Question

A risk-neutral, price-taking firm must set output before it knows the market price. There is a...

A risk-neutral, price-taking firm must set output before it knows the market price. There is a 50 percent chance the market demand curve will be Qd = 10 – 2P and a 50 percent chance it will be Qd = 20 – 2P. The market supply curve is estimated to be QS = 2 + 2P.

a. Calculate the expected (mean) market price.
b. Calculate the variance of the market price.
c. If the firm's marginal cost is given by MC = 0.01 + 5Q, what level of output maximizes expected profits?

Homework Answers

Answer #1

Given

Qd1=10-2P with 50% probability

Qd2=20-2P with 50% probability

Qs=2+2P

So for demand curve 1

Qd1=Qs

10-2P=2+2P

P1=$2

So for demand curve 2

Qd2=Qs

20-2P=2+2P

P2=$4.5

A)

Expected market price E(P)=50%*P1+50%*P2=50%*2+50%*4.5=$3.25

B)

Variance = 50%*(P1-E(P))^2+ 50%*(P2-E(P))^2=50%*(2-3.25)^2+50%*(4.5-3.25)^2=1.5625

C)

Given MC=0.01+5Q

For demand curve 1

Qd1=10-2P

P=5-0.5Qd1=5-0.5Q

TR1=P*Q=5Q-0.5Q^2

For demand curve 1

Qd1=20-2P

P=10-0.5Qd1=10-0.5Q

TR1=P*Q=10Q-0.5Q^2

E(TR)=50%*TR1+50%*TR2=50%*(5Q-0.5Q^2)+50%*(10Q-0.5Q^2)=7.5Q-0.5Q^2

for expected profit maximization

E(MR)=MC

E(MR)=dE(TR)/dQ=7.5-Q

E(MR)=MC

7.5-Q=0.01+5Q

Q=1.248 units

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose there is a market with a big firm and many small price-taking firms (DFCF). Given...
Suppose there is a market with a big firm and many small price-taking firms (DFCF). Given that the inverse market demand function is ?=100−??p=100−Qd, the inverse supply function for small firms is ?=70+???p=70+Qcf and the marginal cost function of the dominant firm is ??=10+1/4⋅???MC=10+1/4⋅qdf. Calculate the equilibrium output of the dominant firm. Round your answer to the first decimal place.
Suppose that the market for some good is competitive and the demand curve can be written...
Suppose that the market for some good is competitive and the demand curve can be written as Qd= 200 - 4P and the supply curve can be written as Qs= 20 + 2P What is the equilibrium price and quantity in the market? Suppose that every firm in the market has total costs which can be expressed as TC= 8+10Q+5Q^2.  What is the marginal cost function of each firm? How much will each firm produce? How many firms are currently in...
Competitive Market Equilibrium. Syracuse Paper supplies printer paper in upstate New York. Like the output of...
Competitive Market Equilibrium. Syracuse Paper supplies printer paper in upstate New York. Like the output of other wholesale distributors, Syracuse Paper must meet strict guidelines and the printer paper supply industry can be regarded as perfectly competitive. Total and marginal cost relations are: TC = $3,600 + $5Q + $0.01Q2 MC = TC/Q = $5 + $0.02Q where Q is cases of printer paper per day. A. Calculate the firm's optimal output and profits if prices are stable at $20...
Question 2. The market supply and demand curves for a product are: QS=0.5P (supply curve) QD=60–2P...
Question 2. The market supply and demand curves for a product are: QS=0.5P (supply curve) QD=60–2P (demand curve) where Q is the quantity of the product and P is the market price. (1). Calculate the equilibrium price, equilibrium quantity and total social welfare. (10 points) (2). Suppose that the market has changed from a perfectly competitive market to a monopoly market, calculate the new price–output combination and the total deadweight loss in the monopoly market. (10 points)
Using the following information solve for the monopolist output and price, the perfectly competitive output and...
Using the following information solve for the monopolist output and price, the perfectly competitive output and price, the profits earned under both models and the deadweight loss that arises as a result of the monopoly: a. Demand: P=500-2Q ; Supply: P=50+3Q; MR=500-4Q b. Demand: P=1000-5Q ; Supply: P=100+5Q ; MR=1000-10Q c. Demand: P=400-4Q; Supply: P=40+2Q; MR=400-8Q Please use calculation instead of graph to find solution. This is a market demand curve.
In a perfectly competitive market, market demand is QD = 380 – 2P and market supply...
In a perfectly competitive market, market demand is QD = 380 – 2P and market supply is QS = 2P - 20. Each firm has short-run MC = 5Q and ATC = 2.5Q + (100/Q) (ATC is at minimum when Q = 6.32). 4. How much output will each firm produce? a. 180 b. 10 c. 20 d. 100 5. What is the profit/loss for each firm in the short-run? a. $-7, 000 b. $900 c. $2, 500 d. $0...
The market demand for coins is Q=800-3P. Assume there is a dominant firm and a set...
The market demand for coins is Q=800-3P. Assume there is a dominant firm and a set of fringe firms. The dominant firm’s total costs are TC=80Qd and the fringe supply is Qf= -200 + 2P. 1. Find the dominant firm’s residual demand curve. 2.Find the dominant firm’s profit-maximizing output and price. 3.Find dominant firm profits. 4.Find fringe firm output and profits.
21. In a competitive market the price is $8. A typical firm in the market has...
21. In a competitive market the price is $8. A typical firm in the market has ATC = $6, AVC = $5, and MC = $8. How much economic profit is the firm earning in the short run? a. $0 per unit b. $1 per unit c. $2 per unit d. $3 per unit 22. Consider a firm operating in a competitive market. The firm is producing 40 units of output, has an average total cost of production equal to...
Problem 3. A price-taking firm produces an output Q which sells for a price of $20...
Problem 3. A price-taking firm produces an output Q which sells for a price of $20 per unit. The firm’s short-run costs are as follows: Fixed costs = 50 Variable cost = 0.1Q2 + 10Q Marginal cost = 0.2Q + 10 a. What output should the firm produce? Don’t forget to consider the possibility that the firm might choose Q = 0. b. What are its profits? Please be thorough
Assume an oligopolistic market with one large dominant firm. The dominant firm's marginal cost is given...
Assume an oligopolistic market with one large dominant firm. The dominant firm's marginal cost is given by the following equation: MC = 0.48 Q The market demand is the following: QD = - 14 P + 309 The supply of the smaller firms combines is given by the following equation: QS = 16 P + 192 What is the profit-maximizing amount of output for the dominant firm? ________________________________________________________________ Assume a duopoly market with quantity competition. The market inverse demand is...