Question

Suppose you took over a grocery store and try to find out the optimal quantity of chicken McNuggets you have to order from suppliers, as well as setting the right price for the chicken in your grocery store. You found the following data points from the previous grocery store owner:

• Per capita consumption (in an arbitrary time interval): 70lbs/person

• Price: $0.7/lb.

• Price elasticity of demand: e = -0.55

Note, that this is the consumption for a price of $0.7. Assume that the inverse market demand is linear, i.e., Q^d=a-bP.

a) Assume first that you offer the chicken McNuggets for a price of $1, instead of $0.7. How many nuggets should you offer p=$1?

b) In general, how many chicken McNuggets should you offer for any arbitrary price p?

Answer 1

Given that P=$0.7/lb, Qd=70lb, e=-0.55

Market demand function Qd=a-bP

Here Change in Qd will be equal to change in bP or we can say b=Change in quantity/change in Price or

b%=elasticity or b=elasticity*100=-.55*100=-55.

Putting the given values and value of b in market demand function Qd=a-bP we get,

70=a-(55*0.7) or a=108.5

a)

At price=$1, quantity of nuggets offered should be equal to quantity demanded, i.e. 108.5-(55*1)=53.5.

b)

For any price P, chicken nuggets offered should be 108.5-55P.

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