<p>Consider that, if two goods are perfect substitutes, their marginal utilities are constant with respect to each other. Hence with two goods, you will consume only one or the other*.</p>

<p>If $\frac{a}{p_x} &gt; \frac{b}{p_y}$, then $x^*(M) = \frac{M}{p_x}; y^* = 0 $</p>

<p>otherwise if $\frac{a}{p_x} &lt; \frac{b}{p_y}$, then $x^* = 0; y^*(M) = \frac{M}{p_y} $</p>

<p>*(assume their prices are not the inverse of their marginal utilities, in which case you are indifferent).</p>

CC BY-SA 3.0
2015-02-23T13:16:59.787Z
2015-02-23T13:33:39.173Z
2015-02-23T13:33:39.173Z
lilster
<p>If I have the utility function of an individual that exhibits perfect substitutes, think (U=ax+by), and I'm given the price of good x and the budget M, then how am I supposed to determine the demand for good Y if I don't have the price of good Y? </p>

<p>I know for Cobb-Douglas style utility functions the optimal choice of good Y is given by Y=BM/price of good Y</p>

CC BY-SA 3.0
2015-02-23T05:38:25.020Z
just solve with X left as a function of Y...
serakfalcon
<microeconomics>
How to determine demand without the price of a good?
KawaiiExpert
# How to determine demand without the price of a good?

(Asked by: username_0 on 2015-02-22)

If I have the utility function of an individual that exhibits perfect substitutes, think (U=ax+by), and I'm given the price of good x and the budget M, then how am I supposed to determine the demand for good Y if I don't have the price of good Y?

I know for Cobb-Douglas style utility functions the optimal choice of good Y is given by Y=BM/price of good Y

**Tags:** microeconomics
> **Comments:**
> **username_1**: just solve with X left as a function of Y...  

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## 1 answers

### Answer by username_2 on 2015-02-23. Score: 2

Consider that, if two goods are perfect substitutes, their marginal utilities are constant with respect to each other. Hence with two goods, you will consume only one or the other\*.

If $\frac{a}{p\_x} > \frac{b}{p\_y}$, then $x^\*(M) = \frac{M}{p\_x}; y^\* = 0 $

otherwise if $\frac{a}{p\_x} < \frac{b}{p\_y}$, then $x^\* = 0; y^\*(M) = \frac{M}{p\_y} $

\*(assume their prices are not the inverse of their marginal utilities, in which case you are indifferent).


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