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Mathematical Economics Assignment

This document contains instructions for Assignment #1 of the Mathematical Economics course at East West University for Fall 2018. It includes 4 questions: 1) Analyzing whether a function is concave/convex and if further parameter restrictions are needed. 2) Checking quasiconcavity of a function. 3) Finding a level curve for a production function, explaining its shape, and checking for quasiconcavity/quasiconvexity. 4) Writing a constrained utility maximization problem, finding the utility maximizing functions and Lagrange multiplier, checking the second order condition, and solving for specific values.

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Shoummo Rubaiyat
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290 views1 page

Mathematical Economics Assignment

This document contains instructions for Assignment #1 of the Mathematical Economics course at East West University for Fall 2018. It includes 4 questions: 1) Analyzing whether a function is concave/convex and if further parameter restrictions are needed. 2) Checking quasiconcavity of a function. 3) Finding a level curve for a production function, explaining its shape, and checking for quasiconcavity/quasiconvexity. 4) Writing a constrained utility maximization problem, finding the utility maximizing functions and Lagrange multiplier, checking the second order condition, and solving for specific values.

Uploaded by

Shoummo Rubaiyat
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Fall 2018

Department of Economics, East West University


ECO 511: Mathematical Economics
Assignment # 1; DUE: 02/10/2018

1-1. Consider the following function:

f (x, y) = Axα y β A > 0, 1 > α, β > 0

Is this function concave/convex? Do we need further parameter restrictions for estab-


lishing concavity/convexity?

1-2. Check quasiconcavity of the following function:

z = f (x, y) = −x2 − y 2 , x, y > 0

1-3. Consider the production function:

y = f (x1 , x2 , x3 ) = Axα1 xβ2 xγ3 , α, β, γ > 0

(a) Find the equation of a level curve for the above function in (x1 , x2 )-space.
(b) Mathematically explain the shape of the level curve derived in part (b).
(c) How would you check for quasi-concavity/quasi-convexity of the f function?

1-4. A consumer’s utility depends on consumption of goods x and y and is given by function

U (x, y) = (x + 2)(y + 1).

Assume that the consumer’s income is m > 0 and the prices are px > 0 and py > 0.

(a) Write down the constrained utility maximization problem with the relevant La-
grange function.
(b) Find the utility maximizing functions x? (px , py , m), y ? (px , py , m) and λ? (px , py , m)
where λ is the Lagrange multiplier.
(c) Check second order sufficient condition for a utility maximum.
(d) Find the optimum values (x? , y ? , λ? ) if px = 4, py = 6, and m = 130. Interpret the
λ? value in the context of this problem.

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