A firm faces a demand function (where q=quantity demanded and p=price): q = 200 – 2p and a total cost (TC) function (where q=output): TC =0.5q2 + 20q +375 Find the firm’s profit maximizing output level using the profit maximizing condition MR = MC
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- A firm faces a demand function (where q=quantity demanded and p=price):
q = 200 – 2p
and a total cost (TC) function (where q=output):
TC =0.5q2 + 20q +375
Find the firm’s profit maximizing output level using the profit maximizing condition
MR = MC
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- Based on Zangwill (1992). Murray Manufacturing runs a day shift and a night shift. Regardless of the number of units produced, the only production cost during a shift is a setup cost. It costs $8000 to run the day shift and $4500 to run the night shift. Demand for the next two days is as follows: day 1, 2000; night 1, 3000; day 2, 2000; night 2, 3000. It costs $1 per unit to hold a unit in inventory for a shift. a. Determine a production schedule that minimizes the sum of setup and inventory costs. All demand must be met on time. (Note: Not all shifts have to be run.) b. After listening to a seminar on the virtues of the Japanese theory of production, Murray has cut the setup cost of its day shift to $1000 per shift and the setup cost of its night shift to $3500 per shift. Now determine a production schedule that minimizes the sum of setup and inventory costs. All demand must be met on time. Show that the decrease in setup costs has actually raised the average inventory level. Is this…The demand function for a good is given by the equation P= 50 – 2Q, while total cost is given by TC = 160 + 2Q Write down the equation for the total revenue. Write down the equation for the profit. Find the value of Q when the firm breaks even.The inverse demand for tea is given by P = 8 – 0.03Q, where Pis the price per a gram of tea and Q is the total number of grams of tea brought to market. There are two tea shops in the market. Shop 1's cost function is given by C = 0.02q,?, where q, is the number of grams of tea it brings to market. Shop 2's cost function is given by C2 = 0.02q22, where q2 is the number of grams of tea it brings to %3D %3D market. Given that the two shops compete by setting output (Cournot), answer the following. a) Identify shop 1's reaction function to shop 2's output to within 2 decimal places (e.g. 0.33). 91= Number Number 92 b) Identify shop 2's reaction function to shop 1's output to within 2 decimal places (e.g. 0.71). q2= Number Number 91 c) To within two decimal places (e.g. 0.63) what is the equilibrium output level of each shop and the equilibrium per gram price for tea. Shop 1 will produce Number grams of tea and shop 2 will produce Number grams of tea. The equilibrium market price is £…
- A competitive firm has a total cost function: TC = 20 + 50q − 6q2 + q3 and a marginal cost function MC = 50 − 12q + 3q2. (a) If the market price is P = $230 per unit, the firm will supply 10 units of the good. Calculate: (i) the profit (ii) the producer's surplus (b) Assume that the market price is P = $50 per unit. Find (i) the level of output supplied by the firm (ii) the firm's profit (use a minus before your answer if the firm incurred a loss) (c) Calculate the range of prices for which the firm will find it optimal to shut down.The inverse demand for tea is given by P= 10 – 0.04Q, where Pis the price per a gram of tea and Qis the total number of grams of tea brought to market. There are two tea shops in the market. Shop 1's cost function is given by C = 0.01q,?, where qı is the number of grams of tea it brings to market. Shop 2's cost function is given by C2 = 0.01q2², where qp is the number of grams of tea it brings to market. Given that the two shops compete by setting output (Cournot), answer the following. a) Identify shop 1's reaction function to shop 2's output to within 2 decimal places (e.g. 0.33). 91= Number - Number 92 b) Identify shop 2's reaction function to shop 1's output to within 2 decimal places (e.g. 0.71). q2= Number Number 91 c) To within two decimal places (e.g. 0.63) what is the equilibrium output level of each shop and the equilibrium per gram price for tea. Shop 1 will produce Number grams of tea and shop 2 will produce Number grams of tea. The equilibrium market price is £ NumberQ1: Analytical part - 8% Best Orange Juice Company is located in Oman. The cost function for total orange juice production (x) is given by C(q) = 0.25x2. Their orange juice is demanded only in Muscat (Muscat demand is Xm- 100-2Pm) and Salalah (Salalah demand is X 100-4Ps). Therefore, the total demand is x-xm+ Xs. If the company can control the quantities supplied to each market, how many should it sell in each location to maximize total profits? What price would it charge in each location? Answer:
- A local microbrewery has total costs of production given by the equation TC=500+10q+5q^2. This implies that the firm's marginal cost is given by the equation MC=10+10q (you do not need to be able to show this). The market demand for beer is given by the equation QD=105 – (1/2)*P. a) Write the equations showing the brewery's average total cost .Given that the demand function is P = 9 - Q and the total cost is TC = 2Q + 10 Find the level of output Q that the profit break even.Exercise 5.4 A company is producing and selling branded milk with the following total cost function: CT(q)= 0.2q²+q+70. If the demand function for this brand of milk is: P=15-0.5q: a) Calculate the optimal price of milk, as well as the optimal quantity sold and the profits of the company. b) Calculate the price elasticity of demand in the equilibrium of the company. c) Justify why the company has an excess of productive capacity. d) Represent graphically.
- A firm's demand function is Q = 16 – P and its total cost function is defined as TC = 3 + Q +0.25Q 2 . Use these two functions to form the firm's profit function and then determine the level ofoutput that yields the profit maximum. What is the level of profit at the optimum?The demand and total profit function, P(x) for rooms in a hotel are given as follows. 3x = 600 - P P(x) = 450x – 3.5x2 - 4000 Where p is the price in ringgit per room and x is the quantity of room rented. Determine the marginal cost when 2 rooms are rentedA firm has a total cost function C(Q) = 100 + 8Q – 8Q 2 + Q 3 and demand function is Qx d = 33 – 2px Required: (i) Calculate the firm's marginal cost when Q = 5
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