MANAGERIAL ECONOMICS2 Question 12 QD = 240 – 20P QD = Quantity demanded = Q while P = Price 20P = 240 – Q P = 12 – 1/20Q From the equation above, the following values in the table have been calculated for the demand curve: P01263 Q2400120180 The marginal revenue is calculated by finding the total revenue derivative TR = P * Q = (12 – 1/20Q) * Q = 12Q – 1/20Q2 MR = d TR/ d Q = 12 – 2/20Q ; hence the marginal revenue curve is two times steeper the demand curve The following values have been calculated for the marginal revenue: MR12063 Q01206090 MC = Change in TC/ Change in quantity produced ATC = TC/Quantity produced AVC = VC/Quantity produced
MANAGERIAL ECONOMICS3 Given Q = 80, P = 12 – ((1/20)80) = 8 ATC = 10 and AVC = 6 Firms maximize their profits at a point whereby the marginal cost equals the marginal revenue (Demsetz 2013, p.375). Given Q = 80, the marginal revenue is MR = 12 – ((2/20)80) = 4 a.The graph is as shown below: b.In the short run period, the firm makes profit. The profit made is calculated below: Profit made = (calculated price at quantity Q which is given as 80 minus the average variable cost which is 6) * the quantity given which is 80
MANAGERIAL ECONOMICS4 Profit = (P - 6) * Q = (8 - 6) * 80 = $ 160 In the short run period, the firm makes a profit of $ 160 and hence remains in business. Also many businesses have not yet entered the market and hence the firm remains in the business. Question 15 Gasoline stations are 100 and are self-service and also identical Demand function is given as QD = 60000 – 25000P Where QD = quantity demanded and p = price which is expressed as dollars per gallon The supply curve is given as QS = 25000p where p > $ 0.6 a.The equilibrium price is calculated as follows: The equilibrium price refers to the price at a point whereby the quantity demanded and the quantity supplied are equal (Burdett and Judd 2010, p.955). In other words at equilibrium point, the quantity demanded and the quantity supplied are equal Hence QD = QS at equilibrium This means that 60000 – 25000p = 25000p But Q = 60000 – 25000p 25000p = 60000 – Q ; p = (60000/25000) – (Q/25000) Hence P = 2.4 - Q/25000 b.The average revenue function is P = 2.4 – Q/25000
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MANAGERIAL ECONOMICS5 The figures for the curve are as calculated in the table below: P02.421 Q6000001000035000 TR = P*Q = (2.4 –Q/25000) * Q TR = 2.4Q – Q2/25000 MR = d TR/ d Q = 2.4 – Q/12500 The values for the marginal revenue curve are calculated as shown: P02.421 Q300000500017500 The supply curve values are calculated as shown from the function QS = 25000P P122.4 Q250005000060000 The graphs are plotted as shown below:
MANAGERIAL ECONOMICS6 From all the drawn curves, the monopolist’s equilibrium output and price has been shown in the diagram above, as 19000 and $0.8 respectively. The equilibrium output and price is found at a point whereby the monopoly obtains the maximum profit, that is, marginal cost and the marginal revenue are equal. c.Yes. A monopoly faces allocative inefficiency. This means that the available resources are underutilized and hence what is produced is less than what is demanded in the market. This occurs in a monopoly due to the cartel like behavior in order to hike prices and make more profits by supplying small amounts of commodities in the entire market. Perfect competition market is more efficient than a monopoly market due to the fact that stiff competition is involved in the perfect competition. This means that the producers in the perfect competition market efficiently use the available resources to produce the