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I True or false. （2points*10）
1. If consumers spend all of their income, it is impossible for all goods to be
inferior goods.
2. A good is a luxury good if the income elasticity of demand for it is greater than
1.
3. If a rational utility maximizer is a net demander of a good, and if an increase in
its price causes him to buy more of it, then it must be an inferior good.
4. If there is a price increase for a good that Josephine consumes, her
compensating variation is the change in her income that allows her to purchase
her new optimal bundle at the original prices.
5. If there are constant returns to scale, then doubling the amount of any input will
exactly double the amount of output.
6. A competitive, cost-minimizing firm has the production function f (x ;y) = x +
2y and uses positive amounts of both inputs. If the price of x doubles and the
price of y triples, then the cost of production will more than double.
7. The short run industry supply curve can be found by horizontally summing the
short run supply curves of all the individual firms in the industry.
8. The marginal rate of transformation between two goods indicates the rate at
which an efficient economy would have to give up one good to obtain more of
the other.
9. For a monopolist who faces a downward sloping demand curve, marginal
revenue is less than price whenever quantity sold is positive.
10. A firm produces one output, using one input, with the production function f (x)
= 2x1/3where
is the amount of input. The cost function for this firm is
proportional to the price of the input times the cube of the amount of output.
11.
II Fill in the blanks for the following questions（2points*10）:
(1) Molly's utility function is U ( x, y)  y  4 x 5 . She has 25 units of x and 12 units of
y. If her consumption of x is reduced to 0, how many units of y would she need in
order to be exactly as well off as before?_____________________
(2) If the Engel curve slopes up, then the demand curve slopes
________________(down or up) .
(3) Sir Plus has a demand function for mead that is given by the
equation D( p)  100  p . If the price of mead is 65, how much is Sir Plus's net
consumer surplus? ___________
(4) An orange grower has discovered a process for producing oranges that requires
two inputs. The productions function is Q  min 2x1 , x2 where x1 and x 2 are
the amounts of inputs 1 and 2 that he uses. The prices of these two inputs are w1
= $2 and w2 = $4; respectively. The minimum cost of producing 80 units is
therefore ___________.
(5) In the town of Torrelodones, each of the N > 2 inhabitants has $100. They are told
that they can all voluntarily contribute to a fund that will be evenly divided among
all residents. If $F are contributed to the fund, the local K-Mart will match the
private contributions so that the total amount to be divided is $2F. That is, each
resident will get back a payment of $ 2 F
N
when the fund is divided. If people in
town care only about their own net incomes, in Nash equilibrium, how much will
each person contribute to the fund? ________________
III. Calculation (25 points)
John consumes only strawberries. He plans his consumption x = ( x 1, x2 ) of
strawberries
in two periods, where xt is his consumption in period t, t = 1, 2. He receives his
disposable
income I for these two periods at the beginning of period 1. The price of
strawberries in period
t is pt, t = 1, 2. While he cannot store strawberries from period 1 to period 2, he can
save a part
of his income I if he so wishes. The interest rate is r > 0, so if he saves the amount s
( 0≤s≤1 ),
then p1x1+s = I and p2x2 = (1+r)s.
1.
Write down the intertemporal budget equation for this decision problem ( in
terms of
x1, x2, p1, p2 and I, but without s). Draw a diagram of the corresponding
budget set. By drawing typical indifference curves, indicate how savings s* is
affected by a rise in the interest rate. In particular, discuss whether the
substitution and income effects on s* work in the same or opposite directions.
[Study these effects on x1* first, and then s*.] (10 points)
2.
John's utility function is u = a log x1 = b log x2, for some a, b > 0 such that a
+ b = 1.
Compute his consumption choice x1*, x2*, and saving decision s*. Use the
expression obtained for s* to compute its partial derivatives with respect to I,
p1, p2, and r, and discuss briefly the (economics of the) signs of these
derivatives. (15 points)
IV. Graphing and Analysis (35 points)
1. In an Edgeworth Box, depict the contract curve under competitive equilibriums. (10
points)
2. Depict the income effect and substitution effect of an non-Giffen inferior good,
under Hicks decomposition.
3. Graph to show that for a profit maximizing firm, what will the use of input x1, the
quantity produced y, and the profit change, corresponding to the following
circumstances: (you might need to briefly explain when graphing is inadequate)
a. the price of output increases.(5 points)
b. the price of fixed input x2 increases.(10 points)