Question

Please check my answers if they are correct! If not, please make corrections. Thank you!

Bob, owner of Bob’s Auto, sells cars. The number of car sales is represented by y. Bob buys autos at a price of A each and has no other costs. He only buys as many cars as he sells.

a) What is his total cost if he sells 10 cars? What if he sells 20 cars? What is the equation for Bob’s total costs assuming he sells “y” cars?

b)What is Bob’s AC(y)? For every additional auto Bob sells, by how much do his costs increase? What is Bob’s MC (y)?

c) What does Bob’s ACV and MC costs look like in a graph if A = $20?

d) Suppose Bob has to pay B per year to produce obnoxious television commercials. What is Bob’s new total cost curve and his average cost curve and his marginal cost curve?

e) If A = 20 and B = 100, evaluate Bob’s AC at y output levels of 5,10, 25 and 40.




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MY ANSWERS:

a)
10A is his total cost if he sells 10.
20A is his total cost if he sells 20.
C(y)=Ay

b)
AC(y)=A/y is his AC function.
His costs increase 1/y. MC(y)=A/y is his MC.

c) a horizontal flat line at AC/MC (or y-axis) = 20 (where the x-axis is his output-number of cars sold- and the y-axis is his AC/MC)

d)
c(y) = Ay + B
AC(y) = A + B/y
MC(y) = A + By

e)
(5,40) at output level (y) = 5
(10,30) at y = 10
(20,25) at y = 20
(25,24) at y = 25
(40,22.5) at y = 40

Answer 1

a) I agree
b) His total cost from a) is Ay. So average cost is Ay/y = A. Since it cost Bob A for each car, regardless of the number, MC=A

c) I agree

d) for C(y) = Ay + B and
AC(y) = (Ay + B)/y = A + B/y (I agree)
However regardless of the advertising expenses, it still cost Bob A per car, so, MC(y) = A

e) I agree