^2 \) can be any real number in \( (0, 0.5] \)
• (B) \( R^2 \) can be any real number in \( (0.5, 1) \)
• (C) \( R^2 \) is any positive real number greater than 1
• (D) \( R^2 = 0 \)

Let \( X_1, X_2, X_3, \dots \) be independent and identically distributed random variables with \( E[X_1] = \mu \). Let \( N \) be a positive integer valued random variable with \( E[N] = n \). If \( S_N = X_1 + X_2 + \dots + X_N \), then \( E[S_N] = \dots \)

• (A) \( \mu \)
• (B) \( N \mu \)
• (C) \( n \mu \)
• (D) \( \mu n \)

A Cobb-Douglas type short-run production function is given by
\[ q = 2\sqrt{L \overline{K}} \]

where \( q, L \) and \( K \) are the output, labour and capital, respectively.

\( K \) is fixed at \( \overline{K} \). The unit price of \( L \) is \( w \) and the unit price of \( K \) is \( r \). It is given that \( w = 12 \).

Considering the above information, which of the following statements is/are CORRECT?

• (A) The short-run marginal cost is s \frac{6q}{K^\bar}
• (B) The short-run average variable cost is \frac{3q}{K^\bar}
• (C) To produce 10 units of the output, the required \( L \) is \frac{25}{K^\bar}
• (D) For K^\bar = 3 and r=4, the total cost is 12+3q²

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?

• (A) Everything else being constant, decrease in private saving would reduce trade surplus.
• (B) Everything else being constant, increase in investment would reduce trade surplus.
• (C) Everything else being constant, increase in government taxes would reduce trade surplus.
• (D) Everything else being constant, decrease in government spending would reduce trade surplus.

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) Increase in \( G \) has no effect on income in Scenario I.
• (B) Decrease in \( T \) lowers income in Scenario II.
• (C) Expansionary fiscal policy raises income in Scenario I and Scenario II.
• (D) Expansionary fiscal policy raises exchange rate in Scenario I and Scenario II.

Which of the following statements is/are CORRECT in the context of Foreign Exchange Market?

• (A) When the value of domestic currency increases vis-à-vis the value of foreign currency, the domestic currency experiences appreciation.
• (B) When the value of domestic currency increases vis-à-vis the value of foreign currency, the domestic currency experiences depreciation.
• (C) When the value of domestic currency decreases vis-à-vis the value of foreign currency, the domestic currency experiences depreciation.
• (D) When the value of domestic currency decreases vis-à-vis the value of foreign currency, the domestic currency experiences appreciation.

Which of the following statements characterize(s) the Indian labour market?

• (A) High workforce participation in agriculture
• (B) A predominant formal sector employment
• (C) Increasing Gig and contractual employment
• (D) A dual structure comprising organised and unorganised sector

Which of the following statements is/are NOT CORRECT?

• (A) According to the “Pollution Haven hypothesis”, trade liberalisation may lead to reallocation of production to countries where either environmental regulations are ineffective or altogether absent.
• (B) According to the “Porter hypothesis”, stringency in ensuring environmental standards often induces firms to become more efficient and prevent technological advancement and innovation.
• (C) According to the “Race to the Bottom hypothesis”, the environmental regulations are progressively made stringent so that economies gain in competition for inward investments.
• (D) According to the “Environmental Kuznets curve hypothesis”, there is an inverted U-shape relationship between per-capita income and environmental quality.

There are two firms in an industry producing a homogeneous product. The market demand function is given by \( P = 1 - (q_1 + q_2) \), where \( q_1 \) and \( q_2 \) are the output levels of Firm 1 and Firm 2, respectively. Firm 1’s cost function is common knowledge and equals zero. Firm 2’s cost function is private information. Firm 1 believes that Firm 2’s cost function is \( 0.5q_2 \) with probability 0.5 and that Firm 2’s cost function is \( 0.25q_2 \) with probability 0.5. The firms choose their quantities simultaneously. Let \( q_1^* \) denote the quantity produced by Firm 1 in the Bayesian Nash equilibrium of this game. Then, the value of \( 24q_1^* \) is ________\ (round off to one decimal place).

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).

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).

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).

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 \leq 2) = 0.977. \]

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.

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 \[ x \geq 0, \quad y \geq 0, \quad 2x + y \leq 6 \]
Then the value of \( f(x^*, y^*) \) is ________ (in integer).

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.
\[
\text{Then the value of p \text{ is _____\ (round off to one decimal place).

If the Marginal Propensity to Consume (MPC) of an economy is 0.75, then the value of the expenditure multiplier will be: