## Description

**Solution Pages:** 11

**Files that you will download:**

Word (.docx) & Excel (.xlsx)

### Questions Covered in the Solution

1. Solve problems 4 (use the point formula for parts b, c, and d), 5, 7 (hint: for part a use

the arc price elasticitiy formula and for part b use the arc cross price elasticity one), 12

(use the arc formulas), 16, 17, 21 on pages 96-99 (7^{th}. Edition) of the textbook (on

pages 105-108 in the 6^{th} edition).

2. For the following demand function, Q_{D} = 100 – P, answer the following questions

- what is the point elasticity of demand at P = 80?
- what is the point elasticity of demand at P = 20?
- at what price is demand unitary price elastic?
- demand is price elastic for prices between __________ and ___________
- Consider your answer to part d., what happens to revenues as prices decrease within this range? Are marginal revenues positive, constant or negative in this range of prices?

- demand is price inelastic for prices between __________ and ___________
- Consider your answer to part f., what happens to revenues as prices decrease within this range? Are marginal revenues positive, constant or negative in this range of prices?

- How many units of this good does a firm facing this demand curve have to produce to maximize its revenues?

- What are maximum revenues for this firm?
- Draw the total revenue curve associated to this demand curve.

3. Assume three demand curves D_{1}, D_{2} and D_{3}, with corresponding price elasticities of demand of -0.3, -1.2 and -1.6, respectively. For which of these curves will a 1% increase in price result in an increase in **total revenue?**

- D
_{1}, D_{2}and D_{3} - D
_{1 }and D_{2} - D
_{2}and D_{3} - D
_{3 }only - D
_{1 }only

You have the following information on monthly income and quantities consumed of steaks, magazines, movies and pizzas for a consumer:

Quantity purchased per month

Monthly income Steaks Magazines Movies Pizzas

$ 2000 2 4 6 8

$ 3000 4 6 6 6

**Assume that all other variables (including the own prices of these goods) remain constant**.

- Calculate the income elasticity of demand for steaks
- Are steaks normal or inferior goods? Use the value of the income elasticity of demand for steaks to answer this question.
- Calculate the income elasticity of demand for movies
- Are pizzas normal or inferior goods? Use the value of the income elasticity of demand for steaks to answer this question.
- Suppose that the extended (generalized) demand function for good Y is:

Q_{d} ^{Y}= 250,000 – 500 P_{Y} – 1.5 M + 240 P_{X}

where: Q_{d} ^{Y }= quantity demanded of good Y

P_{Y} = Price of good Y

M = Average income of consumers

P_{X} = Price of related good X

- a) If M = $ 60,000 and P
_{X}= $100, what is the reduced demand function for good Y? - b) Continue using the reduced demand equation from part a,

**If M = $60,000, P _{X} = $100, and P_{Y} = $200** then

**Q**= ________

_{d}^{Y}**If M = $60,000, P _{X} = $100, and P_{Y} = $300** then

**Q**= ________

_{d}^{Y}Use this information (prices and quantities demanded of good Y) to calculate the price elasticity of demand between these two points on the demand curve of good Y. Show your work.

- c) Use your answer to part b. Between these two points on the demand for good Y, is demand elastic, inelastic or unitary price elastic? Why? What will happen to total revenues if price increases between these two points on the demand curve?
- d)
**In part b**, you found that when:

M = $60,000, **P _{X} = $100**, and P

_{Y}= $200 then

**Q**

_{d}^{Y}= ________Now let’s suppose that the **price of the related good X decreases from $100 to $50** but income remains constant (at $60,000). Assume that the price of good Y is also constant at $200.

