Question

In: Economics

A firm operates a chain of coffee outlets in the city selling a coffee called “smart...

A firm operates a chain of coffee outlets in the city selling a coffee called “smart coffee”. The firm has estimated a regression model that suggests three variables are significant determinants of demand for “smart coffee”. The results obtained from the regression model is provided below.

Q=1000-60P+20DF+1.5A

Q: (dependent variable) is number of cups of “smart coffee” sold per week

P: is the price in dollars of a cup of “smart coffee”

DF: the price in dollars of a cup of a coffee called “daily fix” sold by a competitor

A: the spending on advertising to promote “smart coffee” brand by the firm in dollars per week.

(a). Interpret the meaning of each of the coefficients on the three variables (P, DF, and A)

(b). Suppose “smart coffee” is currently selling for $4 per cup. Compute the point price elasticity of demand for “smart coffee” at this price if the firm spend $4000 on advertising and “daily fix” sells for $3 per cup.

(c). The firm managers are considering lowering the price of “smart coffee” from the current $4 to match “daily fix” as a strategy to increase the market share as well as total revenue. Will this strategy achieve both these objectives? Briefly discuss.

Expert Solution

A) coefficient on p= one dollar change in price of smart coffee , change quantity demanded by 60 in opposite direction.

Coefficient of Df=One dollar change in price of daily fix coffee price, increase quantity demanded of smart coffee by 20 in same direction.

Coefficient of A=one dollar change in spending on adversity of smart coffee, increase quantity demanded of smart coffee by1.5 in same direction.

B)Q=1000-60*4+20*3+1.5*4000=1000-240+60+6000=6820

Point elasticity of demand=(∆Q/∆P)*(P/Q)

∆Q/∆p=-60

Point elasticity=(-60)*(4/5820)=-240/6820=-0.035

C)When they match price of daily fix ,so they reduce their price =3.

New quantity demanded:Q=1000-60*3+20*3+1.5*4000=1000-180+60+6000=6880

Because quantity demanded and thus sale increase of smart coffee,so market share of smart coffee increased.

Total revenue with p=4,=4*6820=27,280

Total revenue with p=3,=3*6880=20,640

So decreasing price lead to decrease total revenue. So increasing total revenue objective couldn't achieve by this strategy.

Rahul Sunny answered 2 years ago

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