Price ($) 40 36 32 28 24 20 16 12 00 4 0 4 8 12 16 20 24 28 32 36 40 Quantity per period a. If the firm wishes to maximize its total revenue, at what price should It sell its pots? 12 What is its total revenue? $ 216 b. Suppose that the firm were to Increase its price by $4 from the price in (a). What will be the change in its total revenue? Give your answer as an absolute number. 56 What is the co-efficient for the price elasticity of demand between those two prices? Round your price answer to two decimal places. -2 Ⓡ c. Suppose that the firm were to decrease its price by $4 from the price in (a). What will be the change in its total revenue? Give your answer as an absolute number. 40 What is the co-efficient for price elasticity of demand between those two prices? Round your price answer to two decimal places. -0.54

Consider a small landscaping company run by Mr. Viemeister. He is considering increasing his firm’s capacity. If he adds one more worker, the firm’s total monthly revenue will increase from $50,000 to $62,000. If he adds one more tractor, monthly revenue will increase from $50,000 to $58,000. Each additional worker costs $4,000 per month, while an additional tractor would also cost $4,000 per month.   Instructions: Enter your answers as a whole number.   a. What is the marginal revenue product of labor?        $         The marginal revenue product of capital?        $    b. What is the ratio of the marginal revenue product of labor to the price of labor (MRPL/PL)? :      What is the ratio of the marginal revenue product of capital to the price of capital (MRPC/PC)? :

①The total cost for producing x items is given by 12x + 3735. Each item is sold for $21. Find the formula for the total items must be sold to break even? revenue. How Many ②Solve the equation x² - 10x = -2x-15 3 A department store will buy 8 items if the price is $40 per item, and 14 items if the price is $28 per item. The Supplier is willing to sell 5 items if the price is $70 per item and 12 items if the price is $140 per item. If the supply and demand functions are linear, find the equilibrium point. invest $10,000 in an account that pays 10% compounded you continuously, how much money will you have in 15 years? (4) If ⑤ het f(x) = 300 √x + 2. Find the average rate of change when x increases from 25 to 100. Calculate derivatives of the following functions. a) 2 2x-3 4x+5 b) (2x5 +1) 9 ⑦Calculate derivatives of the following functions 8 の 2 6x в) че 6) 1) In (3x² + 5x) Calculate the following integral S (8x7 - 12x 5 + 3x² + 4) dx

4 total cost is c(4, r, q) 5 total 75. If Firm A has constant marginal cost, and input prices double to 2r and 2w, how much will it cost to produce q 6 units of output (what is c(6, 2r, 2w))? (HINT: First calculate the marginal cost for c(q, r, w), then calculate c(6, r, w), and then calculate c(6, 2r, 2w)) = Firm A has cost function c(q, r, w). At output q = cost is c(5,r, q) ○ c(6, 2r, 2w) ○ c(6, 2r, 2w) = 90 ○ c(6, 2r, 2w) = 150 c(6, 2r, 2w) O c(6, 2r, 2w) = 180 - = - 75 160 = 60, and at output q -

8. A commodity has price demand function p(x)= 11800 - .01x and each unit costs 1000 and the overhead is 5000. a) what is the revenue function, cost function and profit function ? b) what price should be charged to maximize profits? c) what is the marginal profit for x=400 ? Explain what this marginal profit number means.

Prove it! 2. If the demand function for products A and B is in the order Pa = 36 - 3Qa and Pb = 40 - 5Qb and the common cost function is TC = Qa' + 2QaQb + 3Qb². With the above information, then calculate: a. Production values A and B at the maximum or minimum profit levels. b. The maximum or minimum profit value Did the profit reach its maximum or minimum value? Prove it c.

The following graph plots the marginal cost (MC) curve, average total cost (ATC) curve, and average variable cost (AVC) curve for a firm operating in the competitive market for jumpsuits. COSTS (Dollars) 80 72 64 56 24 16 8 0 0 8 0 MC ATC AVC Price (Dollars per jumpsuit) 4 8 12 36 48 60 ■ 16 24 32 40 48 56 QUANTITY (Thousands of jumpsuits) ☐ Quantity (Jumpsuits) 64 For every price level given in the following table, use the graph to determine the profit-maximizing quantity of jumpsuits for the firm. Further, select whether the firm will choose to produce, shut down, or be indifferent between the two in the short run. (Assume that when price exactly equals average variable cost, the firm is indifferent between producing zero jumpsuits and the profit-maximizing quantity of jumpsuits.) Lastly, determine whether the firm will earn a profit, incur a loss, or break even at each price. 72 80 Produce or Shut Down? Profit or Loss?

11:30 l 4G I Homework 4 (section 2.1-2 & 2.2).pdf Economic Mathematics (1) Name ID Section 2.2 Revenue, cost and profit 1. If the demand function of a good is given by P-80 – 3Q, the fixed costs are 100 and variable cost are 5 per unit. Work out the profit when Q-10. 2. Find an expression for the profit function given the demand function 20+P= 25 and the 32 +5. Find the value of 0 for which the firm average cost function AC = (a) breaks even (b) makes a loss of 432 units (c) maximises profit. 2/2 !!