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# Consumer Budget Constarint

Question 1. Page 154 (with some modifications)

A consumer has \$300 to spend on goods X and Y. The market prices of these two goods are Px = \$15 and Py = \$5.

a. Draw the budget constraint. I.e. provide a carefully labeled diagram
b. What is the market rate of substitution? Give an interpretation.
c. Illustrate the consumer's opportunity set in part a) above.
d. Show how the consumer's opportunity set changes if income increases by \$300.
e. Does the increase of income by \$300 in part d) above alter the market rate of substitution between goods X and Y?

Question 3 (with some modifications to the question). On page 155
A consumer must spend \$600 between the consumption of product X and Y. The relevant market prices are Px = \$10 and Py = 40.

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\$20.
d. Does the change in the price of good X in part c alter the market rate of substitution between goods X and Y?

Instructions: For each part of the above question, show your work. Graphs may be useful. Explain and show all steps of how you have reached your answer. Don't simply state your answer.

#### Solution Preview

Question 1

a. PxX + PyY = 300 : this is consumer's budget constraint
15X + 5Y = 300
Y = 60 - 3X : this is the budget line
Refer to the graph in the first attachment.

b. The marginal rate of substitution is the rate at which a consumer is ready to give up one good in exchange for another good while maintaining the same level of utility. It is the slope of indifference utility curve. Consumer maximizes his/her utility given his/her budget constraint as per (a) above, by consuming at the highest utility curve. This maximum point is the point where the marginal rate of substitution (ie the slope of the indifferent utility curve just tangent to the budget line, which is point A on the graph. The market rate of ...

#### Solution Summary

Consumer maximizes his utility by consuming a combination of goods given goods' prices and consumer income. This is achievable by consuming a bundle of goods in which the highest attainable utility indifferent curve just tangent to his budget line. At this point, the marginal rate of substitution is equal to the market rate of substitution. The market rate of substitution will not change with the change in consumer income provided goods' prices didn't change. However, the market rate of substitution will change if goods' prices change in-proportionately.

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