Consider a consumer whose utility function isu(#1, #2) = – exp(-ar1#2)Can you take first order conditions to solve the utility maximization problem? Explain your argument. Nextsolve the utility maximization problem, and derive Marshallian demands and the indirect utility function.Given your calculations, state and use the duality theorem to find the expenditure function and Hicksiandemands.

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Answered: Consider a consumer whose utility…

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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The price p and the quantity q sold of a certain product obey the demand functionq = −20p + 500, 0 ≤ p ≤ 25 Express the revenue R as a function of x. What is the revenue if 20 units are sold?
Answer all parts. Suppose that a monopolist offers two different products with demand functions P1 = 56 – 4q, Р2 3D 48 — 2q2 The monopolist's joint cost function is C(41, 92) = qỉ + 5q192 + q3 %3D a. Write out the monopolist's profit function as a function of b. Differentiate the profit function with respect to q, and q2.Explain intuitively why we take the derivative of the function. c. Solve the first order conditions using Cramer's rule. d. Use the values that you found in part c to find the prices in each market and the profit that is made by the monopolist. e. Use the second order condition for a maximum to check whether or not the and 92. values that you have computed do represent a maximum.
Carina buys two goods, food, F, and clothing, C, with the utility function, U = FC + F. She has an income of 20. The price of clothing is 4. a) Derive the equation representing Carina's demand for food. b) Calculate the income and substitution effects on Carina's consumption of food when the price of food rises from 1 to 4.
Consider a competitive market in which price adjusts to excess demand or supply and firms enter and exit the industry if profits or losses are being made. Price adjusts to excess demand according to dp 0.5(qº – q$) dt Where qº = 30 – 2p is the demand function, qº = 2N is the supply function, p is price, N is the number of firms in the industry and a is the speed of adjustment coefficient. The number of firms adjust according to dN 5 (p 10) dt Derive a system of differential equation to represent this information. Solve the system.
Answer part (iv)
A firm has the following production function:q = ƒ (z1, z2) = z1αz2βb. Solve for the firm's conditional demand function (simplify)

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