Question 1: Video game industry. Suppose that there are only two companies in the video game industry who produce video game consoles: Xbox by Microsoft and Playstation by Sony. Microsoft’s cost function is T Cm = (qm)2, while Sony’s cost function is T Cs = 12qs. The market demand is Q = 940 − P ,where P is the market price and Q denotes the total quantity of the two companies combined. (a) What is each company’s marginal cost?(b) Derive the reaction function of each duopolist.(c) How much will each company produce?(d) Illustrate your solution using a graph.(e) What will the market price be?(f) Find each company’s profit.

Suppose that you are a manager for a firm like EBC Brakes, which manufactures brakes for automobiles and motorcycles. Your company has two plants, one in the United States and the other in the United Kingdom.  The following tables include estimated demand and marginal revenue for your brakes, along with the marginal costs at the two factories. what quantity and price maximize your firms profit? What is the profit – maximizing number of brakes produced in the U.S. plant? In the U.K. plant? Quantity Demanded (brakes per hour) Price (dollars per brake) Quantity Produced in the U.K. plant (brakes per hour) Quantity Produced in the U.S. (brakes per hour) Total Quantity Produced Marginal Cost (dollars per brake) Marginal Revenue (dollars per brake) 104 196 47 42 89 66 92 105 195 48 44 92 68 90 106 194 49 46 95 70 88 107 193 50 48 98 72 86 108 192 51 50 101 74 84 109 191 52 52 104…

2. A firm has a cost function of C = 1000+20Q + 1/10Q2 and has a demand function as shown in the graph below: 100 90 80 70 70 60 60 50 40 30 20 10 0 10 20 30 40 50 60 70 80 90 100 Quantity (Q) -P (demand) a) Estimate the firm's demand function. You may assume that the slope is a whole number, and the intercept is a multiple of 10. (1 mark) b) Find the firm's revenue function. You do not need to draw it. (2 marks) c) Find the marginal revenue function, and draw it on a copy of the graph. (3 marks) d) Find and draw the marginal cost function. (3 marks) e) Use your results from parts (c) and (d) to find the profit-maximising level of output. (3 marks) f) Find the market price at this level of output. (2 marks)

1) Suppose you are operating a discount movie theater and want to increase profits by charging adults and kids different prices. Assume there are no variable costs, just fixed costs to show the movie. You estimate the inverse demand function for kids to be: p1(y1) = 4 - 0.05y1 You estimate the inverse demand function for adults to be: p2(y2) = 9.6 - 0.08y2 a) How many kids will watch a movie? What price will you charge kids? b) How many adults will watch a movie? What price will you charge adults?

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…

Q1: 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:

James mainly sells confectionery items, newspapers, magazines and cigarettes in his convenience store. Noting his small business is not thriving, he thought of selling hot pies and rolls too. Suppose the total cost function for rolls and pies is, TC = 900 + 50Q,  Q = Q1 + Q2 Where Q1 and Q2denote the quantities of rolls and pies respectfully. If P1 and P2 denote the corresponding prices, the inverse demand equations are.   Q1 = 70 - P1 and 0.5Q2 = 100 - P2   a)If James decides to make a total of 48 rolls and pies per day and charges different prices as above (that is, P1 ≠ P2 ), how many of rolls and pies each should he make in order to maximize the profit of a particular day? Estimate and interpret the Lagrange Multiplier λ [note: assume second-order conditions are satisfied]. b)Using your knowledge of input-output tables, explain which components of the economy will be affected if all convenience stores, including James’, closed down for three months due to the COVID-19. What would…

Problem 2. Suppose the market demand and inverse-demand for pizza in East Lansing is given by: Demand: Qd 1100-5P 220-2₁ Inverse-Demand: P = 220- Currently, there are 100 pizza stores in the East Lansing area that produce identical pizzas and as such the market is perfectly competitive. Suppose each pizza store has identical cost function given by: C(q) = 100 +g+q², fixed-cost I MC(q)=1+2q where C(q) is the total cost, and MC(q) is the marginal cost function. As shown in the total cost function, each pizza store incurs a $100 fixed cost which is a sunk-cost in the short-run but avoidable in the long-run. Recall that the market supply is the sum of individual firm's supply functions, and that individual's (inverse) supply curve is given by its marginal cost function i.e. Individual firm's inverse-supply: P= mc(q) = 1 + 2q Individual firm's supply: 9,= 0.5P - 0.5 Market Supply: 2, 100q, = 50P - 50 (a) What is the short-run equilibrium market price/quantity of pizza in East Lansing? (b)…

There are only two driveway paving companies in a small town, Asphalt, Inc. and Blacktop Bros. The inverse demand curve for paving services is ?= 2040 ―20? where quantity is measured in pave jobs per month and price is measured in dollars per job. Assume Asphalt, Inc. has a marginal cost of $100 per driveway and Blacktop Bros. has a marginal cost of $150. Answer the following questions: Determine each firm’s reaction curve and graph it. How many paving jobs will each firm produce in Cournot equilibrium? What will the market price of a pave job be? How much profit does each firm earn?

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 £ Number