Question: A consumer has the following utility function: U(x, y) =x(y+1), where x and y are quantities of two consumption goods whose prices are P x

A consumer has the following utility function: U(x, y) =x(y+1), where x and y are quantities of two consumption goods whose prices are

Pxand Py respectively. The consumer also has a budget of B. Therefore, the consumer's Lagrangian is

x(y+1)+(BPxxPyy) x

(a) From the first-order conditions find expressions for the demand functions. What kind of good is y? In particular, what happens when Py> B?

(b) Verify that this is a maximum by checking the second-order conditions

Carefully graph x* and y*. Graph imran's indifference curve. What kind of good is y?

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