Suppose that the cost of producing q appliances is c(q)=200-q+0.96q^2 and the demand function is given...

Suppose that the cost of producing q appliances is c(q)=200-q+0.96q^2 and the demand function is given by q=400-25p.

Develop the total revenue, total cost (if not given), and profit functions. Explain these functions in few sentences.
Compute the point elasticity of demand.
Find the intervals where the demand is inelastic, elastic, and the price for which the demand is unit elastic.
Find the quantity that maximizes the total revenue and the corresponding price. Interpret your result.
Find the quantity that minimizes the average cost function and the corresponding price. Interpret your results.
What are the quantity and the price that maximize the profit? What is the maximum profit? Interpret your result.
Discuss the results of 6, 7 and 8.

In this part, we assume that the supply function is given by, p=8+q

Find the price and the quantity at the equilibrium.
Calculate the consumer surplus.
Calculate the producer surplus.

Expert Solution

Rahul Sunny answered 2 years ago

A firm's total cost of producing Q units of output is C (Q) = 200 +...

A firm's total cost of producing Q units of output is C (Q) = 200 + 50Q. The inverse demand curve for the firm's product is P(Q) = 80-Q, where P denotes the price of the product. a) If the price of the product is set equal to the firm's average, how much will the firm produce? (5 points) Hint: choose the larger of the two numbers. Show your work. b) If the firm is under marginal cost pricing, how...

Your firm’s cost function for producing plexiglass is given by C(q) = 30 + 5q +...

Your firm’s cost function for producing plexiglass is given by C(q) = 30 + 5q + 0.25q2. You are currently producing q = 4 units, and you receive a request to produce and sell one additional unit. The difference between your marginal cost of producing one more unit and your average variable cost of producing 5 units is _____. (Input a number, such as "56", with no dollar sign or quotation marks.)

Let market demand be given by Q(P) = 200 ? P. Each firm’s cost function is...

Let market demand be given by Q(P) = 200 ? P. Each firm’s cost function is C(qi ) = 20qi , where i = 1, 2. (a) Using the Cournot model, find each firm’s output, profit, and price. (b) Graph each firm’s reaction function. Show the Cournot equilibrium. (c) Suppose that the duopolists collude. Find their joint profit-maximizing price, output, and profit; find each firm’s output and profit. (d) Does each firm have an incentive to increase output? What is...

Suppose a company's revenue function is given by R(q)=−q^3+360q^2 and its cost function is given by...

Suppose a company's revenue function is given by R(q)=−q^3+360q^2 and its cost function is given by C(q)=300+19q where q is hundreds of units sold/produced, while R(q) and C(q) are in total dollars of revenue and cost, respectively. A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.) MP(q)= B) How many items (in hundreds) need to be sold to maximize profits? (Round your answer to two decimal places.) Answer: hundred...

Suppose a monopolist’s cost is given by C(Q) = 12 + Q2 and the industry demand...

Suppose a monopolist’s cost is given by C(Q) = 12 + Q2 and the industry demand for the product is estimated to be P = 24 – Q. a. Graph demand, marginal revenue and the marginal cost curve. What is the monopolist’s profit maximizing quantity and price? b. If this industry was made up of many firms that produced an identical product what would be the resulting equilibrium quantity and price? c. Is there deadweight loss in the case of...

A toy manufacturer's cost for producing q units of a game is given by C(q) =...

A toy manufacturer's cost for producing q units of a game is given by C(q) = 1460 + 3.5q + 0.0006q2. If the demand for the game is given by p = 8.6 − (1/440)q. How many games should be produced to maximize profit? (Round your answer to the nearest integer.)

A monopoly faces market demand Q = 30−P and has a cost function C(Q) = Q^2...

A monopoly faces market demand Q = 30−P and has a cost function C(Q) = Q^2 (a) Find the profit maximizing price and quantity and the resulting profit to the monopoly. (b) What is the socially optimal price? Calculate the deadweight loss (DWL) due to the monopolist behavior of this firm. Calculate consumer surplus (CS) and producer surplus (PS) given the profit maximizing price. (c) Assume that the government puts a price ceiling on the monopolist at P =22. How...

A monopolist has a cost function given by c(?)=?2 and faces a demand curve given by...

A monopolist has a cost function given by c(?)=?2 and faces a demand curve given by P(?)=120−y. (a)What is its profit-maximizing level of output? What price will the monopolist charge? (b)Calculate the deadweight loss imposed by the monopolist. Show also the deadweight loss in a graph (c)If you put a lump sum tax of $100 on this monopolist, what would its output be? (d)Suppose that you put a specific tax on the monopolist of $20 per unit output. What would...

Suppose that a competitive firm's marginal cost of producing output q is given by MC(q) =...

Suppose that a competitive firm's marginal cost of producing output q is given by MC(q) = 3+2q. Assume that the market price of the firm's product is $9. (a) What level of output will the firm produce? (b) Suppose that the average variable cost of this firm is given by AV C(q) = 3 + q. Suppose that the firm's fixed costs are known to be $3. Will the firm be earning a positive, negative, or zero profit in the...

Suppose the demand for a particular textbook, as a function of price, is given by Q...

Suppose the demand for a particular textbook, as a function of price, is given by Q Demanded (P)=60-P, and supply as a function of price is Q Supplied (P)=P. (a) What is the equilibrium price and quantity in this market? (b) Sketch the supply and demand curves on the same graph. (c) If the price were fixed at P=10 is there a excess supply or excess demand of textbooks, and by how much? (d) In equilibrium, what is the producer...

Question