Answered: The U.S produces two goods. Micro…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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The U.S produces two goods. Micro Lectures (M) and Ice Cream (I) It does so using the function 8M^2 + 2I^2 = 500 Citizens feel that U(M,I) = 10M^0.5I^0.5 Find trade equilibrium using world prices when Pm=2 & Pi =4 Which good is imported and how much of it?

Expert Solution

Step 1

US produces on the PPF

$8 M^{2} + 2 I^{2} = 500$

The citizens utility is given by,

$U (M . I) = 10 M^{0.5} I^{0.5}$

World prices are given by Pm=2 and Pi=4.

First we find the tangential point between the PPF and the price line. The slope of the price line is given by

$- \frac{P_{m}}{P_{i}} = - \frac{1}{2}$

The slope of the PPF is calculated by,

$16 M d M + 4 I d I = o \Rightarrow d I = - \frac{4 M d M}{I} \Rightarrow \frac{d I}{d M} = - \frac{4 M}{I}$

Equating the slopes,

$\frac{4 M}{I} = \frac{1}{2} \Rightarrow I = 8 M$

Plugging that in the PPF equation,

$8 M^{2} + 2 * 64 M^{2} = 500 \Rightarrow M^{2} = \frac{500}{136} \Rightarrow M = \sqrt{\frac{500}{136}} 2 I^{2} = 500 - 8 M^{2} = \frac{4000}{9} \Rightarrow I = \sqrt{\frac{2000}{9}}$

Now that we know that US budget constraint passes through $(\sqrt{\frac{500}{136}}, \sqrt{\frac{2000}{9}}),$ we find the equation of the budget constraint as

$2 M + 4 I = 2 * \sqrt{\frac{500}{136}} + 4 * \sqrt{\frac{2000}{9}} S a y C = 2 * \sqrt{\frac{500}{136}} + 4 * \sqrt{\frac{2000}{9}} 2 M + 4 I = C$

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