Quasi-linear utility. Suppose that the consumer’s preferences can be represented by the quasi-linear...

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Quasi-linear utility. Suppose that the consumer’s preferences can be represented by the quasi-linear utility function u  f(x1)  x2, f′  0, f″  0. (a) Show that the consumer’s indifference curves are vertically parallel, i.e. their slope depends only on x1 and not on x2. (b) Confirm that the income elasticity of demand for good 1 is zero and thus that the CV and EV for changes in p1 are equal. (c) Show that the marginal utility of income is independent of p1 so that the change in Marshallian consumer surplus is a measure of the change in utility caused by changes in p1. (d) What is the relationship between the change in the Marshallian consumer surplus and the EV and CV measures in this case?

Prince · Accepted Answer

(a) Show that the consumer’s indifference curves are vertically parallel, i.e. their slope depends only on 
x1 and not on x2.
Solution: The indifference curves' slope can be calculated as follows: 
 
In this instance, u = f(x1)+x2 As a result, the indifference curves' slope is: 
 
As a result, x1 is the sole variable that influences the slope of the difference curves, not x2.

Quasi-linear utility. Suppose that the consumer’s preferences can be represented by the quasi-linear utility function u f(x1) x2, f′ 0, f″ 0. (a) Show that the consumer’s indifference curves are...

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