Question

(Show your work!) The LED Toy Company has a hot new toy called Dabbdo that it sells in two markets. On the cost side the firm has fixed costs of $150,000 dollars monthly. In addition, its variable costs are MC = AVC = $25 per toy. Assume that the LED Toy Company can engage in third-degree price discrimination and its goal is to maximize its profits.

The monthly demand in Market 1 where P₁ is price in dollars is:

P₁ = 55 – Q₁, where Q₁ is the quantity in thousands of the toy sold in market 1 monthly.

The monthly demand in Market 2 where P₂ is price in dollars is:

P₂ = 35 – 0.5Q₂ where Q₂ is the quantity in thousands of the toy sold in market 2 monthly

(a) (4 pts.) How many toys will be bought and sold in each market monthly?

ANSWERS: In Market 1: ___________ thousand ; Market 2:       ___________ thousand

(b) (3 pts.) What price will be charged in each market?

      ANSWERS: Price in market 1:   ________ ; Price in market 2:   _________

(c) (3 pts.) And what LED’s monthly profits be?

ANSWER: ______________________

Answer 1

a. Profit maximization occurs when marginal revenue= marginal cost

MC= $25/toy

In market 1 demand is:

P1 = 55 – Q1

TR= 55Q1-Q1²

MR=55-2Q1

For profit mximization, MR= MC

55-2Q1=25

Q1=15 thousand units

In market 2 demand is:

P2 = 35 – 0.5Q2

TR= 35Q2-0.5Q2²

MR=35-Q2

For profit mximization, MR= MC

35-Q2=25

Q2 =10 thousand units

Therefore in market1 15 thousand toys will be bought and sold and in market2 10 thousand toys will be bought and sold.

b.Putting value of Q1 in demand function for market1 we get:

P1=55-15

P1=$40

Putting value of Q2 in demand function for market2 we get:

P2 = 35 – 0.5*10

P2=$30

Therefore, price charged in market 1 will be $40 and price charged in market 2 will be $30.

c.Profit = Total Revenue- Total cost

Total revenue in market 1:

TR= P*Q

TR=40*15

TR=$600 thousand

Tottal variable cost in market1= 25*15=375 thousand

TR in market 2:

TR= P*Q

TR=30*10

TR=$300 thousand

Total variable cost in market2 = 25*10=250 thousand

Total cost of LED Toy Company= $250 thousand +$375 thousand +$150 thousand =775 thousand

Total Revenue of LED Toy Company = $600 thousand +$300 thousand =$900 thousand

Profit of LED Toy Company = 900 thousand-775 thousand= $125 thousand