The demand and total cost functions for a monopoly firm are: Q(P) = 39.5 – 0.5P TC (Q) = 60 – Q + 0.5 Q^2 d) What are the firm's fixed and variable costs? e) What would be the socially optimal Q* and P* (round to 1 decimal place if needed)?
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The demand and total cost functions for a
Q(P) = 39.5 – 0.5P TC
(Q) = 60 – Q + 0.5 Q^2
d) What are the firm's fixed and variable costs?
e) What would be the socially optimal Q* and P* (round to 1 decimal place if needed)?
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- The demand and total cost functions for a monopoly firm are: Q(P) = 39.5 – 0.5P TC(Q) = 60 – Q + 0.5 d) What are the firm's fixed and variable costs? e) What would be the socially optimal Q* and P* (round to 1 decimal place if needed)?The demand and total cost functions for a monopoly firm are: Q(P) = 39.5 – 0.5P and TC(Q) = 60 – Q + 0.5 Q^2 What would be the socially optimal Q* and P* (round to 1 decimal place if needed)? - where MC intersects the demand curveSuppose the inverse demand function is linear: p(q) = a - Bq. The monopolist's cost function is c(q) = 6q2 . Assume the monopolist must charge a uniform price. (a) Find the optimum monopoly price and quantity. Also calculate the deadweight loss. (b) Suppose the government can levy a lump-sum tax T (i.e., a fixed amount independent of production) and an excise tax t per unit of production on the monopolist. These taxes can be negative, in which case they are subsidies. The proceeds of these taxes can be transferred to consumers. The monopolist is always free to quit the market, in which case she does not have to pay any taxes. The government wants to maximize the consumer welfare. Find the optimum values of t and T.
- The demand and total cost functions for a monopoly firm are: Q(P) = 39.5 – 0.5P TC(Q) = 60 – Q + 0.5 Q² What would be the socially optimal Q* and P* (round to 1 decimal place if neededConsider a market with 190 consumers. Of these, 90 of them have individual (inverse) demands given by: PM(Q)=10−Q, while each of the other 100 has an individual (inverse) demand of PS(Q)=10−10Q. The cost function of the monopolist serving this market is C(Q) = 6Q - Q^2/400 . (a) Find the aggregate demand. Analyze the cost function and find what kind of returns to scale it exhibits. Compute the efficient total output (ignoring break-even constraints).(b) Compute the optimal linear price (and quantity) for this monopolist, and the deadweight loss.A monopolist has a cost function of c(y)=yso that its marginal costs are constant at $1 per unit. it faces the following demand curve: 0 if p> 20 or 100/y if p is less than or equal to 20 find (1) What is the profit-maximizing choice of output? (2) If the government could set a price ceiling on this monopolist in order to force it to act as a competitor, what price should the government set? 3) What output would the monopolist produce if he is forced to behave as a competitor?
- A monopolist's demand function is given by D(p) = 90 – 2p. This - monopolist is facing a cost function, C(y) = (1/2)y² + 600. (a) Is this a natural monopoly? Explain. (b) How can government regulate this monopolist to produce the efficient amount of products?Let a firm have a cost function C = 100 +5Q2. (a) If the firm can sell as much product as it wants at a price P = 100, how much will it produce and what will her profit be? (b) If the firm is a monopoly and faces a demand function P = 200 – 5Q. Determine the firm's output, price, and profit. (c) At what level of output is the monopolist's revenue maximized and what is the profit in this production?In a monopoly situation, the equation for the demand for a certain commodity in dollars per unit is (P) = 12-0.5x. If the total cost for the production and sale of x units is given by C (x) = - x ^ 3/100 + 3 ^ 2/10, calculate the unit price if profit is to be maximized.
- If D (p) = 100/p and c(y) = y² a) What is the optimal level of output of the monopolist? b) What is the optimal level of output if there is a tax of $0.10 per unit paid by the monopolist? c) What is the optimal level of output if there is a tax of S0.10 per unit paid by the consumer? That is, the consumer pays Sp + 0.10.(a) A monopolist has discovered that the inverse demand function of a person with income Y for the monopolist’s product is P = 0.002Y-Q where P is the price, Y the income, and Q is the output. The monopolist can observe the incomes of its consumers and hence vary its price accordingly. The monopolist has a total cost function C(Q) = 100Q. Calculate the profit maximising price as a function of the consumer’s income Y carefully explaining all the steps in the derivation of the formula. (b) A monopolist has a constant marginal cost of £2 per unit and no fixed costs. He faces two separate markets in the United States and in the UK. The goods sold in one market are never resold in the other. He sets one price P1 for the US market and another price P2 for the UK market (both measured in £). The demand in the United States is given by Q1=7,000-700P1 and the demand in the UK is given by Q2=1,200-200P1. Calculate the profit maximising output produced and price charged in each country by the…Suppose a certain city has a monopoly cable-television company. This company has total costs TC = 0.25Q2 + 30Q + 70. (Hint: using calculus, this means MC = 0.5Q+ 30since MC is the derivative of TC with respect to output.) The demand in the community is approximated by the equationQd = 60- P/2(alternatively, you can write the demand equation as Qd = 60–0.5P). Graphically depict the demand curve as well as the marginal cost (MC) curve. If the cable company is free to choose its own pricePm and quantityQm, graphically depictthe monopoly equilibrium price and quantity. Add any other curve(s) to your diagram that may be required to obtain this outcome. Compute and state the exact monopolist equilibrium pricePm and quantityQm that you depicted graphically.