Question

The following is John’s demand for pizza from a local pizza store called Pizza House:

Marginal value	13	11	9	7	5	3	1
Quantity	1	2	3	4	5	6	7

Currently, Pizza House is selling pizzas at $9 each. Recently, a world-famous chef opened a new pizza store called Pizza Palace that specializes in organic healthy pizzas to compete against Pizza House. So far, Pizza Palace has gotten many good customer reviews. Pizza Palace sells its pizza for $13.50 each. However John’s demand for pizza from Pizza Palace is 50% higher than his marginal value for Pizza House.

a) Prove why it would make sense for John to buy from Pizza Palace rather than from Pizza House even though it will cost him more money.

b) If Pizza House wants to get John back as a customer, what must it do? How much should Pizza House charge for its pizza in order? Show your work.

c) Use your answer in part (b) and compare it to the original price of $9. Determine the price elasticity of demand for Pizza House. Show your work.

d) Based on your elasticity, why does it make sense for the Total Revenue for Pizza House to increase as they decrease their prices?

e) In terms of income elasticity, compare and explain the differences between Pizza House and Pizza Palace. What type of income elasticity can we predict for each? Why?

Answer 1

a).

So, in this problem we have given the “MV” and “Q” of “John” derived from “local pizza store”. So if the price of pizza is “$9”, => the optimum amount that “John” should purchase will be determined by “MV=9”.

So, here the optimum quantity that “John” should purchase is given by “3”, where MV=9. Now, the “Net Total Value” derived from “3” pizza is “13+11+9 – 9*3 = 6”.

Now, the MV derived from “Pizza Palace” is 50% more than “Pizza house”, => the following table shows the ‘John’s” demand for pizza from pizza palace.

So, if the price is “13.50”, => here also the optimum quantity should be “3”, => the “Net Total Value” derived from “3” pizza is “19.5+16.5+13.5 – 3*13.5 = 9”. So, we can see that given the data the “NTV” in more under “pizza palace”, => “John” will buy pizza from “pizza palace” even if it will cost more.

b).

If local shop wants to get John back as a customer, => they should reduce their price of pizza. So, if they charge “7”, => the consumption will increase to “4”, => “NTV” derived from 4 pizza is given below.

=> 13+11+9+7 – 4*7 = 12 > 9”. So, they should reduce the price of pizza to “7”.

c).

So, initially the price and quantity combination is given by, “P=9” and “Q=3”, now the new price and quantity combination is given by, “P=7” and “Q=4”. So, the elasticity is the % change in quantity demanded due to 1% change in price. So, mathematically it is given by.

=> [(∆Q/Q)/( ∆P/P)] = [(1/3)/(-2/9)] = (1/-2)*(9/3) = (-1.5). So, the price elasticity of demand is “-1.5”.

d).

Now, we can see that the absolute value of price elasticity of demand is “1.5 > 1”, => the demand curve is relatively elastic, => the % change in Q is more than % change in P, => total revenue will increase if “P” will decreases. So, here “Local pizza store” can increase it revenue by lowering the price of pizza.

e).

The income elasticity is the % change in quantity demanded due to 1 % change in income. Now, here we don’t given any data about income, but as we can see that the “MV” of pizza from “Pizza Palace” is 50% more compare to “Pizza house”, => if the price of both the pizza will remain same, => % change in quantity demanded of “pizza palace” will be more compare to “pizza house”.

So, the income elasticity of demand for pizza form pizza palace should be more than pizza house, but both should have income elasticity more than “0” and less than “1”, => both are normal goods.