Homework II
Due to Mar 28
Ch.6 Demand
6.2 Douglas Cornfield’s preferences are represented by the utility function ( ,
1 2
)
 2 3 u x x x x
1 2
. The prices of x and
1 x are
2 p and
1 p .
2
(a) The slope of Cornfield’s indifference curve at the point x x
1 2
) is__________.
(b) If Cornfield’s budget line is tangent to his indifference curve at x x
1 2
) , then p x
1 1 p x
2

_____.
When he is consuming the best bundle he can afford, what fraction of his income dose Douglas spend on x ?
1
(c) Other members of Doug’s family have similar functions, but the exponents may be different, or their utilities may be multiplied by a positive constant. If a family member has a utility function
( ,
2
)
 a b
U x x cx x
2
, where a, b, and c are positive numbers, what fraction of his or her income will that family member spend on x ?
1
6.7 Mary’s utility function is ( , )
 
100 c c
2
, where b is the number of silver bells in her garden and c is the number of cockle shells. She has 500 square feet in her garden to allocate between silver bells and cockle shells. Silver bells each take up 1 square foot and cockle shells each take up 4 square feet. She gets both kinds of seeds for free.
(a) To maximize her utility, given the size of her garden, Mary should plant _____ silver bells and
______ cockle shells.
(b) If she suddenly acquires an extra 100 square feet for her garden, how much should she increase her planting of silver bells? How much should she increase her planting of cockle shells?
(c) If Mary had only 144 square feet in her garden, how many cockle shells would she grow?
(d) If Mary grows both silver bells and cockle shells, then we know that the number of square feet in her garden must be greater than ______.
Ch.15 Market Demand
15.5 The demand function for drangles is ( )

( p

1)

2
.
(a) What is the price elasticity of demand at price p ?________________
(b) At what price is the price elasticity of demand for drangles equal to -1?_______________
(c) Write an expression for total revenue from the sale of drangles as a function of their price.
__________ Use calculus to find the revenue-maximizing price. Don’t forget to check the second-order condition._____________
(d) Suppose that the demand function for drangles takes the more general form

( )

( p
 a )
 b
where a

0 and b

1 . Calculate an expression for the price elasticity of demand at price p .____________ At what price is the price elasticity of demand equal to
-1?_______
Ch.14 Consumer’s Surplus
14.8 F.Flintstone has quasilinear preferences and his inverse demand function for Brontosaurus
Burgers is ( )

30 2 b . Mr. Flintstone is currently consuming 10 burgers at a price of 10 dollars.
(a) How much money would he be willing to pay to have this amount rather than no burgers at all?__________ What is his level of (net) consumer’s surplus?________________
(b) The town of Bedrock, the only supplier of Brontosaurus Burgers, decides to raise the price from $10 a burger to $14 a burger. What is Mr. Flintstone’s change in consumer’s surplus?______
Ch.8 Slutsky Equation
8.6 Douglas Cornfield’s demand function for good x is ( x
, y
, )

2 m 5 p x
. His income is
$1,000, the price of x is $5, and the price of y is $20. If the price of x falls to $4, then his demand for x will change from ____ to ______.
(a) If his income were to change at the same time so that he could exactly afford his old commodity bundle at p x

4 and p y

20 , what would his new income be? ______ What would be his demand for x at this new level of income, at prices p

4 and x p

20 ?______ y
(b) The substitution effect is a change in demand from _____ to _____ The income effect of the price change is a change in demand from _____ to ______.
(c) On the axes below, use blue ink to draw Douglas Cornfield’s budget line before the price change. Locate the bundle he chooses at these prices on your graph and label this point A . Use black ink to draw Douglas Cornfield’s budget line after the price change. Label his consumption bundle after the change by B . y
80
0 320 x
(d) On the graph above, use black ink to draw a budget line with the new prices but with an

income that just allows Douglas to buy his old bundle, A . Find the bundle that he would choose with this budget line and label this bundle C .
Ch.9 Buying and Selling
9.15 Dudley’s utility function is ( , ) C (12

R )
2
, where R is the amount of leisure he has per day. He has 16 hours a day to divide between work and leisure. He has an income of $20 a day from nonlabor sources. The price of consumption goods is $1 per unit.
(a) If Dudley can work as many hours a day as he likes but gets zero wages for his labor, how many hours of leisure will he choose?_____
(b) If Dudley can work as many hours a day as he wishes for a wage rate of $10 an hour, how many hours will he choose to work? (Hint: Write down Dudley’s budget constraint. Solve for his labor supply. Remember that the amount of labor he wishes to supply is 16 minus his demand for leisure.)_________
(c) If Dudley’s nonlabor income decreased to $5 a day, how many hours would he choose to work?____________
(d) Suppose that Dudley has to pay an income tax of 20 percent on all of his income, and suppose that his before-tax wage remained at $10 an hour and his before-tax nonlabor income was $20 per day; how many hours would he choose to work?___________.