Econowaugh AP: AlL Utility FRQ's

ALL Utility FRQ's

2019 AP Microeconomics Exam

(A.) Dana's Total Benefit from purchasing 2 bottles of water & 1 unit of good X?

Total Benefit = Marginal Benefits added

So 2 bottles of water = 24 + 18 = $42
1 unit of Good X = $24

Total Benefit = $42 + 18 = $66

(B.) Assume the price of unit X is $5. Calculate the total consumer surplus if Dana purchases 3 units of Good X.

Consumer Surplus is the area under the Demand curve but above the Price.

The Price ($5) must be subtracted from the Marginal Benefit
Unit 1 = MB of 24 - 5 = $19

Unit 2 = MB of 18 - 5 = $13
Unit 3 = MB of 12 - 5 = $7

Total Consumer Surplus = $19 + $13 + $7 = $39

(C.) Assume the price of bottled water is $3, and the price of Unit X is $6. Dana spends her entire budget of $30.

(i) Explain why Dana does not maximize her benefit (Utility) when she purchases 2 bottles of water and 4 units of good X. Use marginal analysis to explain.

The MB per dollar spent is equal to 6 with the second bottle of water
while the MB per dollar spent for the 4th X is 1
We want then to be equal
where
The Marginal Benefit per dollar spent are Equal

(ii) What are the optimal quantity of water and X?

After dividing all of the MB by the prices of the good
we can see that the MB of the 4th bottle of water is 2 per dollar spent
and the MB per dollar spent of Good X = 2
If we add up the prices of 4 bottles of water and 3 units of Good X = $30 = Dana budget

(iii) Price of Good X falls to $3, calculate Dana's cross price elasticity.
Complements or Substitutes?

Price of X falls to $3

Notice, that when the Price of Good X falls to $3
The MB (per dollar spent) on Water will equal the MB (per dollar spent) on Good X
her $30 income is all spent with the purchase of 5 bottles of water & 5 units of Good X

As the price of Good X decrease to $3
then we buy more water

If the P decreases of one good and the demand increases for the other good
the goods are complements

Think tea and sugar
If the price of Tea falls more people will drink tea,
therefore the demand for sugar will increase
Complements

2018 AP Microeconomics Exam

(A.) Nirali spends 3 hours studying macro and 2 studying history, calculate the gain she has the second hour studying history.

First, we should recognize that the Expected Score is the expected Output (grade) gained by studying a certain number of hours. For instance, if I study one hour my expected score will be a 40 on the exam, and if I study an additional hour (2) I'll add 20 points to my score. My marginal score from 1 hour studied to 2 hours studied is 20. I gained 20 points by studying and extra hour.

(B.) Calculate Nirali's opportunity cost of the second hour spent studying history.

(C.) Nirali studies more history, what happens to the opportunity cost of studying more history?
Explain.

We would assume that opportunity cost would increase. Her Opportunity cost (what she gives up) by studying more history is a worse score in Micro.

(D.) Nirali wants to maximize her test scores, how many hours should she study for each exam?

Remember she only has a total of 5 hours to study.

It's clear by looking at the marginal gains, that the best choice is 3 hours of history and 2 hours of Micro.

At 3 hours of history and 2 of micro we gain a total score (utility) of 72 + 82 = 154

At 2 hours of history and 3 of micro we gain a total score (utility) of 60 + 90 = 140

At 4 hours of history and 1 of micro we gain a total score (utility) of 77 + 60 = 137

(E.) Nirali finds out that tennis practice is cancelled giving her an additional hour to study. Will she study history or economics, explain using marginal analysis.

The 3rd hour of micro gains her 8 points while the 4th hour of history only gains her 5 points.

8 > 5 so choose the additional hour of micro.

2016 AP Microeconomics Exam

(A.) What is Martha's marginal benefit of the fifth unit of good X?

At a quantity of 0, we haven’t purchased any units so there is no marginal benefit.

As we purchase from 0 quantity to the first unit of X, we gain a marginal benefit of $16.

As we purchase from the first to the second unit of X, we gain a marginal benefit of $12.

As we purchase from the second to the third unit of X, we gain a marginal benefit of $8.

As we purchase from the third to the fourth unit of X, we gain a marginal benefit of $4.

As we purchase from the fourth to the fifth unit of X, we gain a marginal benefit of $1.

