List of top Microeconomics Questions asked in Indian Institute Of Technology Joint Admission Test for MSc

An industry has 6 firms in Cournot competition. Each of the 6 firms has zero fixed costs, and a constant marginal cost equal to 20. The product is homogenous and the industry inverse demand function is given by 𝑃 = 230 − 𝑄, where 𝑃 is the market price and 𝑄 is the industry output (sum of outputs of the 6 firms). The market price under Cournot-Nash equilibrium is equal to _____ (in integer).

A consumer’s utility function is given by: $𝑢(𝑥_1, 𝑥_2) = (2𝑥_1 − 1)0.25(𝑥_2 − 4)0.75$ If the consumer has a budget of 73 and the unit prices of $𝑥_1$ and $𝑥_2$ are given by 2 and 1, respectively, then the value of ($𝑥_1 + 𝑥_2$) is ________ (rounded off to two decimal places).

Suppose high quality and low quality products are sold at the same price to the buyers. The buyers have less information to determine the quality of the product compared to the sellers at the time of purchase. Which of the following problems arises in this situation?

There are two goods 𝑋 and 𝑌 and there are two consumers 𝐴 and 𝐵 in a pure exchange economy. 𝐴 and 𝐵 have Cobb-Douglas utility functions of the form $𝑈_𝐴 = 2𝑋^{0.4} 𝑌^{0.6}$ and $𝑈_𝐵 = 𝑋^{0.3}𝑌^{0.7}$, respectively. Initially, 𝐴 is endowed with 50 units of good 𝑋 and 20 units of good 𝑌. Similarly, 𝐵 is endowed with 50 units of good 𝑋 and 20 units of good 𝑌. If the unit price of good 𝑌 is normalised to 1, then the equilibrium unit price for good 𝑋 is _____. (rounded off to two decimal places).

The characteristics of pure public good is/are

Consider a closed economy with consumption function $ C = 2 + 0.5𝑌$, where 𝑌 is income. The government expenditure is 3 and investment function is $ I = 4 − 0.5r $ , where r is interest rate. Then, the slope of the IS curve will be

Consider the following three utility functions:
$F = (4x_1 + 2x_2), G = min (4x_1, 2x_2)$ and $H = (\sqrt{x_1} + x_2)$ where, $x_1$ and $x_2$ are two goods available at unit prices $p_{x1}$ and $p_{x2}$ , respectively. Which of the following is/are CORRECT for the above utility functions?

Let an inverse demand function for a commodity be $𝑝 = e^{\frac{-x}{2}$, where 𝑥 is the quantity and 𝑝 is the price. Then, at 𝑝 = 0.5, the consumer surplus is equal to _______ (rounded off to two decimal places).

Consider a production function of the form:
$ Y = 𝑎 log L + (1 − 𝑎) log K , 𝑎 ∈ (0, 1), 𝑎 ≠ 0.5 $
where, Y is output, L is labour, and K is capital. Then, the absolute value of elasticity of substitution is

Two people, 1 and 2, are engaged in a joint project. Person 𝑖∈{1,2} puts in effort 𝑥𝑖 (0≤ 𝑥𝑖 ≤ 1), and incurs cost 𝐶_𝑖 (𝑥_𝑖 ) = 𝑥_𝑖 . The monetary outcome of the project is 4𝑥₁𝑥₂ which is split equally between them. Considering the situation as a strategic game, the set of all Nash Equilibria in pure strategies is

A firm is operating in a perfectly competitive environment. A change in the market condition leads to an increase in the firm’s profit by an amount K. Which of the following describes the change in the Producer’s Surplus due to the above change in the market condition?

For a firm operating in a perfectly competitive market which of the following statements is CORRECT?

Two firms, X and Y, are operating in a perfectly competitive market. The price elasticity of supply of X and Y are respectively 0.5 and 1.5. Then

An economy has three firms: X, Y and Z. Every unit of output that X produces creates a benefit of INR 700 for Y and a cost of INR 300 for Z. Firm X’s cost curve is
\(𝐶(𝑄_𝑋) = 2𝑄^2_X + 10\)
where 𝐶 represents cost and 𝑄_𝑋 is the output. The market price for the output of X is INR 1600 per unit. The difference between the socially optimal output and private profit maximizing output of firm X (in INR) is _____ (in integer).

A consumer has utility function 𝑢(𝑥₁, 𝑥₂ ) = max {0.5 𝑥₁ , 0.5 𝑥₂} + min{𝑥₁ , 𝑥₂}.
She has some positive income 𝑦, and faces positive prices 𝑝₁, 𝑝₂ for goods 1 and 2 respectively. Suppose 𝑝₂ = 1. There exists a lowest price 𝑝̅̅₁ such that if 𝑝₁ > 𝑝̅̅₁ then the unique utility maximizing choice is to buy ONLY good 2. Then 𝑝̅̅₁ is _________ (in integer).

