In Q2, What Was The Total Revenue Generated By Sheilaã¢â‚¬â„¢s Highest Revenue Service?

Man 503��������������������� ���������� Homework VIII��������������������������������� Fall 2009

1)� A house faces the post-obit average revenue (demand) bend:

P = 120 - 0.02Q

where Q is weekly production and P is price, measured in cents per unit of measurement.� The firm�s cost function is given by C = 60Q + 25,000.� Assume that the firm maximizes profits.

a.�������� What is the level of product, toll, and total profit per calendar week?

The turn a profit-maximizing output is establish by setting marginal revenue equal to marginal cost.� Given a linear demand curve in inverse form, P = 120 - 0.02Q, nosotros know that the marginal acquirement bend will have twice the gradient of the need curve.� Thus, the marginal revenue curve for the firm is MR = 120 - 0.04Q.� Marginal price is simply the gradient of the total cost curve.� The slope of TC = sixtyQ + 25,000 is 60, so MC equals threescore. Setting MR = MC to determine the turn a profit-maximizing quantity:

120 - 0.04Q = threescore, or

Q = 1,500.

Substituting the profit-maximizing quantity into the inverse demand function to make up one's mind the toll:

P = 120 - (0.02)(1,500) = 90 cents.

Profit equals total acquirement minus full price:

p = (ninety)(one,500) - (25,000 + (60)(1,500)), or

p = $200 per week.

b.�������� If the authorities decides to levy a taxation of 14 cents per unit on this product, what will be the new level of production, cost, and profit?

Suppose initially that the consumers must pay the revenue enhancement to the government.� Since the total cost (including the tax) consumers would be willing to pay remains unchanged, we know that the demand part is

P* + T = 120 - 0.02Q,� or

���� P* = 120 - 0.02Q - T,

where P* is the price received by the suppliers.� Considering the tax increases the price of each unit, total revenue for the monopolist decreases by TQ, and marginal revenue, the acquirement on each additional unit, decreases by T:

MR = 120 - 0.04Q - T

where T = 14 cents.� To determine the profit-maximizing level of output with the tax, equate marginal acquirement with marginal price:

120 - 0.04Q - 14 = 60, or

Q = 1,150 units.

Substituting Q into the demand part to determine price:

P* = 120 - (0.02)(one,150) - fourteen = 83 cents.

Profit is total revenue minus total price:

cents, or

$14.50 per week.

Notation:� The cost facing the consumer after the imposition of the revenue enhancement is 97 cents. The monopolist receives 83 cents.� Therefore, the consumer and the monopolist each pay vii cents of the taxation.

If the monopolist had to pay the tax instead of the consumer, nosotros would arrive at the same result.� The monopolist�s cost function would and then be

TC = 60Q + 25,000 + TQ = (sixty + T )Q + 25,000.

The gradient of the cost office is (sixty + T), so MC = 60 + T.� We gear up this MC to the marginal acquirement office from part (a):

120 - 0.04Q = sixty + xiv, or

Q = i,150.

Thus, it does not affair who sends the tax payment to the government.� The burden of the revenue enhancement is reflected in the price of the expert.

ii)� Suppose that an industry is characterized equally follows:�

a. If there is only one business firm in the industry, find the monopoly toll, quantity, and level of profit.

If at that place is only one firm in the industry, so the firm will act like a monopolist and produce at the point where marginal acquirement is equal to marginal price:

MC=4Q=xc-4Q=MR

Q=11.25.

For a quantity of 11.25, the firm will charge a toll P=90-ii*11.25=$67.50.� The level of profit is $67.50*eleven.25-100-2*11.25*11.25=$406.25.

b. Discover the price, quantity, and level of profit if the industry is competitive.

If the industry is competitive so price is equal to marginal toll, and then that 90-2Q=4Q, or Q=15.� At a quantity of 15 cost is equal to sixty.� The level of profit is therefore sixty*15-100-2*fifteen*15=$350.

c.�������� Graphically illustrate the need curve, marginal acquirement curve, marginal cost curve, and boilerplate cost curve.� Identify the difference between the profit level of the monopoly and the profit level of the competitive industry in 2 unlike means.� Verify that the ii are numerically equivalent.

The graph below illustrates the demand curve, marginal revenue curve, and marginal toll curve. The average toll curve hits the marginal cost curve at a quantity of approximately 7, and is increasing thereafter (this is not shown in the graph below).� The profit that is lost by having the firm produce at the competitive solution as compared to the monopoly solution is given past the deviation of the ii profit levels as calculated in parts a and b above, or $406.25-$350=$56.25.� On the graph below, this difference is represented by the lost profit expanse, which is the triangle below the marginal price curve and above the marginal revenue bend, between the quantities of 11.25 and 15.� This is lost profit because for each of these 3.75 units actress acquirement earned was less than actress price incurred.� This expanse can be calculated as 0.5*(60-45)*3.75+0.5*(45-30)*iii.75=$56.25.� The 2d method of graphically illustrating the difference in the two turn a profit levels is to describe in the boilerplate cost bend and place the two profit boxes.� The profit box is the departure between the total acquirement box (price times quantity) and the full cost box (boilerplate toll times quantity).� The monopolist will proceeds two areas and lose i surface area as compared to the competitive house, and these areas will sum to $56.25.

iii)� A monopolist faces the following need curve

����������������������� Q = 16 - P

����������� Where Q is the quantity demanded and P is toll.� Its average variable cost is

����������������������� AVC = 3Q,

����������� And its fixed toll is $5.� What is the loss of efficiency (dead weight loss) due to the monopoly?

P = 16- Q

TR = 16Q � Qⁱⁱ

MR = 16 � 2Q

TC = v + 3Q²

MC = 6Q

Monopolist output � MC = MR � Q = 2

Perfectly competitive output � MC = P� � Q = xvi/7

DWL = (14-12)*(16/7 � 2)*0.5 = 2.29

Source: http://akdeniz.bilkent.edu.tr/courses/micro/solhw8.htm

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