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Suppose an industry has 100 firms, each with a supply curve P = 50 + 10Q . Furthermore, suppose the market demand curve is given by P = 200 - 0.9Q . a. What is the industry supply curve? b. What is the equilibrium price and quantity for this market? c. How many units of output will be produced by a firm operating in this market with a marginal cost function, MC = 130Q

User Nabmeister
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Final answer:

The industry supply curve is P = 5000 + 1000Q. The equilibrium price is $140 and the equilibrium quantity is 6,000. A firm operating in this market with a marginal cost function of MC = 130Q will produce 4.17 units of output.

Step-by-step explanation:

To find the industry supply curve, we can add up the supply curves of all individual firms. Given that each firm has a supply curve of P = 50 + 10Q, the industry supply curve would be the sum of all these individual supply curves. In this case, since there are 100 firms, the industry supply curve can be expressed as P = 5000 + 1000Q.

To determine the equilibrium price and quantity for this market, we need to find the point where the market demand curve and the industry supply curve intersect. By setting the demand curve P = 200 - 0.9Q equal to the supply curve P = 5000 + 1000Q, we can solve for the equilibrium quantity Q and substitute it back into either equation to find the equilibrium price P. Solving these equations, we find that the equilibrium price is $140 and the equilibrium quantity is 6,000.

To determine the number of units of output produced by a firm operating in this market with a marginal cost function of MC = 130Q, we can set MC equal to the industry supply curve and solve for Q. Rearranging the equation, we have 130Q = 5000 + 1000Q. Simplifying, we find that the firm will produce 4.17 units of output.

User Chris Gaudreau
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Answer: See explanation

Step-by-step explanation:

The industry supply curve will be the supply curve given multiplied by the total number of firms. This will be:

P = 50 + 0.1Q

Check: since Q = 100

P = 50 + 10/100Q

P = 50 + 0.1Q

To get the Equilibrium price and quantity, we've to equate the market demand curve and supply. This will be:

Market demand = P = 200 - 0.9Q

Market Supply = P = 50 + 0.1Q

Therefore,

200 - 0.9Q = 50 + 0.1Q

200 - 50 = 0.1Q + 0.9Q

150 = Q

Equilibrium quantity = 150 units

Since P = 50 + 0.1Q

P = 50 + 0.1(150)

P = 50 + 15

P = 65

Equilibrium price is 65.

The units of output that will be produced by a firm operating in this market with a marginal cost function, MC = 130Q will be 2.

User Spatak
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