Managerial Economic and Quantitative Analysis Essay

Managerial Economic and Quantitative Analysis - Essay Example Thomas & Maurice, 2007). So in order to obtain the profit equation, total cost equation is subtracted from the total revenue equation (that is, profit = total revenue – total cost). However, from the equations given, there is no total cost and total revenue function. In order to obtain a total revenue function of the two firms, the demand function of each firm is integrated, and in order to obtain the total cost of each firm, the average cost function of each firm is integrated. After obtaining the total revenue and total cost functions, it is now possible to obtain the profit function. Economists argue that profits are maximized where total cost balances total revenue. So in order to obtain optimal price and output of each firm working individually, the total cost function is equated to the total revenue function (R. Thomas, C. Thomas & Maurice, 2007). This helps in obtaining the optimal output and price. Optimal price and output may also be obtained through differentiating t he profit function of each firm and equating it to zero, and then solving for the values of price and output. Consider the second case, where the two companies work together. ... Thomas, C. Thomas & Maurice, 2007). Part Two Estimation of the price per plane The estimated price per plane is as follows. price per plane (million $) probability Estimated price per plane (million $) 125 0.25 500 175 0.25 700 225 0.5 450 Optimal output and price when the firms act individually Airbus optimal price and output Airbus demand function is P = 500 – 0.0003Q. From this demand function, the total revenue function derived by integrating the demand function is TR = 500Q – 0.0003Q2. Airbus has the following Average cost function; AVC = 104.8822Q – 0.001Q2 + 0.09 Q3. By integrating this average cost function, a total cost function is obtained; TC = 104.8822Q2 – 0.001Q3 + 0.09Q4. In order to determine the optimum quantity and price the profit function is obtained first and then differentiated with respect to output. The profit function obtained is 500Q – 104.8825Q2 + 0.001Q3 – 0.09Q4. Differentiating this profit function and solving for the value of Q yields the value of Q as 500 M. Hence, substituting the value of Q in the original demand function, the value of P obtained is $ 499.85 M. thus; the optimal values of price and output are $ 499.85 Million and 500 million respectively. Boeing Optimal Output and Price The demand function of the firm is P = 700 – 0.00013Q. The total revenue function obtained through integration of the demand function is TR = 700Q – 0.00013Q2. The Average cost function of the firm is AVC = 25.8678Q – 0.00023Q2 + 0.4Q3. Integration of this function yields TR = 25.8678Q2 – 0.00023Q3 + 0.4Q4. From the total revenue and total cost functions, the following profit function is obtained, which is then differentiated and equated to zero in order to obtain the value of Q that is