Think of marginal as meaning the next purchase. Obviously we can only purchase full units, so when we have 4 units purchased our next marginal purchase is the 5^th one and we receive a marginal benefit of $1 from the additional/marginal purchase of that 5^th unit.

(B.) Calculate the total consumer surplus if Martha consumes 5 units of X.

Remember, that consumer surplus is the additional value gained from consumption of a good subtracting what has been paid for that good.

Answer - Total Consumer Surplus = $12 + $8 + $4 + $0 + $ -3 = $21 of Total Consumer Surplus

· Understand that the $4 Cost is also part of the benefit. Confusing at first, but understand that if I give you $4 for unit X then unit X is still worth $4, at least to me.

(C.) Martha is consuming 4 units of X and 2 units of Y, use marginal analysis.

This combination of Units X and Units Y are not optimal as the marginal benefit gained from purchasing units X and Y is not equal.

We are use to seeing these problems as Utility problems and recognizing that the Marginal Benefits and Marginal Utility formula’s are the same.

(D.) What is Martha's combination of X and Y.

1^st – using the formula set the two goods equal by using the formula above. Table is helpful. (:

2^nd – Martha chooses her purchases according to the greatest benefit gained with each purchase.

3^rd – Martha purchases until her income is all spent.

(E.) Indicate how each of the following will cause the optimal quantity if good Y?
(I) The price of good Y doubles.

If the benefit per unit of Y decreases, then we would purchase less of the good. Martha’s first purchase would have been X as the benefit is 4, which is greater than the benefit of 2.5 for a unit of Y.

(ii) Martha’s income falls to $10 with no change in prices.

If Martha’s income falls to $10, then she will not be able to purchase 4 units of good Y.

She will purchase the first 3 units of good X & Y exactly the same way, but then she has spent $8 and only has $2 left, so she will then only be able to purchase a unit of Y.

So 1 unit of X and 3 units of Y will be purchased, this will use all of her income. The question above asks if the optimal quantity of good Y will decrease, increase, or stay the same.

Originally Martha, with $20 of income bought 4 units of good Y, so her purchase of good Y has decreased.

(iii) Martha’s income doubles and the price of both goods double.

The answer to this question should be intuitive in that if Martha’s income doubles and all goods prices double then Martha is no better off with a doubling of her income as the ratio of prices to incomes are the same.

3 units of X at $8 each is $24 spent and 4 units of Y at 4 each is $16 and $24 + $16 = $40

Martha has spent $40 (all) of her income and bought the same combination of goods X & Y.

Answer - No change in optimal combination of goods X & Y.

2012 AP Microeconomics Exam

(A.) The table above shows Theresa's marginal utility from bagels and toy cars.
(i) What is here total utility from purchasing three toy cars?

So simple it's easy to get wrong... overthinking again?

3 toy cars (10+8+6) = 24 utils

(ii) Theresa's weekly income is $11, the price of a bagel is $2 dollars, and the price of a toy car is $1.

What quantity of bagels and toy cars will maximise Theresa's utility if she spends her entire weekly income on bagels and toy cars?

Explain using marginal analysis.

First, you must know the formula..

If you get to a place where both purchases have the same utility then you will be indifferent,, either one will do as long as you have cash to spend.

Using Marginal Analysis

MU/PB = 6/2 = 3 and MU/PTC = 3/1 = 3

the marginal utility per dollar spent on bagels equals the marginal utility per dollar spent on toy cars.

Answer - One point is earned for stating that three bagels and five toy cars will be purchased.

Using Marginal Analysis

MU/PB = 6/2 = 3 and MU/PTC = 3/1 = 3

(B.) Assume that the price of wheat, an input for the price of bagels, increases. Will Theresa's demand for bagels increase, decrease, or remain unchanged. Explain.

Remember, that input prices affect suppliers of a good,, not demanders.. So, Theresa will not change her demand for bagels if the price of wheat increases.

(C.) Suppose that Theresa's income elasticity for bagels is -0.2. Does the value of Theresa's income elasticity indicate that bagels are a normal good, inferior good, substitute, or compliments?

If YED is a negative -0.2

that implies that as Theresa's income increases

then the quantity of bagels decreases

(D.) Suppose the price of toy cars increase by 10%. Theresa buys 5% fewer toy cars and 4% less of a different toy, blocks. Calculate the cross-price elasticity for toy cars and blocks, and indicate if it is positive or negative.