Suppose that there are 20 identical firms in a perfectly competitive market.

Each firm has a total cost function of TC = 50 + 0.2q2, where q

is a firm's output

The market demand function is QD = 280 - 20P, where P is the

price per unit of output and QD is total market demand.

1.1 (4 points) Derive the market direct supply equation (QS =

f(P))

The market direct supply equation Qs = f(P) = _____________

1.2 (3 points) Calculate the short run equilibrium market price

(P*) and total quantity (Q*) in the market. P* = $ __________ Q* =

___________ units.

1.3 (2 points) Determine the profit-maximizing quantity (q*)

that each firm would produce. q* = ___________________ units.

1.4 (7 points) Determine the profit, the average total cost

(ATC),

and the average variable cost (AVC) of the firm at its profit-maximizing

quantity (q*).

The firm's profit (i) = $ ____________

The firm's ATC at q* = $ ____________

The firm's AVC at q* = $ ____________

The firm would:

a. shut down because its AVC at q* < P* < its ATC at q*.

b. shut down because P* < its AVC at q*.

c. continue producing because its AVC at q* < P* < its ATC

at q*.

d. continue producing because P* > its ATC at q*.

4 1.5 (4 points) Draw the market supply curve. Calculate the

firm's producer surplus and the market's producer surplus.

The firm's producer surplus = $ ____________

The market's producer surplus = $ __________

The direct market supply equation:

The inverse market supply equation:

Suppose that a monopolist's market demand and total cost equations are

Q = 8 - 0.5P,

TC = Q + 0.5Q2 .

2.1 (2 points) Derive inverse demand, total revenue, marginal

revenue and marginal cost equations.

Inverse demand equation: P = f(Q) =

_______________________________

Total revenue equation: TR = f(Q) =

_______________________________

Marginal revenue equation: MR = f(Q) =

___________________________

Marginal cost equation: MC = f(Q) = ______________________________

2.2 (3 points) Determine the monopolist's profit-maximizing

output (Q*) and price (P*).

Q* = ______________ units.

P* = $_____________

2.3 (7 points) Draw a figure showing demand curve, marginal

revenue curve, and marginal cost curve. In your figure, also show the

profit-maximizing quantity (Q*) and price (P*).

2.4 (18 points) Now suppose that the firm's total cost is TC =

2Q. The market demand equation remains the same.

a) (3 points) Determine the new profit-maximizing quantity (Q*)

and price (P*).

Q* = ______________ units.

P* = $_____________

b) (5 points) Draw a figure showing the demand curve, marginal

revenue curve, and new marginal cost curve. In your figure, also show the

profit-maximizing quantity (Q*) and price (P*).

c) (10 points) From your figure in Question 2.4b, determine the

consumer surplus, the producer surplus and the deadweight loss.

The consumer surplus = $_____________

The producer surplus = $ _____________

The deadweight loss = $ ______________