Suppose the long-run production function for a competitive firm is f(x1,x2)= min {3x1,2x2}. The cost per unit of the first input is w1 and the cost of the second input is w2.A: Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y.B: Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs?C: Write down the formulas and draw the graphs of the average cost and marginal cost functions, as functions of y. Suppose the long-run production function for a competitive firm is f(x₁,x₂)= min {3x1,2x2}. The costper unit of the first input is w₁ and the cost of the second input is w2.a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output levelof y.b. Write down the formula and draw the graph of the firm's total cost function as a function of y,using the conditional input demand functions. What is the relationship between the returns toproduction scale and the behavior of the total costs?c. Write down the formulas and draw the graphs of the average cost and marginal cost functions, asfunctions of y.

Cost minimization problem of producer: For the given output level the firm and per unit cost of…

Answered: Suppose the long-run production…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter10: Cost Functions

Section: Chapter Questions

Problem 10.3P

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Suppose the long-run production function for a competitive firm is f(x1,x2)= min {3x₁,2x₂}. The cost per unit of the first input is w₁ and the cost of the second input is w₂.

A: Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y.

B: Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs?

C: Write down the formulas and draw the graphs of the average cost and marginal cost functions, as functions of y.

Suppose the long-run production function for a competitive firm is f(x₁,x₂)= min {3x1,2x2}. The cost
per unit of the first input is w₁ and the cost of the second input is w2.
a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level
of y.
b. Write down the formula and draw the graph of the firm's total cost function as a function of y,
using the conditional input demand functions. What is the relationship between the returns to
production scale and the behavior of the total costs?
c. Write down the formulas and draw the graphs of the average cost and marginal cost functions, as
functions of y.

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