Suppose the inverse demand function for a monopolistically competitive firm’s product is given by; P = 1000 – 20q and the ,cost function is given by; C(q) = 50 + 20q Required: a. Determine the profit maximizing price (P*) and quantity (Q*) and the maximum profit (π*) b. Why should a monopolist sells output at P > MR?
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P = 1000 – 20q
and the ,cost function is given by;
C(q) = 50 + 20q
Required:
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- The demand and total cost functions for a monopolistically competitive market are: Q(P) = 300/N – P, where N = number of firms TC(Q) = 50 + Q² In the long run, how many firms are in the market (round to the nearest integerSuppose the inverse demand function for a monopolistically competitive firm’s product is given by P=100 − 2Q and the cost function is given by C(Q ) = 5 + 2Q Determine the profit-maximizing price and quantity and the maximum profits.The demand and total cost functions for a monopolistically competitive market are: Q(P) = 300/N – P, where N = number of firms TC(Q) = 50 + Q2 There are currently three firms in this market and they are in a short run equilibrium. c) In the long run, how many firms are in the market (round to the nearest integer)?
- The demand function for a monopolistically competitive firm's product is Q = 100 – 4P, while the firm's cost function is C = 500 + 10Q + 0.5Q2.(a) Determine the firm's equilibrium price and quantity.(b) Is the firm in long-run equilibrium? If not, what is expected to happen in the long run if the firm remains in the industry?Suppose a monopolistically competitive firm is in long-run equilibrium. The firm's demand curve is tangent to its average cost curve at Q = 25. Average cost is minimized at Q = 35, where average cost is $50. Which of the following is true? Group of answer choices This firm maximizes profit at an output level of 35 units. This firm maximizes profit at an output level lower than 25 units. This firm maximizes profit at an output level of 25 units. This firm incurs an economic loss in the long run. This firm maximizes profit at an output level greater than 35 units.1.-Dayna’s Doorstops, INC. (DD) is a monopolist in the doorstop industry. Its total cost function C(⋅) is given by the quadratic function of output C(Q) =100 – 5Q + Q2 . The inverse demand function for doorstops P(⋅) is given by the linear function P(Q) = 55 – 2Q . Note that the marginal cost C′(Q) is not constant. (Also, it happens to be negative for 0 ≤ Q < 2.5.) (a) Write down the profit-maximizing problem for DD, and determine its optimal output, QM. (b) Find the profit-maximizing price set by DD, PM and its marginal cost at the output level QM. From these two pieces of information, can you compute the elasticity of demand at that same level of output without taking any derivative? (c) How much consumer surplus CSM and producer surplus PSM and total surplus does DD generate by its profit-maximizing plan? (d) Find the profit-maximizing output, Qc, if DD acted like a price-taker (i.e., a perfect competitor). (e) Find the profit-maximizing price set by DD, Pc, as well as its…
- Suppose the demand facing the monopolistic firm is given by P(y) = 1 − p. • Calculate the demand elasticity of price at y = 0.5 and y = 1. • Suppose that the total cost function is T C(y) = cy where c is a positive constant.Show formally that the monopolist will chose a point on the elastic portion of the demand.If a monopolistic firm has an increasing marginal cost (MC) curve, it is not in its interest to apply a two-part tariff. Comment on statement by arguing CONCEPTUALLY, GRAPHICALLY and ALGEBRAICALLY.A single-price monopolist faces an inverse demand function of: P(Q,B)=100−Q+B0.5, where Q is the quantity, P is the price, and B is the level of advertising. The marginal cost is a constant $10 per unit, the cost per unit of advertising is $1, and there are no fixed costs. Solve for the firm's profit-maximizing price, quantity, and level of advertising. Hint: the profit function must be maximized with respect to two choice variables (Q and B). The profit-maximizing quantity is -------? units. (round your answer to two decimal places) The profit-maximizing level of advertising is----------? units. (round your answer to two decimal places) The profit-maximizing price is-----? (round your answer to two decimal places)
- Building on problem 5.3 in chapter 5, consider the CES utility function written as in (8.2), (c) Also show that equation (8.9) holds, which we re-write as: Problem 5.3 Suppose that industry 1 is monopolistically competitive, with a CES sub-utility function as described in problem 5.2. We let the marginal costs be denoted by c1(w,r), and the fixed costs in the industry by αc1(w,r). That is, the fixed costs use labor and capital in the same proportions as the marginal costs. Industry 2 is a competitive industry, and each industry uses labor and capital. (a) Write down the relationship between the prices of goods and factor prices. Does the StolperSamuelson Theorem still apply? (b) Write down the full-employment conditions for the two factors. Does the Rybczynski Theorem still apply in some form? How are your answers to (a) and (b) affected if the fixed costs in industry 1 uses different proportions of labor and capital than the marginal costs? Problem 5.2 In…A monopolistically competitive firm is considering selling several units of the same product as a single package. A typical consumer's demand for the product is Q = 10 - 0.5P and the total cost function is C(Q) = 8Q. What is the optimal number of units to put into a package? What is the optimal price to charge for the package? What are the profits for this pricing scheme?The demand function for a monopolist is given by: P1 = 1,250 – 3.5Q and the cost function is given by C(Q) = 1,200 +1.5Q + 0.8Q2. This firm, Otsuka, is a pharmaceutical holding a patent on a depression treatment, Rexulti. However, the patent expired, and a generic treatment is offered in the market. Now, the new market price is P=$400. What is optimal Q given the new market price?
