Question:
Consider a firm that produces a single good using labour and capital. Let \( C, Q, L, K, w, r, p \) denote cost of production, level of output, labour, capital, wage rate, price of capital, and the price of output, respectively.
An example of the cost function for this firm is .........
Consider a firm that produces a single good using labour and capital. Let \( C, Q, L, K, w, r, p \) denote cost of production, level of output, labour, capital, wage rate, price of capital, and the price of output, respectively.
An example of the cost function for this firm is .........
An example of the cost function for this firm is .........
Show Hint
The cost function typically involves a relationship between output and input prices, with additional factors like scaling for labor and capital.
Updated On: Sep 6, 2025
- \( C = wL + rK \)
- \( C = \min\{wL, rK\} \)
- \( C = \frac{pQ}{wL + rK} \)
- \( C = Q\sqrt{w}w \)
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Understand the cost function.
The cost function represents the total cost of producing a certain level of output, taking into account the inputs (labour and capital) and their respective prices (wage rate and price of capital).
Step 2: Analyze the options.
- Option (A) is incorrect because the correct cost function is not simply the sum of labor and capital costs; there is a more complex relationship at play.
- Option (B) is incorrect because the cost function is not the minimum of labor and capital costs.
- Option (C) is incorrect because this formula does not correctly represent a typical cost function for the firm.
- Option (D) is correct because it introduces a relationship between output, the wage rate, and the capital price that fits the nature of cost functions.
Final Answer: \[ \boxed{C = Q\sqrt{w}w} \]
The cost function represents the total cost of producing a certain level of output, taking into account the inputs (labour and capital) and their respective prices (wage rate and price of capital).
Step 2: Analyze the options.
- Option (A) is incorrect because the correct cost function is not simply the sum of labor and capital costs; there is a more complex relationship at play.
- Option (B) is incorrect because the cost function is not the minimum of labor and capital costs.
- Option (C) is incorrect because this formula does not correctly represent a typical cost function for the firm.
- Option (D) is correct because it introduces a relationship between output, the wage rate, and the capital price that fits the nature of cost functions.
Final Answer: \[ \boxed{C = Q\sqrt{w}w} \]
Was this answer helpful?
0
0
Top Questions on Production Function
- If \( Y = L^a K^b \) is a Cobb-Douglas production function with two factors labor and capital, then the presence of constant returns to scale exhibited by the production function can be tested using ...........
- IIT JAM EN - 2025
- Economics
- Production Function
- Consider the following AK model where the production function is given by
$ 𝑌 = 𝐴𝐾$
where 𝑌 is output, 𝐾 is capital, and 𝐴 is a constant that reflects the level of technology. Suppose there is zero technological progress in the economy and 𝐴 = 0.50. In the economy, the savings rate equals 0.60 and the depreciation rate for the capital stock equals 0.05. The population growth rate equals zero and the size of the labour force is normalised to 1. Based on the AK model, the steady state growth rate of output per capita in the economy equals ______ percent (in integer).- IIT JAM EN - 2024
- Macroeconomics
- Production Function
- A manufacturer producing pens has the following information regarding the cost of production of pens:
Output (𝑄) 1 2 3 Total Costs (𝑇𝐶) 4 13 32
"If the total cost function is of the form $𝑇𝐶(𝑄) = 𝑎𝑄^2 + 𝑏𝑄 + 𝑐$ where 𝑎, 𝑏, and 𝑐 are constants, then the value of $𝑇𝐶(𝑄) at 𝑄 = 4$ is (in integer)."- IIT JAM EN - 2024
- Macroeconomics
- Production Function
- Consider the production function:
$ Q(K, L) = (2 \sqrt {K} + 3 \sqrt{L})^2$ where Q is the output, K is capital, and L is labour. If $\eta_K$ and $\eta_L$ denote the output elasticities with respect to capital and labour, respectively, then the value of ($\eta_K$ + $\eta_L$) is- IIT JAM EN - 2024
- Macroeconomics
- Production Function
- Consider an economy where technology is characterised by the production function:
$Y = 50K^{0.4}L^{0.6}$
where, Y is output, K is capital, and L is labour.
Assuming perfect competition in the product market and in the factor markets, the share of total income paid to labour is equal to- IIT JAM EN - 2024
- Macroeconomics
- Production Function
View More Questions
Questions Asked in IIT JAM EN exam
- Consider the matrix \( A = \begin{bmatrix} 4 & -1 \\ 12 & -3 \end{bmatrix} \).
The value of the determinant of \( A^5 \) is .......... (rounded off to two decimal places).- IIT JAM EN - 2025
- Linear Algebra
The sum of the payoffs to the players in the Nash equilibrium of the following simultaneous game is ............
Player Y C NC Player X X: 50, Y: 50 X: 40, Y: 30 X: 30, Y: 40 X: 20, Y: 20 - IIT JAM EN - 2025
- Economics and economic theories
- Consider the economy described by the following: \[ Y = C + I + G \quad \text{with} \quad Y = 5000, \, G = 1000, \, T = 1000, \quad \text{and} \quad C = 250 + 0.75(Y - T), \] where \( Y \), \( C \), \( I \), \( G \), and \( T \) are national income, private consumption spending, investment expenditure, government expenditure, and tax revenue respectively. In this economy, private saving is ............
- IIT JAM EN - 2025
- Microeconomics
- Lerner Index (\( L \)), a measure of market power, is defined as \( L = \frac{P - MC}{P} \), where \( P \) and \( MC \) are, respectively, price and marginal cost of a firm. If a profit maximizing firm faces the demand curve \( P^2 Q = 7 \), the value of \( L \) is ............ (rounded off to one decimal place).
- IIT JAM EN - 2025
- Microeconomics
- You are tossing a fair coin repeatedly until a ‘Head’ appears. The expected number of tosses required for a ‘Head’ to appear is ...........
- IIT JAM EN - 2025
- Probability
View More Questions