Having trouble. Let the market demand for hamburgers be given by Qhburger = 500

Question

Having trouble.

Let the market demand for hamburgers be given by Qhburger = 500 + I - 250Phburges + 400 Ppizza, where Qhburger is monthly demand in number of hamburgers, I is average monthly income in dollars, Ppizza, is the price of a slice of pizza, and Phburger is the price of a hamburger. Initially, I = $1,000, Phburger = $2 and Ppizza = $3, answer the following questions: A) Suppose the price of hamburger increases by 10% and all the other variables remain the same, calculate the arc price elasticity of demand for hamburger. Is the demand elastic, inelastic or unit elastic? What would happen to the total revenue received by hamburger retailers? (Increase or decrease?) Why? B) Assume the price of pizzas rises by 10% with all the other variables at their initial values; calculate the cross-price elasticity of demand for hamburgers. What can you conclude about the relationship between pizza and hamburger? (Hint n : n = % delta Qhburger/% deltaPpizza) C) Now, suppose the monthly income rises by 10% with all the other variables at their initial values; calculate the income elasticity of demand for hamburgers. What can you conclude about hamburger as a market good?

Explanation / Answer

Qhburger = 500 + I - 250*Phburger + 400*Ppizza
I = 1000
Phburger=$2
Ppizza = $3
so Qhburger = 500 + 1000 - 250*2 + 400*3 = 2200

A)

Phburger = 1.1*2 = $2.2
Qhburger = 500 + 1000 - 250*2.2 + 400*3 = 2150
dQ = 2150 - 2200 = -50
Avegrage Q = (2150+2200)/2 = 2175
dP = 2.2 - 2 =0.2
Average P = (2.2+2)/2 = 2.1
arc elasticity = (dQ/Q)/(dP/P) = (-50/2175)/(0.2/2.1) = -0.241
It is less than 1 so inelastic.

B)
Ppizza = 1.1*3 = $3.3
Qhburger = 500 + 1000 - 250*2 + 400*3.3 = 2320
dQ = 2320 - 2200 = 120
Avegrage Q = (2320+2200)/2 = 2260
dP = 3.3 - 3 =0.3
Average P = (3.3+3)/2 = 3.15
arc elasticity = (dQ/Q)/(dP/P) = (120/2260)/(0.3/3.15) = 0.5575
as Price of pizz increase Q of hamburgers increase...thats like substitute

C)
I = 1.1*1000= $1100
Qhburger = 500 + 1100 - 250*2 + 400*3 = 2300
dQ = 2300 - 2200 = 100
Avegrage Q = (2300+2200)/2 = 2250
dI = 1100 - 1000 = 100
Average I = (2100)/2 = 1050
arc elasticity = (dQ/Q)/(dP/P) = (100/2250)/(100/1050) = 0.467
As income increase Q increase ..so it is market good.

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