In a two period model, a consumer is maximizing the present discounted utility
𝑊𝑡 = ln(𝑐_𝑡) +\(\frac{ 1}{ 1 + }\) ln(𝑐_𝑡+1) 
with respect to 𝑐𝑡 and 𝑐𝑡+1 and subject to the following budget constraint 
\(𝑐_𝑡 +\frac{ 𝑐_𝑡+1}{ 1 + 𝑟} ≤ 𝑦_𝑡 +\frac{ 𝑦_𝑡+1 }{1 + 𝑟 }\)
where 𝑐𝑖 and 𝑦𝑖 are the consumption and income in period 𝑖 (𝑖 = 𝑡,𝑡 + 1) respectively, 𝜃 ∈ [0, ∞) is the time discount rate and 𝑟 ∈ [0, ∞) is the rate of interest. Suppose, consumer is in the interior equilibrium and 𝜃 = 0.05 and 𝑟 = 0.08. In equilibrium, the ratio \(\frac{𝑐_𝑡+1}{ 𝑐_𝑡}\) is equal to _____ (round off to 2 decimal places).

Consider a 2-agent, 2-good exchange economy where agent 𝑖 has utility function 𝑢𝑖 (𝑥𝑖 , 𝑦𝑖 ) = max{𝑥𝑖 , 𝑦𝑖 }, 𝑖 = 1,2. The initial endowments of goods 𝑋 and 𝑌 that the agents have are (𝑥̅̅1̅, 𝑦̅̅1̅, 𝑥̅̅2̅, 𝑦̅̅2̅) = (25, 5, 5, 5). Then select the CORRECT choice below where the price vector (𝑝𝑥, 𝑝𝑦) specified is part of a competitive equilibrium.

An industry has 3 firms (1, 2 and 3) in Cournot competition. They have no fixed costs, and their constant marginal costs are respectively\(c_1=\frac{9}{30} , 𝑐_2 =\frac{ 10}{30} , 𝑐_3 = \frac{11}{30} .\)
They face an industry inverse demand function 𝑃=1−𝑄, where 𝑃 is the market price and 𝑄 is the industry output (sum of outputs of the 3 firms). Suppose that 𝑄 𝑐 is the industry output under Cournot-Nash equilibrium. Then (𝑄 ^𝑐 )⁻¹ is equal to _______ (in integer).

A competitive firm can sell any output at price 𝑃 = 1. Production depends on capital alone, and the production function 𝑦 = 𝑓(𝐾) is twice continuously differentiable, with
𝑓(0) = 0, 𝑓 ′ > 0, 𝑓 ′′ < 0, \(lim\\_{ 𝐾→0 }\) 𝑓 ′ (𝐾) = ∞ , \(lim\\_{ 𝐾→∞}\) 𝑓 ′ (𝐾) = 0.
The firm has positive capital stock 𝐾̅  to start with, and can buy and sell capital at price 𝑟 per unit of capital. If the firm is maximizing profit then which of the following statements is NOT CORRECT?

Suppose that the utility function \(𝑢: R^𝑛_+→R_+\) represents a complete, transitive and continuous preference relation over all bundles of 𝑛 goods. Then select the choices below in which the function also represents the same preference relation.

In a 3-player game, player 1 can choose either Up or Down as strategies. Player 2 can chose either Left or Right as strategies. Player 3 can choose either Table 1 or Table 2 as strategies.

Which of the following strategy profile(s) is/are Nash Equilibrium?

Consider a 2-agent, 2-good economy with an aggregate endowment of 30 units of good 𝑋 and 10 units of good 𝑌. Agent 𝑖 has utility function
u_i (x_i , y_i ) = max {x_i , y_i }, 𝑖 = 1, 2. 
Select the choices below in which the specified allocation of the goods to the agents is Pareto optimal for this economy

A firm has production function 𝑦=𝐾 ^0.5𝐿 ^0.5 and faces wage rate 𝑤=4 and rental rate of capital 𝑟=4. The firm’s marginal cost is equal to ______ (in integer).

An economy is characterized by the Solow model, with the production function y = √k, where y is output per worker and k is capital per worker. The steady-state level of output per worker is \(y^{ss}=A^{1/(1-\alpha)}(\frac{\gamma}{\delta})^{\alpha/(1-\alpha)}\) where Α, γ, δ and a denote productivity, share of output invested (in %), depreciation rate (in %) and capital's share in income (in fraction), respectively. Suppose that A = 1, k = 400, \(\gamma\) = 50%, δ = 5% and \(\alpha\)= 1/2. Then the current output, using the above information, is

Let a monopolist demand curve be given by $Q = P^e$, where Q is output, P is price, e is the price elasticity of demand (e <-1), and Marginal Cost = Average Cost = $\alpha$. If $P^c$ and PM represent the price under perfect competition and monopoly, respectively, then which of the following is/are NOT correct?
($CS_M$ and $CS_C$ represent the consumer surplus under monopoly and perfect competition, respectively.)