Problem 1: A company's revenue function can be defined as; TR = Price (P) × Quantity Demanded (Q). If the ordinary demand function for your firm Q=75-0.4P where Q is monthly output: a. Show that MR will be less than AR for any positive level of Q. Why that? b. What is the quantity level that maximizes total revenue? What is the price?

The demand curve for product a is given as Q = 2000 - 20P. a. How many units will be sold at $10? b. At what price would 2,000 units be sold? 0 units? 1,500? c. Write equations for total revenue and marginal revenue (in terms of Q). d. What will be the total revenue at a price of $70? What will be the marginal revenue? e. What is the point elasticity at a price of $70? f. If price were to decrease to $60, what would total revenue, marginal revenue, and point elasticity be now? g. At what price would elasticity be unitary?

Question a) The average cost function of a competitive firm is AC= 5/Q+5+9*Q. The optimal quantity is: 10. How much is the profit? b) The average cost function of a competitive firm is AC= 3/Q +8 +9*Q The optimal quantity is: 3 How much is the profit? c) The marginal utility of x is 100-5x, and that of y is 200- 6y. The price of x is 1, the price of y is 2, the income of the consumer is 100. How many of y is there in the optimal basket?

On the graph input tool, change the number found in the Quantity Demanded field to determine the prices that correspond to the production of 0, 6, 12, 15, 18, 24, and 30 units of output. Calculate the total revenue for each of these production levels. Then, on the following graph, use the green points (triangle symbol) to plot the results.   Calculate the total revenue if the firm produces 6 versus 5 units. Then, calculate the marginal revenue of the sixth unit produced. The marginal revenue of the sixth unit produced is________.   Calculate the total revenue if the firm produces 12 versus 11 units. Then, calculate the marginal revenue of the 12th unit produced. The marginal revenue of the 12th unit produced is_________.