Question

11. a. Suppose David spends his income M on goods x1 and x2, which are priced p1 and p2, respectively. David’s preference is given by the utility function

?(?1, ?2) = √?1 + √?2.

(i) Derive the Marshallian (ordinary) demand functions for x1 and x2.

(ii) Show that the sum of all income and (own and cross) price elasticity of demand

b.for x1 is equal to zero. b. For Jimmy both current and future consumption are normal goods. He has strictly convex and strictly monotonic preferences. The initial real interest rate is positive. If the real interest rate falls, in each of the following cases, argue what will happen to his period 2 consumption level? Clearly illustrate your argument on a graph.

(i) He is initially a borrower.

(ii) He is initially a lender.

Answer #1

A consumer’s preferences over two goods
(x1,x2)
are represented by the utility function
ux1,x2=5x1+2x2.
The income he allocates for the consumption of these two goods is
m. The prices of the two goods are p1
and p2, respectively.
Determine the monotonicity and convexity of these preferences
and briefly define what they mean.
Interpret the marginal rate of substitution
(MRS(x1,x2))
between the two goods for this consumer.
For any p1, p2,
and m, calculate the Marshallian demand functions of
x1 and...

Andrew’s utility function is U(x1,
x2) = 4x21 +
x2. Andrew’s income is $32, the price of good 1
is $16 per unit, and the price of good 2 is $1 per unit. What
happens if Andrew’s income increases to $80 and prices do not
change? (Hint: Does he have convex preferences?) *show work***
1. He will consume 48 more units of good 2 and the same number
of units of good 1 as before.
2. He will increase his...

2. Jerome consumes only two goods, eggs and beans. His
preferences are complete, transitive, monotonic and convex. When
the price of beans rises, he buys fewer eggs and the same amount of
beans. Based on this information, we can say that
a. Beans are necessarily normal and eggs are necessarily
inferior. b. Beans are necessarily inferior and eggs are
necessarily normal. c. We can only conclude that beans are
necessarily normal. d. We can only conclude that eggs are
necessarily...

1. In the short-run IS-LM model with income taxation, taxes are
given by ?=? +??. Suppose that MPC = 0.75 and the marginal tax rate
?=0.2. Then, when ? decreases by 1000, then for any given interest
rate, the IS curve shifts:
Select one:
a. to the left by 1000.
b. to the right by 3000.
c. to the right by 3750
d. to the right by 1875.
2.
Suppose that the adult population in an economy is 28 million,...

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