BE-2202 Intermediate to Microeconomics PDF

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19b 17 th August 2020 BE-220 Intermediate Microeconomics Pg. Dr. Hjh Norulazidah Binti Pg. Omar Ali Suppose the demand curve in a particular market is given by Q =5 - 0. a) Plot this curve in a graph. Inverse; Q = 5 – 0 P = 10-2Qb) At what price will demand be unitary elastic?εQ,P= ΔQd ΔP∙PQ=−b⋅PQTh...

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Asfa Arifah Binti Awang Besar 19b8512 17th August 2020 BE-220 Intermediate Microeconomics Pg. Dr. Hjh Norulazidah Binti Pg. Omar Ali

2.2. Suppose the demand curve in a particular market is given by Q =5 - 0.5P. a) Plot this curve in a graph. Inverse; Q = 5 – 0.5P P = 10-2Q

b) At what price will demand be unitary elastic? P Δ Qd P ∙ =−b ⋅ ΔP Q Q 1 Thus,-b = , at unitary elastic the demand is = -1 2 ε Q ,P =

ε Q ,P =

−1 ⋅ 2

P

=−1

P 5− 2

P =2 P 5− 2 P=10−P 2 P=10 P=5

2.4. Suppose that demand for bagels in the local store is given by equation Q d =¿ 300 - 100P. In this equation, P denotes the price of one bagel in dollars. a) Fill in the following table: Ans: Elasticities of demand formula

Asfa Arifah Binti Awang Besar 19b8512 17th August 2020 BE-220 Intermediate Microeconomics Pg. Dr. Hjh Norulazidah Binti Pg. Omar Ali

ε Q ,P =

Δ Qd P P P = =−100⋅ d 300 −100 ⋅ P P−3 ΔP Q

P 0.10 290 Qd ε Q ,P -0.035 b) Plot this curve in a graph.

0.45 255 -0.176 Is it linear?

0.50 250 -0.2

0.55 245 -0.225

2.50 50 -5

Inverse demand function is P = 3 – 1 Q d , and the demand curve is 100 linear.

c) At what price is demand unitary elastic?

d) At what price is demand inelastic?

Asfa Arifah Binti Awang Besar 19b8512 17th August 2020 BE-220 Intermediate Microeconomics Pg. Dr. Hjh Norulazidah Binti Pg. Omar Ali

e) At what price is demand elastic?

2.5. The demand curve for ice cream in a small town has been stable for the past few years. In most months, when the equilibrium price is $3 per serving for the most popular ice cream, customers buy 300 servings per month. For one month the price of materials used to make ice cream increased, shifting the supply curve to the left. The equilibrium price in that month increased to $4, and customers bought only 200 portions in the month. With these data draw a graph of a linear demand curve for ice cream in the town. Find price elasticity of demand for prices equal to $3 and $4. At what price would the demand be unitary elastic? Ans: Demand curve equation is P = A – 0.01Q As mentioned above Q = 300 and P = 3, in order to find A, we’ll be substituting provided Q and P in the equation. P = A – 0.01Q 3 = A – 0.01 (300) 3=A-3 So lowest price at which the quantity demanded is, A = $6 Equation demand curve P = 6 – 0.01Q Using the formula below, we now can find the elasticity demand d

ε Q ,P =

ΔQ P 6−0.01Q P ∙ =−100 ⋅ =−100 ∙ Q Q ΔP Q d

Hence, at Q = 300 and P = 3, the elasticity is unitary, = -1

Asfa Arifah Binti Awang Besar 19b8512 17th August 2020 BE-220 Intermediate Microeconomics Pg. Dr. Hjh Norulazidah Binti Pg. Omar Ali

At A, the εQ , P =

ε =−2

and at B, the

ε =−1. Slope demand curve

ΔP 3−4 = =−0.01 ΔQ 300−200

Inverse demand function P( Q) 6  0.01Q and put in any of the given points on the graph in the equation

ε Q ∙P =

1 P 1 6−0.01Q 600−Q ⋅ = = ⋅ Q −Q Q −0.01 ΔP ΔQ

When Q= 300, P = 3

ε Q ∙P =

600−Q 600−200 =−2 = −200 −Q

When Q = 200, P = 4

2.6. Granny’s Restaurant sells apple pies. Granny knows that the demand curve for her pies does not shift over time, but she wants to learn more about that demand. She has tested the market for her pies by charging different prices. When she charges $4 per pie, she sells 30 pies per week. When she charges $5, she sells 24 pies per week. If she charges $4.50, she sells 27 apple pies per week. a) With these data draw a graph of the linear demand curve for Granny’s apple pies. Ans: In order to find the equation for the demand is an increase in sale by 3 $0.50 in price. low we can find ΔQ −3 = =−6 the demand. ΔP 0.5 With the demand curve equation form Qd = A – 6P, we can determine the value of A by substituting in any of the points on the demand curve. i.e P = 5, and Q = 24

Asfa Arifah Binti Awang Besar 19b8512 17th August 2020 BE-220 Intermediate Microeconomics Pg. Dr. Hjh Norulazidah Binti Pg. Omar Ali 24 = A – 6(5) A= 54

Hence, the demand of apple pies equation Qd = 54 – 6P. b) Find the price elasticity of demand at each of the three prices. Ans: The price elasticity of demand can be determine using this formula below ε Q ,P =

P Δ Qd P ∙ =−6 ⋅ ΔP Q Q

At A, P= 5, Q= 24, the ε =−1.25 (the demand is elastic) At B, P=4.5, Q=27, the ε =−1 (the demand is unitary) At C, P=4, Q=30, the ε =−0.8 (the demand is inelastic) 2.13. Consider a linear demand curve, Q = 350 - 7P. a) Derive the inverse demand curve corresponding to this demand curve. Ans: Q = 350 – 7P 7P = 350 -Q 1 Q P = 350 7 b) What is the choke price? Ans: Economically choke price is when the quantity demanded of a good is equal to zero and the price is at the lowest. Q = 0; with the inversed demand equation resulting with P= 50 c) What is the price elasticity of demand at P = 50? Ans: The price elasticity if demand will be elastic at P=50 because it’s infinity. 2.15. A firm currently charges a price of $100 per unit of output, and its revenue (price multiplied by quantity) is $70,000. At that price it faces an elastic demand ε Q ∙P...