Exam I

Use Table 1 for questions 1-3. This is a revision for equation of a line. Consider the following two variables “X” and “Y.”

X	Y
20	60
22	64
24	68
26	72
28	76
30	80
32	84
34	88
36	92
38	96
40	100

Table 1. $~$

We are concerned with expressing y, as y = mx + c, where y and x are the “Y” and “X” variables, respectively; m is the slope, and c is the y intercept.

Find m and c.

m = 2, c = 20
m = 2, c = 24
m = 4, c = 20
m = 20, c = 2

Write down the equation of the line describing the relationship between “X” and “Y” and plot the line on a graph.

$y = 2x + 24$
$y = 2x + 40$
$y = 2x + 20$
$y = 2x$

Now say that “Y” is increased by 20. So, basically you are adding the Column “Y” with 20. How would this affect the equation of the line b? Plot the new line along with the one you have for part b.

$y = 2x + 24$
$y = 2x + 40$
$y = 2x + 20$
$y = 2x - 20$

Now consider a new set of “x” and “y” points, whose relationship is depicted in Figure 1.

Figure 1.

$~$ Draw a tangent line across point A. Calculate the slope of a tangent line that goes across the point A (its a straight line that goes across A).

2
-2
0
100

Consider the following production schedule for questions 5-8.

name	Production if 100% of time is spent on one good
Greta	1,250 apples or 50 tonnes of wheat
Carlos	1,000 apples or 20 tonnes of wheat

Draw the production possibility frontier (ppf) for Greta and Carlos. What is true about the ppf.

The slope of the ppf increases as we move to the right of the ppf.
The slope of the ppf is positive.
The slope of the ppf is constant and negative.
The slope of the ppf is constant and positive.

The opportunity cost of producing 1 apple is ___________ tonnes of wheat for Greta.

6
$\frac{1}{6}$
$\frac{1}{20}$
$\frac{1}{25}$

The opportunity cost of producing 1 apple is ___________ tonnes of wheat for Carlos.

$\frac{1}{50}$
$\frac{1}{6}$
$\frac{1}{20}$
$\frac{1}{25}$

Based on your wers for 7. and 8., you can tell that

Carlos has comparative advantage in apples
Carlos has comparative advantage in wheat
Carlos has absolute advantage
none of the above

Consider the following technological options (Table 2) to make 100 meters of cloth for questions 9-13.

Technology option	Number of workers	Coal required (tonnes)
A	1	6
B	4	2
C	3	7
D	5	5
E	10	1

Table 2.

$~$ 9. The price per worker is $20 and price per ton of coal is $10. What technological option is the most efficient one given this cost layout.

both A and C
B
E
A

Which of the following is FALSE

option A dominates C
option B dominates D
option E dominates C
options C and D are irrelevant at any costs

Note that isocost is a curve that shows various combination of technology (coal and workers) with the same exact cost. Write the cost equation in the form \[c=w\times L+p\times R\]. Here, $c$ is the total cost of your most efficient option from part b, $w$ is price per worker (per hour), $L$ is the number of workers, $p$ is price per ton of coal and $R$ is tons of coal.

$80=20R + 10L$
$c=20L+10R$
$80=20L$
$80=20L+10R$

Using the equation in part 11., express the equation in the form as \[R=...\].

$R=8L+8$
$R=-2L+8$
$R=2L$
$R=20L+20$

From the isocost equation in 13. as labor increases ____________

cost increases as it increases the labor expenses.
tonnes of coal used decreases but the cost still increases.
tonnes of coal used decreases and the cost remains the same.
both tonnes of coal and cost remains the same

See the following figure:

Figure 2.

From the Figure 2 above, what can we conclude? Pick among four choices that you think are correct.

Technology B is more energy-intensive than technology A.
Technology B dominates technology A.
Technology A is more energy-intensity than technology B.
Technology A is the cost-minimizing technology at all prices of coal and wages.

Looking at the isocost lines in Figure 2, we can conclude that

When the wage is $10 and the price of coal is $5, the combination of inputs at point N is more costly than the inputs at point B.
Isocosts MN and FG represent the same price ratio (wage/price of coal) but different total costs of production.
Isocost HJ represents a higher (wage/price of coal) ratio than isocost FG.
Isocost HJ represents all points that can produce 100 metres of cloth at a particular price ratio.

$~$

Use the following table for questions 16-19. See the relationship between the number of labors and grain:

labor	grain
200	20000
400	33000
600	42000
800	50000
1000	57000
1200	63000
1400	68400
1600	73200
1800	77400
2000	81000
2200	84000
2400	86400
2600	88200
2800	89400
3000	90000

Table 3.

The production process given by the schedule above (labor is input)

is a straight downward sloping line
is a straight upward sloping line
a curve that flattens out as labor grows
a curve that increases in slope as labor grows

The average product of labor when labor is 200 is ___________.

The MPL of an additional labor when moving from 800 labors to 1000 labors is ___________.

700
1000
70
35

Which of the following is true regarding the production process.

The MPL increases as labor grows
The MPL decreases as labor grows after a point.
The MPL is constant.
The MPL can never be zero.

Use the following table (Table 4) for questions 20-23. You are in process of preparing for your upcoming exam. The production process between hours spent studying (input) and your exam score can be mapped by the following empirical production process.

hours study	exam score
0	0
1	30
2	46
3	55
4	62
5	67
6	71
7	75
8	77
9	81
10	83
11	85
12	87
13	89
14	90
15	90
16	90

Table 4

In a separate column, calculate the average product per hour you spend studying. According to your calculation, in this schedule

APL first increases and eventually falls with hours you spend studying
APL first falls and eventually increases with hours you spend studying
APL first increases with hours you spend studying
APL falls with increment in hours you spend studying

In another column, calculate the marginal product per additional hour you spend studying. You can see that the

marginal product falls with increase in hours spent studying
marginal product rises with hours
after the $15^{th}$ hour, the marginal product is zero
both a and c

The relationship between the marginal product (per additional hour you spend studying) and the average product is such that

as the marginal product is higher than average product, it pulls the average up
as the marginal product is lower than average product, it pulls the average up
the marginal product can never be greater than average product
the marginal product can never be negative

Based on the information given in Table (the empirical production function), which of the following is true?

The marginal product is greater than the average product for the first hour.
The marginal product is zero but the average product keeps decreasing beyond the $15^{th}$ hour.
Slope of the production function is never equal to zero.
The average cost can rise even if the marginal cost falls.

What is the marginal rate of substitution (MRS)?

The ratio of the amounts of the two goods at a point on the indifference curve.
The amount of one good that the consumer is willing to trade for one unit of the other.
The change in the consumer’s utility when one good is substituted for another.
The slope of the indifference curve.
both b and d.

Consider that you care about both your score and your leisure time. Say your preference set between exam score and leisure is as follows:

	A’	B’	C’	D’	E’	F’	G’	H’	I’
Final Score	79.5	80	81	81.8	83	85.5	88.5	91.5	94.5
Free Time	20.0	18	16	15.0	14	13.0	12.0	11.0	10.0

Note that you are indifferent between any of these points – each point gives you the same level of happiness. Calculate the marginal rate of substitution when you move from preference A’ to B’.

-4
4
0
$-\frac{1}{4}$

Exam I

Please note your answers on blackboard online scantron. I won’t be accepting emailed answers.

9/24/2020