Could someone please help me to asnwer these tw economics questions?
The following table shows the marginal benefits (MB) of consuming chocolate bars.
Chocolate Bars (unit) 1 2 3 4 5
MB $10 $8 $6 $4 $2
Suppose that the market price of chocolate bars is $7 per unit and you cannot buy a portion of a chocolate bar. How many chocolate bars should you buy?
b. Peter has a problem of mice. There are 100 mice going into Peter’s barn and they are eating the rice that Peter has stored in his bran. It is estimated that each mouse will cause Peter a damage of $10. The marginal cost of preventing a mouse from getting into his bran can be described by the following equation:
MC=0.125q, where q is the number of mice prevented.
Should Peter keep all the mice out of his bran? If not, how many mice should Peter allow to go into his bran?
To answer the economics questions:
1) How many chocolate bars should you buy?
To determine the optimal quantity of chocolate bars to buy, you need to compare the marginal benefit (MB) of consuming an additional chocolate bar to the market price of the chocolate bars. The rule of thumb is to continue consuming chocolate bars until the marginal benefit equals the market price.
In this case, the market price of chocolate bars is $7 per unit. Looking at the table, we can see that the marginal benefit reduces by $2 for each additional chocolate bar consumed. So, if the MB is greater than or equal to $7, it is worth buying that quantity of chocolate bar.
From the table, we can see that the MB for the first chocolate bar is $10, which is greater than $7. Therefore, it is worth buying at least 1 chocolate bar. However, the MB for the second chocolate bar is $8, which is less than $7. So, you should not buy the second chocolate bar.
Therefore, you should only buy 1 chocolate bar.
2) Should Peter keep all the mice out of his barn?
To determine whether Peter should keep all the mice out of his barn, we need to compare the marginal cost (MC) of preventing a mouse from entering with the damage caused by each mouse.
The given equation represents the marginal cost of preventing mice from getting into the barn: MC = 0.125q, where q is the number of mice prevented.
On the other hand, each mouse causes a damage of $10 to Peter.
To decide whether Peter should keep all the mice out of his barn, we need to find the point where the marginal cost of preventing a mouse equals the damage caused by a mouse.
Setting MC equal to the damage, we have:
0.125q = $10
Solving for q:
q = $10 / 0.125
q = 80
So, Peter should allow up to 80 mice to go into his barn because it would cost him less to prevent 80 mice ($10) than the damage caused by each mouse.
To answer the first question, we need to determine the quantity of chocolate bars that should be bought. The principle of rational decision-making suggests that the optimal quantity to purchase is where the marginal benefit (MB) is equal to the market price (P).
From the given table, the marginal benefits (MB) of consuming chocolate bars are as follows:
Chocolate Bars (unit) | MB ($)
--------------------------------------
1 | $10
2 | $8
3 | $6
4 | $4
5 | $2
Given that the market price of chocolate bars is $7 per unit, we need to find the quantity at which the MB is equal to $7.
Comparing the marginal benefit (MB) with the market price (P), we can create a decision rule as follows:
- If MB > P, buy the chocolate bar.
- If MB < P, do not buy the chocolate bar.
Using this decision rule, we can determine how many chocolate bars should be bought:
1. For the first chocolate bar, the MB ($10) is greater than the market price ($7). Therefore, it is beneficial to buy the first chocolate bar.
2. For the second chocolate bar, the MB ($8) is still greater than the market price ($7). Therefore, it is beneficial to buy the second chocolate bar.
3. For the third chocolate bar, the MB ($6) is still greater than the market price ($7). Therefore, it is beneficial to buy the third chocolate bar.
4. For the fourth chocolate bar, the MB ($4) is less than the market price ($7). Therefore, it is not beneficial to buy the fourth chocolate bar.
5. Similarly, for the fifth chocolate bar, the MB ($2) is less than the market price ($7). Therefore, it is also not beneficial to buy the fifth chocolate bar.
Based on this analysis, you should buy three chocolate bars, as it is the quantity at which the MB is equal to the market price.
Moving on to the second question, we need to determine how many mice Peter should allow to go into his barn. The marginal cost of preventing a mouse from entering the barn can be described by the equation MC = 0.125q, where q is the number of mice prevented.
Given that there are 100 mice going into Peter's barn, and each mouse causes a damage of $10, we need to compare the marginal cost (MC) of preventing a mouse from entering with the damage caused by the mouse.
To find the optimal quantity of mice to allow, we need to compare the marginal cost with the damage caused for different quantities of mice allowed:
1. For preventing the first mouse (q = 1), the marginal cost (MC) is 0.125 * 1 = $0.125.
The total damage caused by the mouse is $10 * 1 = $10.
As the marginal cost is significantly less than the damage caused, it is beneficial to prevent the first mouse.
2. For preventing the second mouse (q = 2), the marginal cost is 0.125 * 2 = $0.25.
The total damage caused by 2 mice is $10 * 2 = $20.
Again, the marginal cost is less than the damage caused, so it is still beneficial to prevent the second mouse.
We can continue this analysis for different quantities of mice prevented and compare the marginal cost with the damage caused.
The optimal quantity of mice to allow into the barn will be where the marginal cost is equal to the damage caused.
Please provide the specific equation for the MC (marginal cost) if you have it, and we can continue the calculation to determine the optimal quantity of mice Peter should allow in his barn.