Suppose that the marginal rate of substitution is 2, the price of X is $3, and the price of Y is $1.

a) If the consumer obtains 1 more unit of X, how many units of Y must be given up in order to keep utility constant?

b) If the consumer obtains 1 more unit of Y, how many units of X must be given up in order to keep utility constant?

c) What is the rate at which the consumer is willing to substitute X for Y?

d) What is the rate at which the consumer is able to substitute X for Y?

e) If the consumer making the utility – maximising choice? Why or why not? If not, what should the consumer do? Explain.

**Technifi Expert’s Answer:**

As we know Marginal rate of Substitution MU_{X}/MU_{Y} = P_{X}/P_{Y}

From given information MU_{X}/MU_{Y} = 2 P_{X}/P_{Y} = 3

As the last dollar is spent,

x gives twice as much utility as y, and costs thrice as much as y.

**a) If the consumer obtains 1 more unit of X, how many units of Y must be given up in order to keep utility constant?**

**Answer:** If 1 unit of x is gained, 2 units of y must be given up.

**b) If the consumer obtains 1 more unit of Y, how many units of X must be given up in order to keep utility constant?**

**Answer:** If 1 unit of y is gained, 1/2 units of x must be given up.

**c) What is the rate at which the consumer is willing to substitute X for Y?**

**Answer:** consumer is willing to substitute 1 unit of x for 2 units of y

**d) What is the rate at which the consumer is able to substitute X for Y?**

**Answer:** consumer is able to substitute 1 unit of x for 3 units of y

**e) If the consumer making the utility – maximising choice? Why or why not? If not, what should the consumer do? Explain.**

**Answer:** This is not the utility max choice. At utility max choice, willingness to replace x with y is as much as the ability to replace x with y. In this case willingness to replace x with y is lower than the ability to replace x with y.

Price ratio is given, that cannot be changed. Thus consumer should move to a point where her marginal utility from y is one-third of that of x. Thus she should increase her consumption of y.

Also, another interpretation is there. y is available for one-third of price, and gives half the utility of x. Thus its consumption can be increased as long as it gives one-third the utility of x.

If you happen to run into some problem while following the steps, please make sure to let us know in the comment section below, and we’ll do our best to solve it. Apart from that, you can contact us on Facebook and Twitter, however we can’t guarantee a rapid reaction time over those platform

## 0 Comments