Question

    31. The following is the annual demand function for good A:

                Q_DA = 400 – 20P_A + 10P_B + 0.01Y

where P_A is the price of good A; P_B is the price of another good, good B; Y is income.

1. Is good A a normal good or an inferior good? Explain.
   
2. Is good B a complement or a substitute for good A? Explain.
   

Assume that the current price of good B is £5, income is £50 000, and the annual supply function for good A is:

                Q_SA = 100 + 10P_A

3. Calculate the equilibrium price and quantity.

4. Calculate price elasticity of demand if the price of good A rises by £5 from the equillibrium price and the demand decreases by 7% and what does this show about the product ?

5. Calculate the price elasticity of supply if the amount supplied increases by 26.60 units (from the equillibrium) and this results in a decrease in price of 4%. Suggest what this figure shows              

Answer 1

QDA = 400 – 20PA + 10PB + 0.01Y

where PA is the price of good A; PB is the price of another good, good B; Y is income and QDA is annual demand for good A

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A. We can see that Demand for A and Price of A have a negative relation .This means that Demand for A increases with a fall in its price and decreases with a rise in its price

Demand for A and income have a positive relation which means the demand increases with a rise in income and decreases with a fall in income.

Thus we can say that A is a normal good because inferior goods have a negative relationship with income.

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B. There is a positive relationship between Demand for A and Price of B. This means that A and B are substitutes.

When Price of B rises, it demand falls because it gets substituted with more of A and thus the demand for A rises.

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Demand and supply equilibrium is based on law of demand and supply respectively. This means that all factors other than price must be constant

the current price of good B is £5, income is £50 000

So QDA will become

QDA=400 – 20PA + 10*5 + 0.01*50000

QDA= 400-20PA+50+500=950-20PA

Supply function is given as

QSA= 100+ 10PA

At equilibrium, demand= supply

This implies 100+10PA= 950-20PA

PA=(950-100)/30= 28.33

When PA=28.33

QDA = 950-20(28.33)=383.4

So we can say that equilibrium price is 28.33 pounds and equilibrium quantity is 383.4 units Approximately

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Price elasticity of demand= percentage change in quantity demanded/ percentage change in price

percentage change in quantity demanded= 7

percentage change in price= (change in price/ original price)*100= (5/28.33)*100=17.65

Price elasticity of demand= 7/17.65=0.397

This shows that price elasticity of demand for the good A is 0.397 which relatively price inelastic and thus the demand for the A does not respond much to any price change.

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Price elasticity of supply= percentage change in quantity supplied/ percentage change in price

percentage change in quantity supplied= (change in quantity supplied/ original supply)*100= (26.60/383.4)*100=6.94

percentage change in price= 4

Price elasticity of supply= 6.94/4= 1.735

This shows that the price elaticity of supply is 1.735 which is highly elastic which means that the proportion change in quantity supplied more than a proportionate change in the price

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