Question

In: Economics

Joy’s Frozen Yogurt shops have enjoyed rapid growth in northeastern states in recent years. From the...

Joy’s Frozen Yogurt shops have enjoyed rapid growth in northeastern states in recent years. From the analysis of Joy’s various outlets, it was found that the demand curve follows this pattern:

Q = 200 - 300P + 120I +65T - 250Ac + 400Aj

where Q = number of cups served per week

P = average price paid for each cup

I = per capita income in the given market (thousands of dollars)

T = average outdoor temperature

Ac = competition’s monthly advertising expenditures (thousands of dollars)

Aj = Joy’s own monthly advertising expenditures (thousands of dollars)

One of the outlets has the following conditions: P = 1.5, I = 10, T = 60, Ac = 15, Aj = 10.

A. Estimate the number of cups served per week by this outlet. Determine the outlet’s demand curve.

B. What would be the effect of a 5 thousand dollar increase in the competitor’s advertising expenditure?

C. What would Joy’s advertising expenditure have to be to counteract this effect?

Solutions

Expert Solution

Solution :-

Given :-

the demand curve follows this pattern:

Q = 200 - 300P + 120I +65T - 250Ac + 400Aj

where Q = number of cups served per week

P = average price paid for each cup

I = per capita income in the given market (thousands of dollars)

T = average outdoor temperature

Ac = competition’s monthly advertising expenditures (thousands of dollars)

Aj = Joy’s own monthly advertising expenditures (thousands of dollars)

One of the outlets has the following conditions:

P = 1.5, I = 10, T = 60, Ac = 15, Aj = 10.

(A) :-

We have ,

Q = 200 - 300P + 120I +65T - 250Ac + 400Aj

So, put

P = 1.5, I = 10, T = 60, Ac = 15, Aj = 10.

I , Ac & Aj are in thousands of dollars.

So,

Q = 200 - 300 x 1.5 + 120 x 10000 + 65 x 60 - 250 x 15000 + 400 x 10000

Q = 200 - 450 + 1200000 + 3900 - 3750000+ 4000000

Q = 5204100 - 3750450

[ Q = 1453650 ]

(B) :-

the effect of a 5 thousand dollar increase in the competitor’s advertising expenditure :-

Ac = 15000 + 5000 ( increase)

So, Ac = 20000

Q = 200 - 300P + 120I +65T - 250Ac + 400Aj

Q = 200 - 300 x 1.5 + 120 x 10000 + 65 x 60 - 250 x 20000 + 400 x 10000

Q = 200 - 450 + 1200000 + 3900 - 5000000 + 4000000

Q = 5204100 - 5000450

Q = 203650

(C) :-

Effect of Joy’s advertising expenditure :-

Q = 200 - 300P + 120I +65T - 250Ac + 400Aj

Q = 200 - 300 x 1.5 + 120 x 10000 + 65 x 60 - 250 x 20000 + 400 x (10000 + X)

Q = 200 - 300 x 1.5 + 120 x 10000 + 65 x 60 - 250 x 20000 + 400 x 10000 + 400X

We calculated,

Q = 1453650

1453650 = 203650 + 400X

1453650 - 203650 = 400X

1250000 = 400X

400X = 1250000

X = 1250000/400

X = 3125

So, Joy’s advertising expenditure have to be increased by 3125 to counteract the effect.

Rahul Sunny answered 2 years ago
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