Question

A cake baker bakes cake. His short run cost function is C(y) = 100 + 10y - 2y² + y³, where y is the number of cakes

(a) derive and graph his average total cost, average variable cost and marginal cost curves

(b) what is his short run supply curve

Answer 1

a)

Given

C(y)=100+10y-2y^2+y^3

Average total cost is given by

ATC=C(y)/y=(100/y)+10-2y+y^2

TVC is the portion of C(y) that is output dependent. So,

TVC=10y-2y^2+y^3

Average variable cost is given by

AVC=TVC/y=10-2y+y^2

Marginal Cost is given as

MC=dC(y)/dy=10-4y+3y^2

y	ATC	AVC	MC
1	109.00	9.00	9.00
2	60.00	10.00	14.00
3	46.33	13.00	25.00
4	43.00	18.00	42.00
5	45.00	25.00	65.00
6	50.67	34.00	94.00
7	59.29	45.00	129.00

b)

A firm will shut down if price is less than minimum AVC.

Refer to table given in part a, we observe that MC=AVC=$9.

We know that if MC=AVC at some output level, AVC reaches to its minimum value at that output. So, we can say that minimum AVC is $9.

Now, short run supply curve of a competitive firm is given by its marginal cost. So,

MC=P

10-4y+3y^2=P where Pminimum AVC (or say P9)

(Its a inverse supply curve of a given firm)

On rearranging we get

3y^2-4y+(10-p)=0

or

(Supply curve of given firm)