Question

4. Suppose Dan's cost of making pizzas is -4 40 Dan is a price taker. (a) What is Dan's supply function? b) What if Dan has an avoidable fixed cost of $10?

Answer 1

C = 4Q + Q²/40

(a) Dan's supply function is represented by upward portion of the MC curve curve.

MC = 4 + 2Q/40

MC = 4 + Q/20

P = 4+ Q/20

P- 4 = Q/20

Q = 20P -80

Shutdown rule : P>AVC_min

AVC = ( 4Q + Q²/40)/ Q = 4 + Q/40

MC cuts the AVC at its minimum .

So by equating  MC and AVC, we get the output level at which AVC is minimum.

4+Q/20 = 4+ Q/40

Q/20 - Q/40 = 0

Q =0

So, AVC_min = 4+ Q/40 = 4+0/40 = 4

Thus, Dan will produce at any price greater than or equal to $4 .

S(P)= 0 If P<4.

And S(P) = 20P- 80 If P$\geq$ 4.

(b) What if Dan has an avoidable fixed cost of $10 .

Now , AC = (4Q + Q²/40 + 10)/Q

= 4 + Q/40 + 10/Q

AC = MC when AC at its minimum .

So, equate MC and AC ,we get :

4 + Q/40 + 10/Q = 4+ Q/20

Q = 20

At this output level , AC= (4+ 20/40 + 10/20) = $5

Thus, Dan will produce at any price greater than or equal to $5.

S(P)= 0 If P<5

And S(P) = 20P- 80 If P$\geq$ 5