Question

1. (15 pts) Suppose firm A is one of many perfectly competitive firm and it total cost function is given as TC = 0.1q2+20q+1000 AVC = 0,19 +20 I looo 0,2q +20 0.19 +20 (a) Find firm A's total fixed cost. Find its average variable cost function. (b) Find the shut down point. Find firm A's supply function. shut Find firm A's supply function. shut down MO AVC AVO (c) If there are 100 firms whose cost functions are identical to firm A's cost in the market, find market supply function. (d) Suppose market demand function is given Qp = 25,000 - 200P. Find the market equilibrium price How much output does firm A produce to maximize his profit? What is the value of profit? Find price elasticity of market demand and supply respectively at equilibrium price. What is the value of price elasticity of demand for firm A's product? (e)Suppose the government imposed license fee of $100 on all firms. Would firm A change the level of production? Why or why not? Would the profit change? Why or why not?! 2.5 nts) Tayt Chat

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Answer 1

TC = 0.1q² + 20q + 1000

a) TFC = 1000

TVC =   0.1q² + 20q

AVC = TVC/q  

= ( 0.1q² + 20q )/q

= 0.1q + 20  

b) Shut down point is given by P = min AVC

and AVC is minimum where AVC = MC

dTC/dq = 0.2q + 20  

MC = 0.2q + 20

AVC = MC  

0.1q + 20 = 0.2q + 20  

q = 0  

So min. AVC = 0.1(0) + 20

= 20

THUS, shut down price is 20

Supply function is given by  

P = MC  

P = 0.2q + 20

P - 20 = 0.2q

q = 1/0.2(P - 20)

q = 5P - 100

Therefore firm A's supply function q = 5P - 100

C) Since there are 100 firms so market supply function

Qs = nq

= 100(5P - 100)

= 500P - 10000

D)

Qd = 25000 - 200P

Qs = Qd

500P - 10000 = 25000 - 200P

500P + 200P = 25000 + 10000

700P = 35000

P = 35000/700

= 50

Q = 500(50) - 10000

= 25000 - 10000

= 15000

q = 5P - 100

= 5(50) - 100

= 250 - 100

= 150

THUS, Firm A produces 150 units of output to maximize profit

Firm A 's profit = Pq - TC  

= 50(150) - 0.1(150)² - 20(150) - 1000

= 7500 - 2250 - 3000 - 1000

= 7500 - 6250  

= 1250

Price elasticity of demand

Qd = 25000 - 200P

dQ/dP = - 200

Ed = (dQ/dP)(P/Q)

= (- 200)(50/15000) = - 10000/15000

= - 0.66

Price elasticity of supply

Qs = 500P - 10000

dQ/dP = 500

Es = (dQ/dP)(P/Q)

= (500)(50/15000)

= 25000/15000

= 1.66