Answer to Question #296020 in Microeconomics for akein

Question

A consumer must divide P6,000 between the consumption of product X and Y. The relevant market prices are Px= P100 and Py= P400.

a. Write the equation for the consumer's budget line.

b. Illustrate the consumer's opportunity set in a carefully labeled diagram.

c. Show how the consumer's opportunity set changes when the price of good X increases to P200. How does this change alter the market rate of substitution between goods X and Y?

Answer 1

a. Write the equation for the consumer's budget line.

The equation for consumer's budget line is:

XP_x + YP_y = M

The consumer’s budget line is: $100x + $400y = $6000

Rearranging terms and solving for Y results:

400y = 6000 - 100x

y = 15 - 0.25x

b. Illustrate the consumer's opportunity set in a carefully labeled diagram.

The consumer's opportunity set is given below:

The opportunity set of the consumer is that colored region.

c. Show how the consumer's opportunity set changes when the price of good X increases to P200. How does this change alter the market rate of substitution between goods X and Y?

When the price of good X increases to P200.

XP_x^' + YP_y = M is given as:

The new consumer’s budget line is: $200x + $400y = $6000

Thus, y = 15 - 0.5x

Therefore, the new budget set is depicted below:

With the rise in the price of product X, the new budget set has been reduced.

The first substitution rate on the market was:

MRS_xy = $\frac{Px}{Py}$

= $\frac{100}{400}$

= $0.25$

The new substitution rate on the market is:

MRS_xy = $\frac{Px'}{Py}$

= $\frac{200}{400}$

= $0.5$

Therefore, as the price of product X rises, so does the market rate of substitution.