Babydrink is a monopolist due to its patent in infant formula. The total cost for production in dollars is given by C(q) = 24q² + 600q +9600. The market demand it faces is P = 700 -9. (a) To maximize profit, how much should Babydrink produce? And what is the price it charges? (b) Verify (answer from a) gives and maximum and not minimum?
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- Q. Suppose that the demand equation for a monopolist is p = 100 − .01x and the cost function is C(x) = 50x + 10,000.(a) Find the value of x that maximizes the profit.(b) Determine the corresponding price and total profit for this level ofproduction.(c) Find the highest price that can be charged per unit to sell all.(d) The revenue function is R(x) = 100x − 0.01x2, so the marginal revenuefunction is R (x) = 100 − 0.02x. The cost function is C(x) = 50x + 10,000, so the marginal cost function is C (x) = 50. Let us now equate the two marginal functions and solve for x:(e) If the fixed cost is increased from $10,000 to $15,000, the new cost function will be C(x) = 50x + 15,000, but the marginal cost function will still be C (x) = 50. Therefore, the solution will be the same: 2500 units should be produced and sold at $75 per unit. (Increases in fixed costs should not necessarily be passed on to the consumer if the objective is to maximize the profit.)(2) function p = A monopolist (public utility company) serves a market with inverse demand 20 – q. The monopolist's long-run cost function is C(q) = 10 + 2q if q > 0 and C(0) = 0. %3| (a) If the monopolist is not regulated, what price does it charge and how much output does produce? (b) The government wants to regulate the monopolist to maximize social surplus. Describe an optimal regulation policy that ensures the monopolist does not exit the market. How much does social surplus increase with this policy?A monopolist faces a demand curve Q(p) c = 1.5 and there is no fixed cost. What is the profit-maximizing quantity? = 18p-2. The marginal cost is constant at (a) The monopolist does not enter the market. (b) The monopolist enters and the quantity is q = 2. (c) The monopolist enters and the quantity is q = 3. (d) The monopolist enters and the quantity is q (e) The monopolist enters, but chooses a quantity not listed above. = 10.
- Suppose you own a tax preparation services company, with fixed costs of $3,000/month and marginal costs of $25/appt.If the price is $60/appt, 500 appointments would be sold. If the price is $50/appt, 760appointments would be sold. a.)Use these figures to calculate the price elasticity of demand for your services. b.)Calculate the monthly profits and profit margins (profit/revenue) associated with the price of $60/appt and $50/appt. c.)Given these calculations, what price should you charge for your services, $50/apptor $60/appt? ExplainYou are the manager of a monopoly, and your analysts have estimated your demand and cost functionsas P = 300 − 3Q and C(Q) = 2, 000 + 2Q2, respectively.(a) What price-quantity combination maximizes your firm’s profits?(b) Calculate the maximum profits.(c) Is demand elastic, inelastic, or unit elastic at the profit maximizing price-quantity combination?(d) What price-quantity combination maximizes revenue?(e) Calculate the maximum revenues.(f) Is demand elastic, inelastic, or unit elastic at the revenue maximizing price-quantity combination?Exercise A.6 A monopolist facing the demand curve Q = 42 – 0.6P operates with constant average and marginal costs equal to 20. a) Calculate the quantity, price and profit obtained by the monopolist. Represent graphically. (b) What quantity, what price and what benefit will you get if you can apply first-degree price discrimination? Calculate the consumer surplus and represent graphically. c) The monopolist warns that he can separate consumers into two distinct groups with demands Q1 = 12 - 0.1P1 and Q2 = 30 - 0.5P2. Calculate the quantities, the prices you will set in each market, and the profit you will make. Represent graphically.
- (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…For a monopolist, pricing the output where the demand is relatively inelastic _____ (a) leads to decline in total revenues. (b) increases economic profits. (c) total revenue is maximised. (d) increases its market power, as consumers will not respond to price change.A monopolist produces a product with price, quantity sold and marginal cost as shown in the table below. The fixed cost is $50. Price ($) Quantity Sold Marginal Cost ($) 100 1 20 90 2 30 80 3 40 70 4 50 60 5 60 (a) If the monopolist need to sell at a standard price, determine the optimal quantity, the price, and the profit of the monopolist. (b) If the monopolist can practice perfect price discrimination, determine the optimal quantity, the price and the profit of the monopolist.
- The monthly demand function for a product sold by a monopoly is p=1960-1/3x2 dollars, and the average cost is c=1000+x2 + x2 dollars.production is limited to 1000 units and x is in hundred units. (a) Find the quanity (in hundreds of units) that will give maximum profits. (b) Find the maximum profit. (Round your answers to the nearest cent)Which of the following statements about a monopoly is true? (a) The monopolist has a flat demand curve because of high barriers to entry.(b) For a monopolistic firm, profit will be maximised where price = marginalrevenue.(c) In the long run, a monopolist can earn only normal profits.(d) Price, in the long run, is not usually equal to the minimum average totalcost.Q.1.19 Which of the following will NOT shift the market supply of labour curve? (a) A change in the wages of the labourers.(b) A change in migration.(c) A change in the size of the population due to a change in birth or deathrates.(d) Trade union action.Under what conditions is cost-plus pricing mostappropriate?