Asked Mar 20, 2019

Donna and Jim are two consumers purchasing strawberries and chocolate. Jim’s utility function is U(x,y) = xy and Donna’s utility function is U(x,y) = x2y where is strawberries and is chocolate. Jim’s marginal utility functions are MUX=y and MUy=x while Donna’s are MUX=2xy and MUy=x2Jim’s income is $100, andDonna’s income is $150.

Are strawberries a normal good or an inferior good for Jim? Explain your answer.


Expert Answer

Step 1

MUx (for Jim) = y 

MUy (for Jim) = x

Px = $2     and  Py = $4   ( as given in another subpart of question)

X is strawberries and Y is chocolates


Step 2

As per equilibrium condition, MUX/PX = MUY/PY 

We will at some point observe that  the last dollar spent on strawberries will yield greater utility than last dollar spent on chocolate i.e. MUX/PX > MUY / PY.

Consumer can thus increase his total utility by consuming more of strawberries which will reduce marginal utility of strawberries and the consumer will continue to increase his expenditure on strawberries until the equilibrium is restored.

In case of a normal good, a fall in the price will, all other things being constant, give rise to an increase in a consumer’s demand for that good.

Suppose, initially we have MUX = y, MUY = x , PX = 2 and PY = 4 so that the condition of utility (MUX /PX = MUY /PY) is satisfied.

 y/2  = x/4 or ...

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