# ECN 502

**Topics:**Supply and demand, Elasticity, Price elasticity of demand

**Pages:**5 (1168 words)

**Published:**November 5, 2013

1) Problem 6: Suppose demand and supply are given by Qd = 60 – P and Qs = P – 20. a) What are the equilibrium quantity and price in this market? b) Determine the quantity demanded, the quantity supplied and the magnitude of the surplus if a price floor of $50 is imposed in this market. c) Determine the quantity demanded, the quantity supplied and the magnitude of the shortage if a price ceiling of $32 is imposed in this market.

Solution:

a. For the equilibrium

i) Price: Qd = Qs

60-P=P-20 => P= $40.

ii) Quantity: Equilibrium quantity can be found substituting the value of P found in (i). Q = 60-40 = $20

b. i) Quantity Demanded = Qd= 60-50= 10

ii) Quantity supplied = Qs= 50-20 = 30

iii) Magnitude of surplus = Qs- Qd = 30-10 = 20

c) i) Quantity Demanded = Qd= 60-32= 28

ii) Quantity supplied = Qs= 32-20 = 12

iii) Magnitude of surplus = Qd- Qs = 28-12 = 16

2) Problem 11: You are the manager of a midsized company that assembles personal computers. You purchase most components-such as random access memory (RAM) – in a competitive market. Based on your marketing research, consumers earning over $80000 purchase 1.5 times more RAM than consumers with lower incomes. One morning, you pick up a copy of wall street journal and read an article indicating that input components for RAM are expected to rise in price, forcing manufacturers to produce RAM at a higher unit cost. Based on this information, what can you expect to happen to the price you pay for RAM?

Solution:

Based on the information given, a general equation can be derived as below: Let Cg be the purchase of consumer with income greater than $80000 and Cl be the consumer with income less than $80000, and R be the quantity of RAM. Cg – Cl = 1.5 R

As per the article, the Ram will be produced at a higher unit price, but the article doesn’t state whether selling price of RAM will increase or not. The RAM producers may continue working with a lower profit margin in order to gain more market share. So, it cannot be concluded about the price change based on this information.

Would your answer change if, in addition to this change in RAM input prices, the article indicated that consumer incomes are expected to fall over the next two years as the economy dips into recession? Explain.

As the quantity of RAM purchased is dependent on number of consumers with certain income, the dip in salary will result in lesser number of consumers in bracket with salary more than $80000. That means, as per the Law of Demand there will be lesser demand for RAM, which will further result in increase of selling price of RAM as sellers will look forward to earn profit by raising the price.

CHAPTER 3:

1) Answer the following questions based on the accompanying diagram. a) How much would the firm’s revenue change if it lowered the price from $12 to $10? Is demand elastic or inelastic in this range? b) How much would the firm’s revenue change if it lowered the price from $4 to $2? Is demand elastic or inelastic in this range? c) What price maximizes the firm’s total revenues? What is the elasticity of demand at this point on the demand curve?

Solution:

a) Revenue at $12 = 12 x 1= $12

Revenue at $10 = 10 x 2 = $20

Change in revenue = $20 - $12 = $8.

Using the Mid point elasticity method, elasticity for this range is: {(Q2-Q1)/(Q2+Q1)/2}/ {(P2-P1)/(P2+P1)/2} = 3.66. Clearly the curve in this range is relatively elastic as E>1.

b) b) Revenue at $4 = 4 x 5 = $20

Revenue at $2 = 2 x 6 = $12

Change in revenue = $20 - $12 = $8.

Using the Mid point elasticity method, elasticity for this range is: {(Q2-Q1)/(Q2+Q1)/2}/ {(P2-P1)/(P2+P1)/2} = 0.274 . Clearly the curve in this range is relatively inelastic as E< 1.

c) The firm’s revenue will be maximum when the demand and price are in equilibrium i.e the midpoint of the line with coordinates (0,14) and (6,2), which is (3,8). So a price of $8 will ensure maximum revenue for the...

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