Question

You own a restaurant. You just read that a recession will cause income to decrease by 10% this year. If this forecast turns out to be true, it will impact your restaurant. Income elasticity is 2.2. Current dinner prices are $15. You sell 350 dinners each week. Calculate the % change in the number of dinners, assuming that you don’t change your price.

a) what do you want to calculate?         Write the words first:_________________________

Rewrite using symbols:

b) what information is provided in the problem?

10% = _____________       2.2 = _______________        $15 = ______________           350 = __________

will price change? ________      what changed that will cause the change in Q? _________

c) look at the information you have & the question you want to answer, so we can think about how to build a bridge from the information to the answer:

what changed? _____________   what do you want to calculate? _______________

what elasticity will connect these 2 things? ____________________________.    The elasticity number is important, so think about it for a minute: Elasticity shows the response of one variable (usually Q) to a change in another variable.

This problem gives you a number for ______________ elasticity. This is the response of Q to a change in ____________.    Write this as a formula, remembering that elasticity measures responses as % change:                                 

                                                                                               ______

            e__________         =          % change in____               =        __________.

                                                  % change in                        ______

Does this formula include the variable that you want to calculate? What is it? _________________

In order to solve for this variable, you will need to fill in the other numbers. Do you have enough information to do that? ________ (Assume this answer is “yes”, so plug in the numbers.) Do a little algebra to solve:

Answer 1

A) Write the word first: % change in the number of dinners.

Rewrite using symbols: Δ number of dinners.

B) 10% = % change in income.

2.2 = Income elasticity of demand.

$15 = Dinner price

350 = Number of dinner per week.

  will price change = NO

Change that causes the change in Q = Due to recession income is decrease and it causes decrease in the quantity of dinners since price is constant.

C)

What changed = Income

What do you want to calculate = Quantity change in the dinners.

What elasticity will connect these two things = Income elasticity of demand.

The problem gives a number of Income elasticity.

This is the response of Q to a change in Income.

e = Elasticity of income of demand = (% change in Quantity demanded of dinners / % Change in income)

This formula includes the variable which we want to calculate . Which is Change in Quantity of Dinners.

We do have enough information to calculate the other variable.

Solution: Calculation of % change in the number of dinners =

according to the formula = e = % change in quantity demand / % change in income

2.2 = % change in quantity demanded / 10%

% change in quantity demanded = (2.2 * 10%) = 22%

Which means new number of dinners = (350 - 22%) = 273 dinners per week.