Managerial Economics Study Set 10

Business

Quiz 10 :
Special Pricing Practices

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Quiz 10 :
Special Pricing Practices

There are only two firms in the Widget industry. The total demand for widgets is img . The two firms have identical cost functions, img . The two firms agree to collude and act as though the industry were a monopoly. The Price and Quantity at which this cartel would maximize its profit can be calculated by inverting the demand function for P: Given: img Total Revenue for both firms can be calculated by img Total Cost of both firms img For Maximum Profit MC = MR img From (1) we can find equilibrium P img Thus, we can say that Profit Maximizing price is P=12.5 and Profit Maximizing quantity is Q = 5.

The given statement state that "If a company sets its price on the basis of a cost-plus calculation, it cannot possibly suffer a loss on its products.", This statement is false because company profit depends on the market price. If the market price is lower than the company's price then company have to bear the losses. Thus, it is False , that setting prices on the basic of cost-plus calculation cannot leads to loss.

The demand of a good is the quantity necessary of that good by the persons of an economy. The prerequisite turn out to be a demand when individuals are ready and able to pay for the good. Supply of a good is the amount of a good that the manufacturers are ready to sell in a market. Equilibrium price is the price at which demand and supply are equal. Similarly, equilibrium quantity is the quantity of a good exchanged in the market after arbitration. a. The demand function and the cost function is given as: img 1. The price and quantity if B well maximize profits is calculated as follows: img First, calculate total revenue (TR) by multiplying price and quantity and calculate marginal revenue (MR) as follows: img Calculate marginal cost (MC) as follows: img img Now, using the profit maximizing condition calculate Q as follows: img Now substitute the values of Q in the given demand function and solve for P as follows: img Hence, if B well maximize profits then the price would be img and the quantity would be img . 2. In order to find price and quantity when revenue is maximized, first find the average revenue (AR) by dividing the TR by Q as follows: img Now, calculate average cost (AC) by dividing TC by Q as follows: img Now, using the revenue maximizing condition, the price and quantity is calculated as follows: img img Substitute the value of Q in the demand function and solve for P as follows: img Hence, the revenue maximizing price is img and quantity is img . 3. In this case, minimum profit is required to be $300, before maximizing revenue. So when P = 350 and Q = 7.5 (calculated in part 1.) the profit will be calculated as: img img Since, profit estimated here is $425, thus satisfies the minimum profit condition. Now consider the revenue maximization (calculated in part 2.). Hence, img and img b. The demand function and the cost function is given as: img 1. The profit maximizing price and quantity is calculated as follows: Since, the demand function is same as given in part (a), therefore the TR and MR will be same. Now calculate MC as follows: img It shows that MC is also same as calculated in part (a). Thus, the price and quantity will be same as calculated in part (a). Hence, the profit maximizing price is img and quantity is img . 2. In order to find price and quantity when revenue is maximized, first find the AR and AC. Since, TR is same as calculated in part (a), so AR will also be same. Now calculate average cost (AC) by dividing TC by Q as follows: img Now using the revenue maximizing condition, the price and quantity is calculated as follows: img img Substitute the value of Q in the demand function and solve for P as follows: img Hence, the revenue maximizing price is img and quantity is img . 3. In this case, minimum profit is required to be $300, before maximizing revenue. So when P = 350 and Q = 7.5 (calculated in part a (1)) the profit will be calculated as: img img Since, profit estimated here is $345, thus satisfies the minimum profit condition. Now consider the revenue maximization (calculated in b (2)). Hence, the img and img c. The answer is same in a(1) and b(1) because the MR and MC are same and thus, the profit maximizing price and quantity are same. On the other hand, answer is not same in a(3) and b(3) because AC is different in both cases.