Income & Substitution Effects

Question 1

Suppose a consumer's utility function is U=X0.5Y0.5 with marginal utilities of MUx=0.5X-0.5Y0.5 and MUy=0.5X0.5Y-0.5.
They have an income of 32 to purchase goods X and Y. Round answers to one decimal place.

1) What is the consumer's optimal bundle when the price of X is 2 and the price of Y is 2?

X*= Y*=

2) What is the consumer's optimal bundle when the price of X is 8 and the price of Y is 2?

X*= Y*=

3) Using your intuition for standard preferences, what are the signs of the income and substitution effects from the price change?

X
Y
Income Effect:
Substitution Effect:

4) What are the values of the income and substitution effects using the decomposition bundle technique?

X
Y
Income Effect:
Substitution Effect:

5) Does your intuition in 3) match the values in 4)?



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