If M = $60,000, **P _{X} = $50**, and P

_{Y}= $200 then

**Q**

_{d}^{Y}= ________

Use these prices of good X and the quantities demanded of good Y to **calculate the cross-price elasticity of the demand of good Y when the price of good X decreases from $100 to $50.**

- e) Consider your answer to part d. Based on the value of the cross-price elasticity of demand you just estimated, are goods X and Y substitutes, complements or unrelated? Why?
- f)
**In part b,**you found that when:

**M = $60,000**, P_{X} = $100, and P_{Y} = $200 then **Q _{d} ^{Y} = ________**

Now let’s suppose that consumer income **increases from $60,000 to $80,000** but the price of good X remains constant (at $100). Assume that the price of good Y is also constant at $200.

If **M = 80,000** , P_{X} = $100 and P_{Y }= $200 then **Q _{d} ^{Y}** = _________

Use these income levels and quantities demanded of good Y to **calculate the income elasticity of the demand for good Y when income increases from $60,000 to $80,000. **Show your work

- g) Consider your answer to part f. Based on the value of the income elasticity of demand you just estimated, is good Y normal, inferior or income independent?

### Sample of Solution

**Question # 01 Textbook Questions**

**(a) Intercept the equation**

The given demand equation explicit the relationship in which quantity demanded is a function of *Price *and *Income of individuals.* Quantity demanded is inversely related to price, as with every $ 1 increase in price the quantity demanded decreases by 10. Whereas, Quantity demanded is directly related to the income of individuals, as with every $ 1 increase in income, quantity demanded increases by 0.5.

**(b) At a price of 7, what is price elasticity?**

Since price elasticity of demand can be calculated as whereas is just the slope in demand function which is actually the coefficient of Price. So, in the given demand function the slope is -10. So the price elasticity would be as quantity demanded at price 7 and Y 50 is 55 (). So, price elasticity becomes – = -1.27

**(c) At an income level of 50, what is income elasticity?**

Income elasticity of demand is just the similar and can be calculated as where is the slope of Income variable in the demand function , that in this case is 0.5. So the income elasticity of demand would be = 0.45

**(d) Now assume income is 70. What is the price elasticity at P = 8?**

With income = 70 and Price = 8 quantity would be 55 (). And the price elasticity would be with as -10, as = – 1.45

**(a) At a price of $ 7, what is point elasticity?**

Given demand equation is , at price $ 7 the quantity would be 16. Whereas of is -2 as it is the coefficient of Price variable. So the point price elasticity of demand would be = – 0.875

…….

**Question # 02**

**(a) What is the point elasticity of demand at P = 80?**

Since demand function is the quantity demanded at price P = $ 80 would be 20 (). While putting the values in it becomes as . Thus point elasticity of demand is -4

**(b) What is the point elasticity of demand at P = 20?**

Quantity demanded at P = $ 20 is , 80. So the point elasticity of demand becomes as – 0.25

**(c) At what price is demand unitary price elastic?**

Point Elasticity to be unitary means it has the value – 1, so by using this equation we can find the price which make the price elasticity of demand as unitary. So, the price is $ 50 as

- 2P = 100
- P = $50

……….

**(c) Use your answer to part b. Between these two points on the demand for good Y, is demand elastic, inelastic or unitary price elastic? Why? What will happen to total revenues if price increases between these two points on the demand curve?**

The demand is price elastic as the value of Price Elasticity is -1.19. Whereas its impact on the total revenue can be realized by using the equation below

It can be realized from the above value that with the increase in price, the total revenue would be decreased between the two price points.

**(d) In part b, you found that when: **

**M = $60,000, P _{X} = $100, and P_{Y} = $200 then Q_{D} ^{Y} **

**If M = $60,000, P _{X} = $50, and P_{Y} = $200 then Q_{D} ^{Y}**

Cross-Price elasticity of demand can be calculated as by using the formula below

……

**(g) Consider your answer to part f. Based on the value of the income elasticity of demand you just estimated, is good Y normal, inferior or income independent?**

Income elasticity of demand can be calculated as

Since the income elasticity of demand is negative, the goods Y are inferior as their quantity demanded decreases with the increase in income.

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