Suppose that in the US beer industry, there are two differentiated products: regular beer (e.g. Bud) and premium beer (e.g. Guinness). Consider the market for regular beer.

1. A demand curve for regular beer shows the relationship between the quantity demanded and its price holding all-else-constant. Many factors other than price influence the demand for regular beer; please list five of them (not in question 2), and explain how they affect demand.

i) The consumers level of income

The demand for regular beer depends with the level of income of the consumers; greater income among the consumers will lead to high regular beer sales (or increase in quantity demanded), while reduced consumer incomes will lead to less regular beer sales (or decrease in quantity demanded).

Arguably, greater income among the regular beer- takers means that they have a greater purchasing power. Therefore, their ability to buy more of the beer increases with increase in income (an increase in income has a positive effect on demand for regular beer).

On the other hand, their ability to purchase decreases with any reductions in the consumers' income levels.

ii) Effects of advertisements

A product is advertised so as to promote its sales. Adverts inform consumers of the presence of new product in the market, or improvement in quality of the existing one. It will inform the consumers about the price, quality, and quantity of regular beer. Some of the Medias used are the newspapers, televisions, radios, etc. Adverts are crucial factors affecting demand for regular beer. That is, more adverts means increased conviction about the product, thus increased demand, while less adverts means low conviction of the product thus decrease in demand.

Arguably, consumers may lose interest for regular beer if it is not adequately publicized: due to lack of information about the quality, quantity, price, and benefits of regular beer.

iii) Changes in tastes and preferences among the consumers

This is an important factor that determines the demand for regular beer. There is increased demand when the taste and preference is greater among the consumers.

Improved taste or preference for regular beer among the consumers is affected by increase in adverts. Also, lack of taste or preference may fall if the advert levels are low. Additionally, a change in preference or taste may mean that the regular beer is out of fashion (there are other new brands in the market). Therefore, it is advisable to constantly improve the quality of regular beer so as to improve its taste and preference among the consumers. This will lead to increased demand.

iv) Change in price for a related product

The demand for regular beer is determined by other related product (premium beer). In this case, premium beer is a substitute of regular beer. This implies that a fall in price for premium beer will lead to decrease in demand for regular beer.

This is due to the fact that consumers will turn to premium beer (due to its reduced prices), and buy less of regular beer (which is at constant and high price). Thus, a decrease in price of a substitute negatively affects the demand for the other good.

On the other hand, demand for regular beer will increase if the price for premium beer is increased. Assuming that the price for regular beer is constant, it then implies that consumers will demand more of that product and demand less of premium beer (which has increased prices).

v) The number of consumers available in the market

The number of consumers in the market determines the amount of regular beer demanded. More consumers would mean increased willingness and ability to buy, while fewer consumers would mean decreased willingness and ability to buy. For example, a regular beer point located in the midst of a big city will experience more sales than the one situated in the outskirts of the city. This implies that more consumers in the city will lead to increased demand of the product compared to fewer consumers in other remote areas.

2. For our simple model, suppose that the quantity of regular beer demanded per year (Q) is a function of the price of regular beer (p), the price of premium beer (p'), the temperature (t), and the income of consumers (Y): Q = D (p, p', t, Y). Quantity demanded is in billions of 2.25- gallon cases and prices are per 2.25-gallon case. Specifically, assume that the demand function for regular beer is:

Q = 1.25 - 0.25 p + 0.05 p' + 0.025 t + 0.05 y

If the average price of premium beer this year is $30 a case, the average temperature is 60°F, and the average income is $15 in thousands of dollars per year, rewrite the quantity demanded of regular beer as a function of its price only

Solution

Q = 1.25 - 0.25 p + 0.05 p' + 0.025 t + 0.05 y
Since p'= $30, t= 600F, and Y= $15
Then, Q= 1.25- 0.25p + 0.05(30) + 0.025(60) + 0.05(15)
Thus, Q= 5- 0.25p

3. Based on the demand function you just derived, what is the change in the quantity demanded of regular beer (in billions of cases) associated with a $1 increase in the price of a case of beer?

Solution

Q0= 5- 0.25p
Q1= (5- 0.25p) + 1,

Thus, Q1= 5- 1.25p

Change in quantity demanded is determined by Q1- Q0

That is, (5- 1.25p) - (5- 0.25p) = -1

The answer is -1, implying that the quantity demanded decreases when price increases by $1 per case

4. Rewrite the demand function as an inverse demand function. By how much must the price decrease for consumers to purchase an additional 1 billion cases of beer per year?

5. Suppose that the supply of regular beer is Q = 0.5 + 0.35 p. Solve for the market equilibrium (i.e. the price and quantity such that quantity supplied equals quantity demanded). Continue to consider the US beer industry. There are two types of beer (regular and premium) and we assume that these markets are perfectly competitive (a single price in each market).

6. In the market for regular beer, suppose that there are two suppliers: Kors and Vud. The individual supply functions for Kors (K) and Vud (V), using the same units, are as follows: QK = 0.4 + 0.20 p Qv = 0.1 + 0.15 p. What is the market (total) supply function (Q = S (p)) for regular beer?

7. Again, the market demand function for regular beer is given by Q= 1.25- 0.25 p + 0.05 p' + 0.025 t + 0.05 Y. If the average temperature last yearwas60°Fandthe average income was $15(thousand), rewrite the demand function so that the quantity demanded only depends on the price of regular beer (p) and the price of premium beer (p').

8. Using the market supply function you obtained in Question 6 and the simplified market demand function from Question 7, find the reduced-form relationship between the price of regular beer (p) and the price of premium beer (p') at equilibrium.
(To check that you get the right answer, you can plug in the average price of premium beer (p'=$30) and verify that you get the same equilibrium price as for Question 5.)

9. By how much would the price of a case of regular beer increase if the price of a case of premium beer increases from $30 to $35?

10. Using your answer to Question 7 and an average price of premium beer of $30 a case (p'= $30), rewrite the demand function so that the quantity demanded is only a function of price (Q = D (p)) (you should obtain the same answer as for

Question 2). What is the slope of the demand function (AQ/Ap)? Ifthepriceofregularbeeris$10acase, what is the price elasticity of demand (c)? If the price of regular beer is $5 a case, what is the price elasticity of demand? Why does the (point) price elasticity vary?

11. Using the full market demand function and the typical values of p=$7.50,p'=$30,t=60°, and Y = $15, answer the following questions:

a.) What is the income elasticity of demand?

b.) Is regular beer a normal good or inferior good? Why?

c.) What is the cross-price elasticity of demand (w.r.t. premium beer)?

d.)Is premium beer a substitute or complement of regular beer? Why?

12. Using the market supply function obtained in Question 6, if the market price of regular beer is $7.50 a case (p= $7.50),

what is the price elasticity of supply (p)? Compare the price elasticity of supply to the price elasticity of demand at this point.

What is your intuition behind these numbers?