Economics for Manager

Questions: 1). We have demand equation: P = 6 Q and supply equation: P = Q. Calculate the equilibrium price, equilibrium quantity and the total surplus. Suppose government imposes lump sum tax 1$ per unit of output. Derive the new supply curve (assuming linearity) and also calculate the new equilibrium price and quantity. Is there any dead weight loss? Given the above demand equation, calculate the price elasticity of demand when Q = 5. 2). Suppose a monopolist faces a demand curve P= 10-Q. The monopolist incurs average cost (AC) which equals his marginal cost (MC). Let assume that AC=MC=8. If the monopolists marginal revenue (MR) is given by the equation MR=10-2Q then answer the following questions: Suppose this monopolist is not allowed to discriminate the price then what will be his profit maximizing output level? What will be the monopolists total profit and price at the profit maximizing output level? Suppose this monopolist knows exactly whose reservation price is what and starts price discrimination (first degree) then what will be the output level the monopolist produce and what will be total profit at that level of output? 3). Do you think Law of minimum wage is a problem? Explain. Answers: (1). The demand equation is, P= 6- Q and supply equation is, P=Q. At equilibrium the demand and supply is equal (Baumol and Blinder 2015). Therefore, 6- Q = Q 2Q = 6 Q= 6/2 = 3 By putting the value of Q = 3 (Equilibrium quantity) in the demand function or supply function, the value of P (equilibrium price) will be equal to 3. The total surplus (Revenue) is equal to PQ = 3 3 = 9 Suppose the government imposes lump sum tax of $1 per unit of output, then the new supply equation assuming linearity will look like P= Q+ 1 Therefore, the equilibrium condition will be 6- Q = Q+ 1 6- 1 = 2Q Q = 5/2 = 2.5 Hence, the new equilibrium quantity is 2.5 unit and putting the value of Q in the new supply equation, the equilibrium price will be P= 3.5. The total surplus (Revenue) is equal to PQ = 3.5 2.5 = 8.75 Therefore, the loss of revenue can be considered as deadweight loss. The amount of deadweight loss is 9- 8.75= .25. Another way of calculating dead weight loss can be obtained from the above diagram. ABC area is the dead weight loss. The area of ABC triangle is double of two small triangles within it. Hence, area of ABC triangle will be, 2 [ (3.5 3) (3-2.5) ]= 2 0.125 = 0.25. The price elasticity of demand = (Nicholson and Snyder 2014) The demand equation is Q= Q-P = -1 When Q= 5, then P= 6- 5 = 1. Therefore, the price elasticity of demand will be = -1 1/5 = -1/5 (2). The demand curve of the monopoly P= 10-Q. This is also the Average Revenue Curve. The Average Cost and Marginal Cost is equal to 8. The marginal revenue is 10-2Q. When the monopolist is not allowed to discriminate price, then the profit maximizing output is decided at a price level where, MR = MC (Rader 2014). 10-2Q = 8 2Q = 2 Q= 2/2 =1 Hence, without price discrimination the monopolists profit maximizing output level is 1. The price of monopolist will be P= 10- Q = 10- 1 = 9. The area colored in green is the monopolists surplus. The amount will be the difference between the revenue and cost. The monopolists revenue is P Q = 9 1= 9. The total cost = AC Q = 8 1 = 8. Therefore, the profit will be 9-8= 1unit. Since the monopoly knows the reservation price and starts price discrimination of first degree, then the final output will be higher. Here the quantity will be set where the AR curve equals the MC curve. Therefore, 10- Q = 8 (since, AR =MC) Q = 10-8 = 2 However, the first-degree price discrimination is known as perfect price discrimination (Rayna, Darlington and Striukova 2015). The monopoly will charge the price, which is the maximum price the consumer is willing to pay. Hence, the reservation price is 10, which is the intercept of AR curve. The monopolists profit is the area ACD. The profit of the monopoly will be (10-8) 2 = 2 unit. (3). If the minimum wage is set below the equilibrium wage of market, then imposing the minimum wage is not an issue for the firm or for the economy. This is because; if the minimum wage is below the market wage, then the firm can increase the wage rate to maintain the equilibrium in the market. However, the problem arises, when the minimum wage is set above the market price. This is because the, at the point of minimum wage above market wage rate, the demand for labor is less than the supply of labor. At this wage rate, the firm will demand less. Therefore, due to minimum wage, the problem of unemployment takes place (Meer and West 2015). More people are willing to work at this higher price but the firms reduce their demand in order to reduce their labor cost. This can be represented in the following diagram.