The Theory of Perfect Competition and
Applications of the Competitive Model

True/ False Questions.

1. Since long-run economic profits for a competitive firm are always zero, it will never pay acompetitive firm to adopt a cost reducing innovation.

2. If a lump sum tax is placed on firms in a competitive industry, the entire tax will be passed on to the consumers in the form of a higher price in the short-run, but none of the tax will be passed on to the consumers in the long-run.

3. If each firm is initially earning positive profits in a perfectly competitive industry, then there will be entry of new firms, price will fall, and the output of each firm will fall in the long-run equilibrium.

4. If all firms minimize costs and face the same input prices but different production functions, then all firms will use inputs in the same proportion.

5. The horizontal summation of the LMC(y) curves of individual firms is not the long run supply curve for the industry.

Answers: 1.F    2.F    3.T    4.F    5.T.

3. Short Questions

1. An industry has 50 identical, perfectly competitive firm. Each firm has a short run cost function given by: C=192+12q² . What are the firm and industry short run supply functions?

Answers:q=p/24; Q=50p/24.

4. Long Questions

1. B.D. Shovel Ltd. is one of many identical competitive firms producing spades. Its cost function is given by C(Q)=Q²+4, where Q is the number of spades produced.

a). Give an equation for and graph the spade industry long run supply curve.
b). Suppose the demand for spades is given by Q^D=D(p)=5000-500p. Graph the demand curve. Find the equilibrium price and quantity of spades. (Hint: at the equilibrium Q^D=Q^S).
c). Bowing to pressure from the mechanical digger lobby, the government decides to impose a $1 per unit tax on spades. What is the effect of the tax on the price paid by consumers and the equilibrium quantity?

2. The market demand curve for swim goggles is given by: Q_D = 225 - 25P where Q_D is the quantity of swim goggles demanded and P is the price of swim goggles. The supply curve for swim goggles is Q_S = - 150 + 50P where Q_S is the quantity of swim goggles supplied.

a). Find the equilibrium price of swim goggles and quantity sold.
b). Calculate the consumers' surplus and producers' surplus at the price and quantity found in part (a).
c). Explain in words and using diagrams what is meant by the terms "consumers' surplus" and "producers' surplus".

3. The demand for cigarettes is given by: Q^D = 140,000-25,000P.
where Q^D is the quantity of cigarettes demanded (in packs) and P is the price of a pack of cigarettes. The supply of cigarettes is given by: Q^S = 20,000+75,000P   where Q^S is the quantity of cigarettes supplied (in packs).
Suppose that a tax of $0.40 per pack was imposed on cigarettes.

a). How much would consumers' surplus be reduced? How much would producers' surplus be reduced?
b). What is the deadweight loss associated with the tax? Explain using words and diagrams what is meant by the term "deadweight loss".

4. Tim Long is is one of many identical dairy farmers in Subsidyland. His cost function for milk production is given by: C=Q²/200 where C represents costs (in dollars) and Q represents daily milk production in litres. The government of Subsidyland decides that, in order to guarantee farmers a reasonable and stable income, it will intervene in the milk industry. It decides to issue a limited number of milk production quotas. Only farmers with quotas will be allowed to sell milk. Farmers with quotas can sell up to 40 litres of milk a day, at a guaranteed price of $0.25 a litre. Quotas, once issued, cannot be bought and sold.

a). How much (per day) would Tim Long be prepared to pay for a milk quota?
b). If Tim is issued a milk quota by the government, what will be his economic profits?

5.  Hair Apparent is one of many identical firms in the highly competitive baldness treatment industry.
Its cost function is given by: C = (1/4)y²+1

a). Give an equation for and graph the firm's short-run supply curve.
b). Give an equation for and graph the industry's long-run supply curve.
c). If the demand for baldness treatment is given by Q = 108 - 12p  how many firms will there be in the baldness treatment industry in the long-run competitive equilibrium?
d). How much profits will a typical firm make in the long-run equilibrium? How much producer's surplus?

6. Violent Toys Inc is a competitive firm which produces Teenage Mutant Ninja Tortoise dolls according to the cost function: C=Q²/20 where Q is the number of dolls produced. The dolls sell for $10 each.
After losing a court case, Violent Toys is ordered to pay a licence fee to Turtles Ltd.

a). If the licence fee is $500, regardless of how many dolls Violent Toys produces, what happens to Violent Toy's cost function? To the marginal cost function? To the level of output? Explain you answer with math and with a graph.
b). If the licence fee is $5 per doll, what happens to Violent Toy's cost function? To the marginal cost function? To the level of output? Explain you answer with math and with a graph.

Answers:
1. a) LRS is given by p=4 and is a horizontal line. b) The demand is adownward sloping straight line. The equilibrium price and quantity are p*=4 and Q*=3000. c) The tax will increase the total cost by Q ($1 times the quantity produced Q). The tax will increase the price by $1 and the quantity will decrease by 500.
2. a) p=5, Q=100; b) CS=200, PS=100.
3. a) CS will be reduced by 31.875 and PS will be reduced by 10.625; b) DWL=1500.
4. Tim will be willing to pay at most 3.125. This is his economic profit.
5. a)p=y/2, b) LRS is given by p=1; c) At p=1 the quantity demanded (and supplied) in the market is 96. Each firm produces 2 units, therefore n=48. d) profit =0, Producer Surplus=0.
6. a) The total cost will increase by 500, MC will not change, therefore the output will not change. b)  The total cost will increase by 5Q, MC will increase by 5 and the output will decrease by 50.