A firm employs a Cobb-Douglas production function of the form Y = K04L04. The output price is P and the input prices are r and w for K and L, respectively. a. Set up the firm's profit maximization problem and find the input demands for K and L b. Derive the firm's output supply function c. Derive the firm's profit function

A firm employs a Cobb-Douglas production function of the form Y = K04L04. The output price is P and the input prices are r and w for K and L, respectively. a. Set up the firm's profit maximization problem and find the input demands for K and L b. Derive the firm's output supply function c. Derive the firm's profit function

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Short-Run Costs and Long-Run Costs

Cost of short-run and the long-run is an economic term that describes the cost involved in the production of goods in a firm in the short as well as long period.

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A firm's technology is characterized by a Cobb - Douglas production function of the form 1 1 y = f(K,L) = 2K² + 1² a. The output price is p, and the input prices are r and w for K and L, respectively. Set up the problem for a profit - maximizing firm and solve for the factor demand functions for K and L. b. Find the firm's supply function. c. Find the firm's profit function. d. Assume now that p = 2, r = 1, and w = 1. Using the functions you have found in parts (a), (b) and (c), calculate the profit - maximizing levels of the factors and (K* and L*), the profit - maximizing output level (v) and the maximum profit of the firm (). Please solve it by explaining and explaining.
Two months ago, on July 1, 2019, the State of Illinois raised gasoline taxes by $.19 (19 cents) per gallon of gas Question 3: For this question, please model the short-run impact of this tax on a typical Illinois gas station. The horizontal axis will be qgas (the output of this particular producer) and the vertical axis will measure price in dollars, $. This firm is subject to the Law of Diminishing Marginal Product. Begin by graphically depicting the “Family of Short Run Cost Curves” (AFC, AVC, ATC, MC) for this producer in late June, prior to the implementation of the new gasoline tax (you must submit a graph).