Suppose demand for good 1 is given by pi = 26- 3¹ and demand for good 2 is given by p2 = 72 — 292. The firm has the cost function C = 120+q² for both goods where q = 9₁ +92. Compute the following 92. • The profit maximizing level of output for each good, i.e., 9₁ and • Verification that the quantities obtained in the first bullet will indeed maximize profit • The prices p₁ and på that the firm will charge for each good to maximize profit

Suppose demand for good 1 is given by pi = 26- 3¹ and demand for good 2 is given by p2 = 72 — 292. The firm has the cost function C = 120+q² for both goods where q = 9₁ +92. Compute the following 92. • The profit maximizing level of output for each good, i.e., 9₁ and • Verification that the quantities obtained in the first bullet will indeed maximize profit • The prices p₁ and på that the firm will charge for each good to maximize profit

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter12: The Partial Equilibrium Competitive Model

Section: Chapter Questions

Problem 12.9P

See similar textbooks

Similar questions

A local company is planning to manufacture and market a four-slice toaster. For this toaster, the research department’s estimates are aweekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a price of $20. The financial department’s estimates are fixed weekly costs of$5,000 and variable costs of $5 per toaster. a) Assume that the relationship between price ? and demand ? is linear. Use the research department’s estimates to express ? as a function of ? and determine the domain of the function. b) Using your knowledge from Finite Math, determine the Revenue function in terms of ?. c) Determine the Marginal Revenue at 2 different production levels for example 250 and 500 units. Interpret these results. (HINT: Consider what a positive or negative first derivative implies) d) Assume that the cost function is linear. Use the financial department’s estimates to express the cost function interms of ?. e) Determinethe Marginal costand interpret the…
(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p 40 – 4q²where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (1) Write an equation giving profit as a function of the number of lightweight compasses produced. (11) At the moment the company produces 2 million lightweight compasses and makes a pre of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? Σ BIUG G |卡三 = 9 ..
Ja-Q if Qsa QUESTION (5) The market demand for a good is described by the following inverse demand function: P(Q) = if Q> a where Q is total quantity demanded, P(Q) is the market price and a >0. Three firms, i = 1, 2,3, have identical cost functions: C,(q.) = q where q, denotes firm i's output quantity, hence Q = q, +q, + q3 Consider a two stage non-cooperative game. At Stage I Firm 1 produces quantity q, then at Stage II Firm 2 and Firm 3 observe the first stage quantity and then move simultaneously and produce q, and q3. (а) How many sub-games are there in this game? Describe the sub-games. Use backwards induction solution method by identifying the history of the game and specifying correct anticipations for later stages. Find all subgame Nash equilibria of the game. Find the sub-game perfect outcome of the game (b) (b.i) (b.ii)
The BCY Corporation provides accounting services to a wide variety of customers, most ofwhom have had a business association with BCY for more than five years.BCY's demand is: P = 24,000 – 20Q, and BCY's marginal cost of service is: MC = 40Q.a. If BCY charges a uniform price for a unit of accounting service, Q, what price must itcharge per unit, and how many units must it produce per time period in order to maximizeprofit? Calculate the consumer surplus.b. If BCY could enforce first-degree price discrimination, what would be the lowest pricethat it would charge and how many units would it produce per time period?c. With perfect price discrimination and ignoring any fixed cost, what is total profit andwhat is the amount of consumer surplus?
A small firm operating in a purely competitive market has fixed costs of $45 per day compensates each employee $96 per day and has daily input and raw material costs as indicated in the table below. A. What would be the profit maximizing level of production if demand increased such that each unit sold for $130?, will the company make an economic profit producing this quantity of output? b: suppose the demand significantly decreased so that price for a unit of ouput sold to $115 each. What should the firm do? Why?
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 !!
The accompanying graph shows the short-run demand and cost situation for a price searcher in a market with low barriers to entry. Price (dollars) 24 10 V ATC The firm will receive $ MR Quantity/time The firm will maximize its profit at a quantity of▼ units. D Options: 6, 8, 9, or 10 After choosing the profit maximizing quantity, the firm will charge a price of in revenue at the profit-maximizing quantity. The total cost of production for this profit-maximizing quantity is $ The maximum profit the firm can earn in this situation is How will the situation change over time? Options: 6,8 10, or 24 per unit for this output. O Profits will attract rival firms into the market until the profit-maximizing price falls to the level of per-unit cost. O The market will adjust until the price charged by this firm no longer exceeds marginal cost at the profit-maximizing quantity. O This market is already in long-run equilibrium, and will not change throughout time. O Losses will induce firms to leave…
A manufacturer knows that: His TR is given by Revenue = 23Q – Q2 His total cost of production is; Cost = 36 + 2Q + 0.1Q2 Where Q is the weekly production in thousands a) Economists define MR as the rate of change of Total revenue. Derive an expression for Marginal Revenue (MR) b) How do you think Economists’ would define ‘Marginal Cost’? Derive an expression for marginal Cost (MC) c) What output will make marginal Revenue equal Marginal cost?
1.i) Assuming you are the managing director of a firm that produces goods: A,B and C .The price elasticity of demand for A is 1.2, for B it is 1.oo and C is 0.75. It is known that he's firm is experiencing serious cash flow problems and you have to increase total revenue as soon as possible. If you were in a position to set the prices for these goods, what would be your pricing strategy for each product ii) price falls from N$ 16 to N$ 12 per bottle and demand rises from 200 to 300 per bottle.calculate the PED using midpoint formula Output prices average (total)cost Total cost marginal cost Total profit/loss 10 10 -108 20 10 4 -48 30 10 5 3 40 10 6.20 40 50 10 8 60 60 10 10 60 2. i) fill in the gaps ii)in which market structure doess Johnson Electronics (Pty)Ltd operate? iii)what level of output maximizes the firms profit
A7 You are the manager of a bakery that produces and packages gourmet muffins, and you currently sell muffins in packages of 3. A consultant’s report has estimated the (inverse) demand of a typical consumer to: P = 3 − 0.5Q If your cost of producing bran muffins is C(Q) = Q: (a) What is the marginal cost of muffins? (b) Draw the demand and marginal cost on a diagram. (c) Determine the optimal number of muffins to sell in a single package. (d) What price should the firm charge for each park?
The graph below plots the firm's total revenue curve: that is, the relationship between quantity and total revenue given by the two right columns in the table above. The five choices are also labeled. Finally, two black lines are shown; these lines are tangent to the green curve at points B and D. 90 81 72 63 54 В D 45 36 27 18 A E 100 200 300 400 500 600 700 800 QUANTITY (Dishwashers per year) TOTAL REVENUE (Thousands of dollars per year)
Y6 Suppose that a market consists of 300 identical firms, all with the same cost curve: TC(4) = 0.1 + 150g?. The market demand is given by Qd(p) = 60 - p (a) What is the equilibrium price and quantity? (b) What quantity must each firm produce and sell at equilibrium? (c) Do firms make positive profits in the market equilibrium? (d) Calculate consumers' surplus, producers' surplus and total surplus.