A bakery works out a demand function for its chocolate chip cookies and finds it to be q = D (x) = 943 - 17 x, where q is the quantity of cookies sold when the price per cookie, in cents, is x. A) Find the elasticity.
B) At what price is the elasticity of demand equal to 1?
C) At what prices is the elasticity of demand elastic?
D) At what prices is the elasticity of demand inelastic?
E) At what price is the revenue a maximum?
F) At a price of 21c per cookie, will a small increase in price cause the total revenue to increase or decrease?
1. Increase
2. Decrease

See expla below

Step-by-step explanation:

Given the demand function:

q = D (x) = 943 - 17 x

a) Find the elasticity:

Find the derivative of the demand function.

D'(x)= -17

Thus, elasticity expression is:

Elasticity expression =

b) At what price is the elasticity of demand equal to 1?

This means E(x) = 1

Substitute 1 for E(x) in the elasticity equation:

Cross multiply:

Collect like terms

x = 27.74

Elasticity at the price of demand = 1 is 27.74

c) At what prices is the elasticity of demand elastic?

This means E(x) > 1

Therefore,

Cross multiply:

Collect like terms

x > 27.74

The elasticity of demand is elastic at x > 27.74

d) At what prices is the elasticity of demand inelastic?

This means E(x) < 1

Therefore,

Cross multiply:

Collect like terms

x < 27.74

The elasticity of demand is inelastic at x < 27.74

e) At what price is the revenue a maximum:

Total  revenue will be:

R(x) = x D(x)

= x (943 - 17x)

= 943x - 17x²

R(x) = 934 - 17x(price that maximizes total revenue)

Take R(x) = 0

Thus,

0 = 943 - 17x

17x = 943x

Total revenue is maximun at x= 27.74 per cookie

f) At x = 21 per cookie, find the price:

Thus,

R (21) = (943 * 21) - (17 * 21²)

= 19803 - 7497

= 12306

At x = 27.74, find the price:

R(27.74) = (943 * 27.74) - (17 - 27.74²)

= 26158.82 - 13081.63

= 13077.19

We can see the new price of cookie causes the total revenue to decrease.

Therefore, with a small increase in price the total revenue will decrease.

the fist one is not equalvalent but i think th second one isand the third isnt definetly or the last one is i think. hope this !

step-by-step explanation:

b is the answer that makes most sense

step-by-step explanation: