Problem 2
The demand function for Newton’s Donuts has been estimated as follows:
Qx = -14 – 54Px + 45Py + 0.62Ax
where Qx represents thousands of donuts; Px is the price per donut; Py is the average price per donut of other brands of donuts; and Ax represents thousands of dollars spent on advertising Newton’s Donuts. The current values of the independent variables are Ax=120, Px=0.95, and Py=0.64.
Show all of your calculations and processes. Describe your answer for each question in complete sentences, whenever it is necessary.
Problem 2 Question 2.a
The price elasticity of demand for Newton’s Donuts is -1.35
(calculations:
dQ/dPx =-54
Px = 0.95
Qx = -14-54(0.95) + 45(0.64) + 0.62(120) = -14 – 51.3 + 28.8 + 74.4 = 37.9
Price elasticity of demand = (-54)(0.95/37.9) = -1.35).
The demand function “refers to the relationship that exists between quantity demanded of a particular product and all the determinants of that demand” (Douglas, 2012). Qx represents the quantity demanded for Newton’s Donuts.
Problem 2 Question 2.b
The formula for the inverse demand curve is
Px = 0.95 according to the
Derive an expression for the inverse demand curve for Newton’s Donuts. Describe your answer and show your calculations.
Problem 2 Question 2.c
Yes, they should reduce the cost of the donuts because the demand increases for donuts at 15.85 which will sell less donuts than the price of 0.64
(calculation: Qx = -14-54(0.95) + 45(0.15) + 0.62(120)
Qx = -14 – 51.3 + 6.75 + 74.4
Qx = 15.85).
Problem 2 Question 2.d
Yes, Newton’s Donuts should spend more on advertising because demand increases. For example, if the cost of advertising increases to 200 thousand dollars than the demand increases to 87.5 and it is elastic
(calculation: Qx = -14-54(0.95) + 45(0.64) + 0.62(200)
Qx = -14 – 51.3 + 28.8 + 124
Qx = 87.5).
References:
Douglas, E. (2012). Managerial Economics (1st ed.). San Diego, CA: Bridgepoint...