midterm 1 solutions - THE UNIVERSITY OF MARYLAND COLLEGE...

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THE UNIVERSITY OF MARYLAND COLLEGE PARK MD Daniel R. Vincent ECONOMICS 600 October 19, 2000 Office: 4128b Phone: 301 405 3485 Mathematical Economics: Midterm Examination Consumer preferences over consumption of Beer and Water can be represented by the utility function: U(W,B; )=logW+ log(B+1) , >0. Much of this question will be concerned with how consumer choices may differ depending on different values of their exogenously given preference parameter, . Only non-negative units of either good may be consumed. Consumers have income of $100 . The price of water is $1 per unit. The price of beer is $1 per unit for any purchases less than or equal to 50 units. For any ADDITIONAL purchases above 50 units, the price rises to $2 per unit. 1. Carefully draw in (W,B) space, the consumer’s choice set and show that it can be expressed as the intersection of two half-spaces in the postive orthant. (That is, show that the choice set can be expressed as C={(W,B):g 1 (W,B) 0,g 2 (W,B) 0 , W 0,B 0} where g 1 ,g 2 , are of the general form, g i (W,B)=a i W+b i B+c i .) For B<50, the budget set is just 100-W-B 0. If B>50, then consumers spend
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