Homework 3 Due July 25, 2018 1. (a) Suppose you are selling a product for $10 pe

Question

Homework 3 Due July 25, 2018 1. (a) Suppose you are selling a product for $10 per unit in a competitive industry; using the perfectly competitive model, show and explain what your profit will be if you sell 20 units at a cost of $5 per unit. (5 Points) (b) What will you do to maximize profit if your marginal cost falls from $10 to $6? (5 Points) 2. Suppose you decide to manage a monopoly instead. If your demand and cost functions are estimated as follows: (a) What is the price-quantity combination that will (b) What will be your maximum profit? (5 Points) P-200-2Q and C(Q1,200 2Q maximize profit? (5 Points) (c) What will be the maximum revenue to be obtained? Hint solve for MR quantity, use the quantity to solve for price, and multiply price by MR quantity. (5 Points)

Explanation / Answer

Answer

Part 1 done after part 2

2)

a) Suppose you have a monopoly

Profit = Totar Revenue - Total Cost

= P*Q - C(Q)

= 200Q - 2Q2 - 1200 - 2Q2

In order to maximize profit We have to:

Max : 200Q - 2Q2 - 1200 - 2Q2

Using First order condition we have

200-4Q-4Q = 0

=> 200 = 8Q

=> Q = 25

By doing second order derivative we have

P''(Q) = -8 < 0

Hence Q = 25 We have maximum profit.

b)

Maximum Profit is when Q = 25

and P = TR - TC at Q = 25

=> 200*25 - 2*25*25 - 1200 - 2*25*25

= 5000 - 1200 - 2500

= 1300

c)

Total Revenue = P*Q

TR = (200 -2Q)Q

= 200Q - 2Q2

Using First Order Derivative We have

200 - 4Q = 0

=> Q = 50

By doing second order derivative we have

TR''(Q) = -4 < 0

Hence P = 200 - 2*50

= 100

Hence Maximum Total Revenue = 50*100

=5000

1)

a) In perfect competitive Market Profit Maximizes when MC = P and Profit = - TFC = - Total Fixed Cost

Here Competitive Price = $10, Hence P = $10

Lets Assume TFC = F

If he is selling at Price = $5

He will incurring a loss as

P = TR - TC = 100 - 200 - F

= -100 - F

and If we assume F = 0,

We have loss of $100

b)

If MC falls from $10 to $6

Then According To Profit Maximizing Condition

P = MC = 6

We will Charge $6.

Reason

i) If We charge less than 6 then we will not be able to recover our Total Variable Cost, Hence we cannot charge less than 6

ii) If we charge more than 6 then as it is a perfect competitive market All aur consumers will shift towards our rivals and our demand will be Zero.

Hence We will charge P = $6

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