ECON 1580 Written Assignment Unit 4 PDF

Preview

Summary

ECON 1580 Written Assignment Unit 4...

Description

A monopoly firm faces a demand curve given by the following equation: P = $500 − 10Q, where Q equals quantity sold per day. Its marginal cost curve is MC = $100 per day. Assume that the firm faces no fixed cost. You may wish to arrive at the answers mathematically, or by using a graph (the graph is not required to be presented), either way, please provide a brief description of how you arrived at your results. a)

How much will the firm produce?

The firm produces 20. b)

How much will it charge?

The firm charge is: P =500-(10x20) =500-200 =$300 c)

Can you determine its profit per day? (Hint: you can; state how much it is.)

The profit per day is: PxQ-100Q= 300x20- 100x20 = 6000-2000 = $4000 d)

Suppose a tax of $1,000 per day is imposed on the firm. How will this affect its price?

As we can see, tax is a fixed cost and it will not change the derivative of profit-maximizing equation above. So the price and the quantity will remain the same. The only things that we need to consider is whether the company is still making money. The profit

=4000- 1000 = $3000 The firm still has an incentive to produce.

e)

How would the $1,000 per day tax its output per day?

Profits = $4000 - $1000 = $3000 The output currently is 20 when profits are $4000 Output = (20 x $3000) / $4000 = 15 Output would decrease from 20 to 15 f)

How would the $1,000 per day tax affect its profit per day?

Profit = Total Revenue- Total Cost

Total Revenue= 350x 15= $5250 Total Cost= 100x15= $1500 Profit= 5250- 1500= $3750 Decrease in Profit= 4000- 3750= $250 Profit decreased by $250.

g)

Now suppose a tax of $100 per unit is imposed. How will this affect the firm’s price?

$100 tax reduces profits 4000-100= $3900 $4000 profit produces quantity of 20. $3900 produces quantity= (3900x 20)/ 4000= 19.5 P= 500- (19.5x 10)= $305 $305 is the firm’s new price. h)

How would a $100 per unit tax affect the firm’s profit-maximizing output per day?

Marginal Cost = $100 x 19.5 = $1950 Marginal Revenue is then also $1950 Total Output = $1950 / $350 = 6.4 Output has reduced. i)

How would the $100 per unit tax affect the firm's profit per day?

Profit = Total Revenue - Total Cost = ($305 x 19.5) - $1950 = $3997.50 Profit reduces by $4000 - $3997.50 = $2.50...