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.

Question 1 A boutique fruit juice manufacturer produces 2 types of juices, Apple and Fig daily with a total cost function: TC = 6A + A × F +9F where: A is the quantity of the Apple juice (in kegs) and F is the quantity of the Fig juice (in kegs). The prices that can be charged are determined by supply and demand forces and are influenced by the quantities of each type of juice according to the following equations: P₁ = 17-A + F for the price (in dollars per keg) of the Apple juice and PF = 23+2A-F for the price (in dollars per keg) of the Fig juice. The total revenue is given by the equation: TR = PAXA + PF XF and the profit given by the equation Profit = TR - TC First, use a substitution of the price variables to express the profit in terms of A and F only. Using the method of Lagrange Multipliers find the maximum profit when total production (quantity) is restricted to 2023 kegs. Note A or F need not be whole numbers. Be sure to show that your solution is a maximum point.

Suppose that each firm in a competitive pizza market has the following identical cost: Total cost: TC=25+1.5Q2 The market demand function for the pizza market in the above question 2(a) is: Q= 120-P, where P is the price and Q is the total quantity of the pizza. Currently, there are 12 firms in the market.  i. Formulate the equation or level of fixed cost, variable cost, marginal cost, average variable cost (AVC) and average total cost (ATC) for each firm.  ii. Formulate each firm’s supply function based on the cost information prior to innovation and determine the market supply function in the short run. The total number of firms in the market is assumed to be fixed. iii. Calculate the price and quantity of pizza in the market and the quantity produced by each firm while the market is at the short-run equilibrium. Use a diagram to illustrate this short-run equilibrium and calculate each firm’s profit or loss. Discuss whether each firm has an incentive to leave or stay in the market.…

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…

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…

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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)…

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

Jesaki Inc. is trying to enter the widget market. The research department established the following price-demand, cost, and revenue functions: p(x) = 60 - 1.20x C(x) = 210 + 12x R(x) = xp(x) = x(60 - 1.20x) Revenue function Price-demand function Cost function where x is in thousands of widgets and C(x) and R(x) are in thousands of dollars. The price p(x) is the price in dollars of one widget when the demand is a thousand widgets. All three functions have domain 1 ≤ x ≤ 50. Use this information to answer questions 1-10 below.

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