Consider an industry in the U.S. facing aggregate (inverse) demand function: p(y) = 1050 – 5y...

Consider an industry in the U.S. facing aggregate (inverse) demand function:

p(y) = 1050 – 5y

The industry is currently in long run equilibrium. The market price is $225 and there are n = 11 firms producing. Each firm’s variable cost is:

c_v(y) = 1/3 y³

What is each firm’s fixed cost?

Solutions

Expert Solution

Let the fixed cost be F

Total Cost =TC(y)=F+(1/3)y^3

Marginal Cost=MC(y)=dTC(y)/dy=y^2

Average Cost=TC(y)/y=(F/y)+(1/3)y^2

Set MC(y)=AC(y) to determine the output level at which AC(y) is minimized

y^2=(F/y)+(1/3)y^2

(2/3)y^2=F/y

y^3=(3/2)F

y=(1.5F)^(1/3)

So, MC at this output is given by

MC(y*)=(1.5F)^(2/3)

Set MC(y*)=Long run price

(1.5F)^(2/3)=225

1.5F=225^(3/2)=3375

F=$2250 (Fixed Cost)

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

Consider the following industry where the inverse market demand is given by the function: p=180-Y where...

Consider the following industry where the inverse market demand is given by the function: p=180-Y where Y is the total market output. There are two firms in the market, each has a total cost function: ci (yi)=3(yi)2 where i=1,2 is the label of the firm. Suppose the firms act as Cournot duopolists. What output level will each firm produce in order to maximize profits?.

Consider a monopoly with inverse demand function p = 24 - y and cost function c( y) = 5...

Consider a monopoly with inverse demand function p = 24 - y and cost function c( y) = 5 y 2 + 4: i) Find the profit maximizing output and price, and calculate the monopolist's profits. ii) Now consider the case in which the monopolist has now another plant with the cost structure c 2( y 2) = 10 y 2. How much will the monopolist produce in each plant, what is the price, and the total profits of the monopoly? iii) Now suppose...

Consider a market with 4 firms, each facing the same (inverse) demand function given by p...

Consider a market with 4 firms, each facing the same (inverse) demand function given by p = ( 6 − q/50 if q > 200 4.5 − q/200 if 0 ≤ q ≤ 200 If there is a drop in one of the firm’s marginal cost from c = $3 to c = $2, do you think this firm would greatly increase its sales? Explain!

Monopoly with linear inverse demand. Consider a monopolist facing a linear inverse demand curve p(q)= a-...

Monopoly with linear inverse demand. Consider a monopolist facing a linear inverse demand curve p(q)= a- bq, and cost function C(q)= F + cq, where F denotes its fixed costs and c represents the monopolist's (constant) magical cost a>c 1. Graph demand, marginal revenue and marginal cost. Label your graph carefully, including intercepts 2. Solve the profit maximizing output q^m. To do this, first write down the expression for MR=MC and solve for the optimal quantity. Next find the price...

An industry has two firms. The inverse demand function for this industry is p = 74...

An industry has two firms. The inverse demand function for this industry is p = 74 - 4q. Both firms produce at a constant unit cost of $14 per unit. What is the Cournot equilibrium price for this industry?

Consider a monopoly facing inverse demand function ?(?) = 12 − ?, where ? = ?1...

Consider a monopoly facing inverse demand function ?(?) = 12 − ?, where ? = ?1 + ?2 denotes the monopolist’s production across two plants, 1 and 2. Assume that total cost in plant 1 is given by ??1 (?1 ) = (5 + 4?1)?1, while that of plant 2 is ??2 (?2 ) = [5 + (4 + ?)?2]?2, where parameter ? ≥ 0 represents plant 2’s inefficiency to plant 1. When ? = 0, the total (and marginal)...

6. Assume an industry with two firms facing an inverse market demand of P = 100...

6. Assume an industry with two firms facing an inverse market demand of P = 100 - Q. The product is homogeneous, and each firm has a cost function of 600 + 10q + 0.25q2. Assume firms agree to equally share the market. a. Derive each firm’s demand curve. b. Find each firm’s preferred price when it faces the demand curve in part a. Now assume that firm 1’s cost function is instead 25q + 0.5q2 while firm 2’s is...

Consider a market for a homogenous good (Hobbit beer) with the following inverse demand function: p(y)...

Consider a market for a homogenous good (Hobbit beer) with the following inverse demand function: p(y) = 22 − 2y where y is total sold quantity of the beer in litres on the market and p(y) is the price it sells for. There is only one firm serving the market, Samwise beer inc. The firm’s cost function is c(y) = 4y. a) What quantity of beer will be sold on the market? What will be the market price? Suddenly, a...

Consider an industry with inverse demand P = 32 − 4Q. The industry has an incumbent...

Consider an industry with inverse demand P = 32 − 4Q. The industry has an incumbent firm (i) and a potential entrant (e). Each firm has a marginal cost of 0. The entrant pays a fixed cost of 9 only if it enters the industry. Assume it enters the industry only if its profits are greater than 0. (a) What is the incumbent’s output as a monopoly without threat of entry? (b) What is the incumbent’s output and profit with...

Afirm faces an (inverse) demand function p(y)=10 –y, where p is price,yis quantity.The cost function of...

Afirm faces an (inverse) demand function p(y)=10 –y, where p is price,yis quantity.The cost function of the firm is given by c(y) = y^2+1. Dont copy other guys solution!!! (1) Draw thecurves of(inverse) demand function and marginal revenue. Show your detailed work such as slope, intercept. (2) What is the optimal choice of output and corresponding profitof the firm?Show each of your steps clearly.(Results might not be integers. Do NOTround your answer)

Subjects