ECO 305 Assignment 1

| March 14, 2016

Assignment 1
1. If the price level yesterday was P0 = 8 and today it is P1 = 13, calculate the
percentage change of prices between yesterday and today.
2. Calculate ?y
?k ,
?y
?l and ?y
?A for the following functions (if the function does not
depend on k, l or A just calculate the other derivatives):
y = Ak?
l
1??
y = Ak 1
3 l
2
3
y =
?
k
y = l
3 + 4k
4
y = 2k
3 ? l
2
y = 2k
5 + 3A + 40
3. Simplify the following expressions (for example x
2x = x
3
):
x
1
3 x
1
5 x
1
8 =
(x
3x
4
)
2
8 =
x
3
x
4x
7
=
?k??1
l
1??
k =
(1 ? ?)k
?
l
??
l =
1
4. Solve each of the following equations for x:
5x ? 2x = 6x + 7
?
x = 8
x
2 = 36
x
1
3 = 3
x
3 = 27
0.1x
1
2 = 0.7x
2x
? 1
3 = 0.2
0.78x = 0.78x
1
3
0.2x
?0.8 = 0.25
5. Find the maximum or minimum of the following functions, and identify
whether it is the maximum or the minimum using second derivatives.
y = 3x
2 ? 5x
y = 2x
1/2 ? x
(Hint: Find x
? and y
?
such that the slope is 0)
6. Plot the following functions showing clearly at least two points for each
y = 2x + 7
y = x
2 ? 2x + 3
7. Let Qd and Qs denote the demand and the supply for pizza respectively.
Also let P be the price of a pizza. Assume that
Q
d = 85 ? 5P
Q
s = 3P + 70
Find the market clearing price P
?
. How many pizzas are actually sold at this
price?
2

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