5. Labor Markets; Basic Probability Theory

Question 1

A local club plans to invest $10,000 to host a baseball game. If it doesn’t rain, they expect to sell tickets worth $15,000. But if it rains on the day of the game, they won’t sell any tickets. If the weather forecast for the day of game is 20% possibility of rain, is this a good investment?
a. Yes, because the expected profit is $2,000
b. No, because the expected profit is negative $5,000
c. Yes, because the expected profit is $3,500
d. No, because I have a hunch that it will rain
e. None of the above

Answer 1

a. Yes, because the expected profit is $2,000

Make a table of probability distribution. (see image)
Use the weighted average formula.
Expected  Value=5000(0.8)−10000(0.2)=4000−2000=2000
The club can expect a return of $2000.
So, it’s a good investment, though a bit risky.

Question 2

Suppose that Peter Quill accepts to pay $50 to buy a lottery ticket, which pays $0 with probability 0.5 and $80 with probability 0.5. Which of the below is correct with respect to Peter’s risk attitude with respect to this lottery?
a. It is consistent with him being risk averse.
b. It is consistent with him being risk neutral.
c. It is consistent with him being risk seeking.
d. None of the above.

Answer 2

c. It is consistent with him being risk seeking.
To determine Peter Quill’s risk attitude, we can calculate the expected value of the lottery.

Given:
- The cost of the lottery ticket ((C)) is $50.
- There are two possible outcomes with their respective probabilities and payoffs:
- Winning $0 with probability 0.5
- Winning $80 with probability 0.5

The expected value (E) of the lottery is calculated as follows:

E = P1 times X1 + P2 times X2

where:
* P1 and P2 are the probabilities of the respective outcomes,
* X1 and X2 are the payoffs associated with each outcome.

In this case:

E = 0.5 x 0 + 0.5 x 80
E = 0 + 40
E = 40

Now, compare the expected value ($40) with the cost of the ticket ($50).

Since the expected value is less than the cost of the ticket ($40 < $50), Peter Quill is expected to, on average, lose money by buying this lottery ticket. If Peter is willing to pay $50 for a ticket that, on average, results in a loss, it suggests he is willing to take a risk for the chance of winning a higher amount.

Therefore, this behavior is consistent with him being risk-seeking.

So, the correct answer is:
c. It is consistent with him being risk-seeking.

Question 3

You have a bag of marbles. There are 3 red marbles, 2 green marbles, 7 yellow marbles, 3 blue marbles, 4 orange marbles, 5 brown marbles, 8 white marbles, 4 grey marbles, and 2 black marbles. What is the probability of drawing something other than a red marble?
a. 0.0789
b. 0.3333
c. 0.9211
d. 0.9999
e. 1

Answer 3

c. 0.9211
To find the probability of drawing something other than a red marble, you need to determine the total number of marbles that are not red and then divide that by the total number of marbles.

Total number of marbles that are not red:
Green + Yellow + Blue + Orange + Brown + White + Grey + Black
2+7+3+4+5+8+4+2=352+7+3+4+5+8+4+2=35

Total number of marbles:
3+2+7+3+4+5+8+4+2=383+2+7+3+4+5+8+4+2=38

Probability of drawing something other than a red marble:
Number of marbles that are not red / Total number of marbles
35 / 38

So, the correct probability is 35 / 38, which is approximately 0.9211.

Therefore, the correct answer is:
c. 0.9211

Question 4

Suppose you own a condo that is worth $100,000. A blizzard is predicted to be coming in the next month with a 50% probability, which would reduce the value of your condo to $0. See graph.

Now suppose that the forecast is revised, and the probability of the blizzard is now 25%. The new expected value is
a. $18,000
b. $25,000
c. $50,000
d. $75,000
e. $100,000

Answer 4

d. $75,000
The expected value is calculated by multiplying the possible outcomes by their respective probabilities and then summing them up. In this case, there are two possible outcomes: the condo being worth $100,000 (with a probability of 75%) or the condo being worth $0 (with a probability of 25%).

Let’s calculate the new expected value:

Expected Value=(Probability1×Value1)+(Probability2×Value2)

Given:
Probability of no blizzard (P1): 75%
Value of the condo in the case of no blizzard (V1): $100,000
Probability of blizzard (P2): 25%
Value of the condo in the case of a blizzard (V2): $0

Expected Value=(0.75×100,000)+(0.25×0)

Expected Value=75,000+0

Expected Value=75,000

So, the new expected value of the condo is $75,000.

Question 5

If a firm is continually applying additional units of a variable resource to a fixed number of other resources (e.g., capital), and the firm’s output increases at a decreasing rate, then this indicates that
a. the firm is producing under conditions of decreasing returns to scale.
b. average fixed costs must be rising.
c. the firm should expand its plant capacity.
d. the firm is experiencing diminishing marginal returns.

Answer 5

d. the firm is experiencing diminishing marginal returns.
This scenario describes a concept in economics known as the law of diminishing marginal returns. The law of diminishing marginal returns states that if a firm keeps adding additional units of a variable resource (like labor) to a fixed amount of other resources (like capital), at some point, the marginal (additional) output of the variable resource will begin to decrease.

Variable and Fixed Resources:
The firm has a fixed quantity of one resource (e.g., capital) and is adding more units of another resource (e.g., labor).

Decreasing Marginal Returns:
Initially, as more units of the variable resource are added, the total output of the firm increases. However, the law of diminishing marginal returns asserts that as more units of the variable resource are added, the additional output (marginal product) from each additional unit of the variable resource will eventually start to decline.

Graphical Representation:
If you were to graph the relationship between the quantity of the variable resource and the firm’s output, you would observe a curve where the slope of the curve initially increases but then starts to decrease, indicating diminishing marginal returns.

Implications:
Diminishing marginal returns have important implications for production efficiency. Beyond a certain point, adding more units of the variable resource becomes less productive, and the firm may experience inefficiencies, increased costs, and a reduction in the overall productivity of the production process.