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- A firm has a linear demand function for its product. When the price of the product isSh.220, the quantity demanded is 40 units. When the price increases to Sh.240, thequantity demanded becomes 30 units. In addition, the firm’s marginal cost function isgiven by:MC = 40q – 2q2 + 2Fixed cost = Sh.5 millionWhere q = quantity demanded, MC = marginal cost (Sh. million)Evaluate the level of output that maximizes profits.1. A firm’s production function is , where Ldenotes the size of the workforce. Find the value of MPLin the case when: (a) L=1, (b) L=10, (c) L=100, (d) L=1000 Does the law of diminishing marginal productivity apply to this particular function? 2. Show that the price elasticity of demand is constant for demand functions of the form where A and n are positive constants. 3. The demand and total cost functions of a good arerespectively and a) Find expressions for TR, (profit) , MR, and MC in terms of Q. b) Solve the equation and hence determine the value of Q which maximizes profit. c) Verify that, at the point of maximum profit, MR=MC. 4. The cost of building an office complex, x floors high, in a prime location in Accra is made up of three components: (a) GH¢10 million for the land (b) GH¢1/4 million per floor (c) Specialized costs of GH¢10000x per floor. How many floors should the office complex contain if the average cost per floor is to be minimized? 5. The supply…Given cost and price (demand) functions C(g)= 110q + 44,600 and p(g) = - 2g + 860, what is the marginal revenue at a production level of 55 items? The marginal revenue is $ . (Round answer to nearest dollar.) Pr rith
- 8. The production function for a price-taking firm is given by q = 2.5k0.4L0.4. What is the supply function q(v,w,p)? [Show your work]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.What is the cheapest way of producing 850 units of output if a firm operates with theproduction function 0.5 0.5 Q = 30K L and can buy input K at 75 $ per unit and L at 40 $per unit?
- The demand function for specialty steel products is given, where p is in dollars and q is the number of units. p = 180 3 125 − qy = min(x1, x2) find input demand function find profit function.A local newspaper currently has 84,000 subscribers at a quarterly charge of $30.Market research has suggested that if the owners raise the price to $32, they wouldlose 5,000 subscribers. Assuming that subscriptions are linearly related to theprice, what price should the newspaper charge for a quarterly subscription tomaximize their revenue?a) Find the cost function (Hint: find slope and use point-slope form to find thecost function) b) Find the revenue function c) Find the maximum revenue d) Find the profit function
- Calculate how many units of x1 the profit-maximizing firm will demand in the short run if the production function is f(x1, x2) = x43 x24. The level of x2 is fixed at 14. Price of output „0.43 „0.24 p = 32.6 and prices of inputs are wi 8.5 and w2 = 5.9. Type your answer with at least 4 decimal digits! Answer:1/3 1/3 Assume y = f(x1, x2) = x1 x2 . If the input prices are w₁ and w₂ what is profit maximizing y level of output? What is the profit?The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Buddies, a purely competitive firm that produces novelty ear buds. Assume the market for novelty ear buds is a competitive market and that the price of ear buds is $6.00 per pair. Buddies Production Costs Quantity MC ATC of Ear Buds ($) ($) 25 2.20 30 2.02 2.17 35 2.45 2.21 40 3.57 2.38 45 4.00 2.56 50 5.46 2.85 55 5.93 3.13 60 8.53 3.58 Instructions: In part a, enter your answer as the closest given whole number. In parts b-d, round your answers to two decimal places. a. If Buddies wants to maximize profits, how many pairs of ear buds should it produce each week? pairs b. At the profit-maximizing quantity, what is the total cost of producing ear buds?
