BC 807 – The Dolly Madison Inc at Emporia estimated the following elasticities

Q1)The Dolly Madison Inc at Emporia estimated
the following elasticities for a special type of doughnuts: price elasticity EP= 2, income elasticity EI
= 1, and cross elasticity EXY= 1.5, where X refers to doughnuts and Y to bagels. Next year, the firm
would like to increase the price of the doughnuts it sells by 6 percent.
Management forecasts that income will rise by 4 percent next year and that the
price of bagels will fall by 2 percent.

(a) If the sales this year are 120,000 doughnuts, how
many doughnuts can the firm expect to sell next year?

(b) By what
percentage must the firm change the price of doughnuts to keep its sales at
120,000 tons next year?

Q2)The demand curve for a Puppy Chow the most
popular dog food produced by Pet Marts is given by:
.png”>= 1,000 – 2Px+ .02Pz, where Pz= $400 (X = Puppy Chow; Y = another product
from Pet Mart, P is price and Q is quantity)

(a) What is the price elasticity of demand when PX= $154? Is the demand elastic or inelastic at this price? What would
happen to the firm’s revenue if it decided to charge a price below $154?

(b) What is the price elasticity of demand when PX= $354? Is demand elastic or inelastic at this price? What would happen
to the firm’s revenue if it decided to charge a price above $354?

(c) What is the
cross-price elasticity of demand between good X and good Z when PX= $154? Are goods X and Z substitutes or complements?

Q3)Consider the
following nonlinear (multiplicative) demand function for Kelley’s Country Mart
where Q is the quantity of the product sold, P is the price of product, M is
the average income of the household in Emporia, and PRis
the price of related goods (R). The method of least-squares is used to estimate
the parameters..png”>

The results of the
estimation are:

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a. Before the
nonlinear demand equation can be estimated using regression analysis, the
demand equation must be transformed into a log-linear form. Write the equation
with t-stat,.png”>, F-stat information.

b. Are the slope
parameter estimates statistically significant at the 5 percent level of
significance?
c. Estimated value
of a,the intercept?

d. Is this good a
normal or inferior good?

e. Is this good a
substitute or complement with respect to related good R?

f. Compute estimates
of the following elasticities:

(i) The price
elasticity of demand.

(ii) The income
elasticity of demand.

(iii) The
cross-price elasticity of demand.

g. For a 23.15
percent decrease in household income, holding all other things constant, what
will happen
to quantity demand
for the good?

h. All else
constant, a 4 percent increase in price of the good will cause what percentage
increase or decrease in the quantity sold of the good?

i. A 12.82 percent decrease in the price of
R, holding all other things constant, will cause what percent change in
the quantity demanded of the good?