Problem: You have a business job where you are helping track revenue and sales. Suppose that p is the price in dollars of a gadget and q = f(p) is the quantity sold (in hundreds). Then the revenue (in thousands of dollars) is given by R = p - f{p), depending on the price. There are two parts to this problem. a. Match each of the mathematical expressions below with the best interpretation. There will be interpretations which do not have a corresponding mathematical expression. I. f'(15) = 3 III. f-" (60) = 3 R(20) – R(15) 5 II. 12 1._ If the price increases from $15 to $16 then the company expects revenue to increase by about 3 thousand dollars. 2. If the price increases from $15 to $20 then the revenue will increase by about 60 thousand dollars. 3. When the company sells 15 hundred gadgets, the revenue is 60 thousand dollars. 4. If the price increases from $15 to $20 then the revenue will increase by about 12 thousand dollars. 5. If the price increases from $15 to $20 then the company expects to sell 3 hun- dred more gadgets. 6. - When the price is $3, the company sells 60 hundred gadgets. 7. - When the company sells 3 hundred gadgets, the price is $60 cach. If the price increases from $15 to $16 then the company expects to sell about 3 hundred more gadgets.
Problem: You have a business job where you are helping track revenue and sales. Suppose that p is the price in dollars of a gadget and q = f(p) is the quantity sold (in hundreds). Then the revenue (in thousands of dollars) is given by R = p - f{p), depending on the price. There are two parts to this problem. a. Match each of the mathematical expressions below with the best interpretation. There will be interpretations which do not have a corresponding mathematical expression. I. f'(15) = 3 III. f-" (60) = 3 R(20) – R(15) 5 II. 12 1._ If the price increases from $15 to $16 then the company expects revenue to increase by about 3 thousand dollars. 2. If the price increases from $15 to $20 then the revenue will increase by about 60 thousand dollars. 3. When the company sells 15 hundred gadgets, the revenue is 60 thousand dollars. 4. If the price increases from $15 to $20 then the revenue will increase by about 12 thousand dollars. 5. If the price increases from $15 to $20 then the company expects to sell 3 hun- dred more gadgets. 6. - When the price is $3, the company sells 60 hundred gadgets. 7. - When the company sells 3 hundred gadgets, the price is $60 cach. If the price increases from $15 to $16 then the company expects to sell about 3 hundred more gadgets.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Problem: You have a business job where you are helping track revenue and sales. Suppose that p is the
price in dollars of a gadget and q = f(p) is the quantity sold (in hundreds). Then the revenue (in thousands
of dollars) is given by R = p - f(p), depending on the price.
There are two parts to this problem.
a. Match each of the mathematical expressions below with the best interpretation. There will be
interpretations which do not have a corresponding mathematical expression.
R(20) – R(15)
I. f'(15) = 3
III. f-'(60) = 3
II.
12
1. If the price increases from $15 to $16 then the company expects revenue to
increase by about 3 thousand dollars.
2.
If the price increases from $15 to $20 then the revenue will increase by about
60 thousand dollars.
3.
_When the company sells 15 hundred gadgets, the revenue is 60 thousand dollars.
4.
If the price increases from $15 to $20 then the revenue will increase by about
12 thousand dollars.
5._If the price increases from $15 to $20 then the company expects to sell 3 hun-
dred more gadgets.
When the price is $3, the company sells 60 hundred gadgets.
When the company sells 3 hundred gadgets, the price is $60 each.
8.
If the price increases from $15 to $16 then the company expects to sell about
3 hundred more gadgets.
B. Your fellow intern claims that if f' (p) is negative then the revenue will decrease as well. In a sentence
or two, briefly explain if this statement is necessarily true or not.
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