4. A firm has production function f(L,K) = min Lt, K. Let w be the price oflabor and r be the price of capital.(a) Find the firm's short-run cost function (for Qs 5) when the capital is fixedat K = 1000.(b) Find the firm's long-run cost function.(c) Let p = 2 be the price of the output good, and let w = 4 and r= 1. Find thefirm's long-run profit-maximizing output level.

Answered: Image /qna-images/answer/923acc3d-802c-440f-9892-dea9f3dd5b6a.jpg

Answered: 4. A firm has production function…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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We are trying whether, a new low fat diet actually helps obese people lose weight. 100 randomly obese people are assigned to group 1 and put on a low fat-diet. another 100 people are assigned to group 2 and put on a diet of approximately the same amount of food, but not as low in fat. After 4 months, the mean net weight loss was 9.31 pounds for group 1 with a standard deviation of 4.67 pounds, and for group 2 the mean net weight loss was 7.40 pounds with a standard deviation of 4.04 pounds. Is the low-fat diet more effective? Perform a hypothesis test at the 5% significance level a) Define Parameters and state null and alternative hypothesis b) Find test statistics c) Find p-value d) Conclusion
Suppose that a demand function is given by q = D(p) = 20(7 - ((p) with superscript (2)/square root of ((p) with superscript (3) + 1))) , where q is the demand for a product and p is the price per unit in dollars. Find the rate of change in the demand for the product per unit change in price. a.(dq/dp) = (-20(p) with superscript (4) + 80p/(((p) with superscript (3) + 1)) with superscript (1/2)) b.(dq/dp) = (10(p) with superscript (4) - 40p/ (((p) with superscript (3) + 1)) with superscript (3/2) ) c.(dq/dp) = (-10(p) with superscript (4) - 40p/ (((p) with superscript (3) + 1)) with superscript (1/2) ) d.(dq/dp) = (-10(p) with superscript (4) - 40p/ (((p) with superscript (3) + 1)) with superscript (3/2) )
10. A company sells a microprocessor for $450 each. The total cost that the company incurs in manufacturing q units of the microprocessor is C(q) = 10,000 + 5q^2.(a) Find the profit function. (b) At what quantity is the profit maximized? Justify your results with agraph.
The demand function for a good is given by the equation P = a − bQ while the totalcost function is TC = dQ^2 + eQ + f, where a, b, d, e and f are positive constants.(a) Derive the equation for profit.(b) Derive an expression for the value of Q for which profit is maximized.
(3) The demand curve of a firm is p= 1200 – 21g and its total cost is C(q) = 2g - 66q +600q +1000 where q is the output of the firm (in thousands). 3 (i) Derive an expression R(q) for the firm's revenue function. (ii) Derive an expression II(g) for the firm' s profit function. (iii) Is the rate of change of profit inereasing or decreasing when the output level of the firm is 10,000 units? (iv) Determine the level of output at which profit is maximized.
The marginal cost and marginal revenue of a company are MC (q) = 0.03q² − 1.5q + 35 and MR(q) 25, where q is the number of items manufactured. To increase profits, should the company increase or decrease production from each of the following levels? (a) 25 items: The company should production. (b) 50 items: The company should (c) 80 items: The company should production. production. =

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